rigid body concept for geometric nonlinear analysis of 3d frames plates and shells based on the updated lagrangian formulation abstract in the nonlinear analysis of elastic structures the displacement increments generated at each incremental step can be decomposed into two components as the rigid displacements and natural deformations based on the updated lagrangian ul formulation the geometric stiffness matrix kg is derived for a 3d rigid beam element from the virtual work equation using a rigid displacement field further by treating the three node triangular plate element tpe as the composition of three rigid beams lying along the three sides the kg matrix for the tpe can be assembled from those of the rigid beams the idea for the ul type incremental iterative nonlinear analysis is that if the rigid rotation effects are fully taken into account at each stage of analysis then the remaining effects of natural deformations can be treated using the small deformation linearized theory the present approach is featured by the fact that the formulation is simple the expressions are explicit and all kinds of actions are considered in the stiffness matrices the robustness of the procedure is demonstrated in the solution of several benchmark problems involving the postbuckling response

conditions for the alignment of the principal null directions of two weyl like tensors a possible means to classify the interaction between the weyl and ricci tensors is to look at the number of principal null directions that the weyl and plebanski tensors have in common this paper presents algebraic conditions that can be used to determine this number without explicitly calculating the principal null directions themselves

a dynamic rotating blade model at an arbitrary stagger angle based on classical plate theory and the hamilton s principle a dynamic model based on classical plate theory is presented to investigate the vibration behavior of a rotating blade at an arbitrary stagger angle and rotation speed the hamilton s principle is

free vibration analysis of a flat plate using the hierarchical finite element method abstract the hierarchical finite element method is used to determined the natural frequencies and modes of a flat rectangular plate ten different boundary conditions including free edges and point supports are considered in this paper extensive results are presented for each case including the variation of frequency with the aspect ratio and the poisson ratio and these are shown to be in very good agreement with the work of other investigators this confirms both the applicability and accuracy of solution of the hfem to problem of this type

on the problem of algebraic completeness for the invariants of the riemann tensor iii we study the set cz of invariants zakhary and carminati j math phys 42 1474 2001 for the class of space times whose ricci tensors possess a null eigenvector we show that all cases are maximally backsolvable in terms of sets of invariants from cz but that some cases are not completely backsolvable and these all possess an alignment between an eigenvector of the ricci tensor with a repeated principal null vector of the weyl tensor we provide algebraically complete sets for each canonically different space time and hence conclude with these results and those of a previous article carminati zakhary and mclenaghan j math phys 43 492 2002 that the cz set is determining or maximal

the forced vibration and boundary control of pretwisted timoshenko beams with general time dependent elastic boundary conditions abstract the governing differential equations and the general time dependent elastic boundary conditions for the coupled bending bending forced vibration of a pretwisted non uniform timoshenko beam are derived by hamilton s principle by introducing a general change of dependent variable with shifting functions the original system is transformed into a system composed of four non homogeneous governing differential equations and eight homogeneous boundary conditions the transformed system is proved to be self adjoint consequently the method of separation of variables can be used to solve the transformed problem the physical meanings of these shifting functions are explored the orthogonality condition for the eigenfunctions of a pretwisted non uniform beam with elastic boundary conditions is also derived the relation between the shifting functions and the stiffness matrix is derived the boundary control of a pretwist timoshenko beam is studied the effects of the total pretwist angle the position of loading and the boundary spring constants on the energy required to control the performance of a pretwisted beam are investigated

free vibration of centrifugally stiffened uniform and tapered beams using the dynamic stiffness method abstract starting from the governing differential equations of motion in free vibration the dynamic stiffness matrix of a uniform rotating bernoulli euler beam is derived using the frobenius method of solution in power series the derivation includes the presence of an axial force at the outboard end of the beam in addition to the existence of the usual centrifugal force arising from the rotational motion this makes the general assembly of dynamic stiffness matrices of several elements possible so that a non uniform or tapered rotating beam can be analyzed for its free vibration characteristics by idealizing it as an assemblage of many uniform rotating beams the application of the derived dynamic stiffness matrix is demonstrated by investigating the free vibration characteristics of uniform and non uniform tapered rotating beams with particular reference to the wittrick williams algorithm the results from the present theory are compared with published results it is shown that the proposed dynamic stiffness method offers an accurate and effective method of free vibration analysis of rotating beams

effects of initial twist and thickness variation on the vibration behaviour of shallow conical shells abstract a thorough computational investigation is presented into the effects of initial twist and thickness variation on the vibratory characteristics of cantilevered pretwisted thin shallow conical shells with generally varying thickness an energy approach with the ritz minimization procedure is employed to arrive at a governing eigenvalue equation the admissiblepb 2shape functions which comprise sets of mathematically complete two dimensional orthogonal polynomials and a basic function are introduced to account for the boundary constraints and to approximate the three dimensional displacements of the conical shell the effects of angle of twist thickness variation and geometric parameters on the vibration response are presented in a comprehensive parametric study which provides useful new design data selected vibration mode shapes are also included to enhance the existing literature it is found that an increase in the angle of twist does not necessarily increase the torsional stiffness on the contrary the fundamental frequencies is reduced in the present analysis it is also observed that non zero angle of twist and non uniform chordwise thickness variation cause the absent of vibration mode symmetry

hierarchical finite element analysis of the vibration of membranes abstract a hierachical finite element for the vibration of membranes is presented the element has the ability to be joined to neighbouring elements and the numbers of hierarchical terms are allowed to vary in both directions of the element co ordinate axes the element transverse displacement is described by four linear shape functions plus a variable number of hierarchical functions which are forms of legendre orthogonal polynomials the four nodal displacements and the amplitudes of the hierarchical functions on the edges and in the interior of the element are used as generalized co ordinates inter element compatibility is achieved by matching the generalized co ordinates at the nodes and edges shared by elements results are obtained for simply supported square and l shaped membranes comparisons are made with exact solutions for the square membrane and with highly accurate approximate and linear finite element solutions for the l shaped membrane the results for the square membrane confirm that the solutions always converge from above to the exact values as the numbers of hierarchical terms are increased and highly accurate answers are obtained depite the use of a very few hierarchical terms the results of the l shaped membrane show that the hierarchical finite element solutions are largely more accurate than the linear finite element solutions despite the use of fewer system degrees of freedom

the algebra of two symmetric matrices proving completeness and deriving syzygies for a set of invariants of the riemann tensor a large number of riemann tensor invariants can be written as traces of products of two 3 3 matrices representing the weyl tensor and the weyl like square of the ricci tensor it is pointed out that finding a complete set i for all of these invariants is a simple consequence of the more general problem of finding a complete set of symmetric matrices m in terms of which all symmetric matrix polynomials in these two matrices can be expressed such a set is constructed and a formal proof of its completeness is given several matrix identities and a scalar syzygy obtained recently by sneddon are rederived and their interrelationships clarified they are shown to be ultimately consequences of the cayley hamilton theorem a minimal set of invariants that must be contained in the complete set of invariants of the general problem is identified and it is concluded that no set proposed so far is complete

analytical formulation and evaluation for free vibration of naturally curved and twisted beams abstract an analytical study for free vibration of naturally curved and twisted beams with uniform cross sectional shapes is carried out using spatial curved beam theory based on the washizu s static model in the governing equations of motion of the beams all displacement functions and the generalized warping coordinate are defined at the centroid axis and also the effects of rotary inertia transverse shear deformations and torsion related warping are included in the proposed model explicit analytical expressions are derived for the vibrating mode shapes of a curved bending torsional shearing coupled beam under clamped clamped boundary condition with the help of symbolic computing package mathematica and a process of searching is used to determine the natural frequencies comparisons of the present results with the fem results using beam elements in ansys code show good accuracy in computation and validity of the model further the present model is used for cylindrical helical springs with circular cross section fixed at both ends and the results indicate that the natural frequencies agree well with the theoretical and experimental results available

on a class of uniformly accurate imex runge kutta schemes and applications to hyperbolic systems with relaxation in this paper we consider hyperbolic systems with relaxation in which the relaxation time varepsilon may vary from values of order one to very small values when varepsilon is very small the relaxation term becomes very strong and highly stiff and underresolved numerical schemes may produce spurious results in such cases it is important to have schemes that work uniformly with respect to varepsilon implicit explicit imex runge kutta r k schemes have been widely used for the time evolution of hyperbolic partial differential equations but the schemes existing in literature do not exhibit uniform accuracy with respect to the relaxation time we develop new imex r k schemes for hyperbolic systems with relaxation that present better uniform accuracy than the ones existing in the literature and in particular produce good behavior with high order accuracy in the asymptotic limit i e when varepsilon is very small these schemes are obtained by imposing new additional order conditions to guarantee better accuracy over a wide range of the relaxation time we propose the construction of new third order imex r k schemes of type ck s boscarino siam j numer anal 45 2008 pp 1600 1621 in several test problems these schemes with a fixed spatial discretization exhibit for all range of the relaxation time an almost uniform third order accuracy

natural frequencies of a pre twisted blade in a centrifugal force field abstract in this paper starting with the thin shell theory the governing partial differential equation of motion for the transverse deflection of a rotating pre twisted plate is derived strain displacement relationships include the effect of warping of the cross section due to twist bend coupling effect introduced as a result of pre twist in the plate of non circular rectangular cross section then the equation of motion thus derived is used to formulate the free vibration of a typical turbo machinery cantilevered airfoil blade by considering it as a plate of an equivalent rectangular cross section subjected to a quasi static load due to centrifugal force field the analytical derivation considers both the stress stiffening as well as stress softening effects of the centrifugal forces on the spinning airfoil the partial differential equation governing the flexural motion of the plate is transformed into a matrix eigenvalue form using a rayleigh ritz technique the plate deformations are represented by a set of admissible sinusoidal trial functions which fully satisfy all the clamped end constrains as well as the free edge boundary conditions the results of the analytical model exhibit an excellent agreement with the previously published test data both for thin and thick plate geometries and even in highly twisted configurations the results of the eigenvalue solution are presented in a non dimensional form for plates of varying aspect ratios and different amounts of pre twist in the plate the numerical results are directly applicable in determining the static and running frequencies of typical blades used in turbo machinery

numerical schemes for hyperbolic conservation laws with stiff relaxation terms hyperbolic systems often have relaxation terms that give them a partially conservative form and that lead to a long time behavior governed by reduced systems that are parabolic in nature in this article it is shown by asymptotic analysis and numerical examples that semidiscrete high resolution methods for hyperbolic conservation laws fail to capture this asymptotic behavior unless the small relaxation rate is resolved by a fine spatial grid we introduce a modification of higher order godunov methods that possesses the correct asymptotic behavior allowing the use of coarse grids large cell peclet numbers the idea is to build into the numerical scheme the asymptotic balances that lead to this behavior numerical experiments on 2 2 systems verify our analysis

modal analysis of cantilever plates undergoing accelerated in plane motion a modeling method for the modal analysis of cantilever plates undergoing accelerated in plane motion is presented in this paper von karman strain measures are employed to derive the in plane and the lateral equations of motion in plane strain measures of the accelerated plates are obtained from the in plane equations and substituted into the lateral equations to obtain the linear equations for modal analysis the resulting equations are transformed into dimensionless forms in which dimensionless parameters are identified the effects of dimensionless parameter variations on the modal characteristics of the accelerated plates are investigated through numerical studies

asymptotic analysis of upwind discontinuous galerkin approximation of the radiative transport equation in the diffusive limit we revisit some results from m l adams nucl sci engrg 137 2001 pp 298 333 using functional analytic tools we prove that a necessary and sufficient condition for the standard upwind discontinuous galerkin approximation to converge to the correct limit solution in the diffusive regime is that the approximation space contains a linear space of continuous functions and the restrictions of the functions of this space to each mesh cell contain the linear polynomials furthermore the discrete diffusion limit converges in the sobolev space h 1 to the continuous one if the boundary data is isotropic with anisotropic boundary data a boundary layer occurs and convergence holds in the broken sobolev space h s with s frac 1 2 only

propagating waves and end modes in pretwisted beams abstract a method is presented for studying propagating waves and end modes in a uniformly pretwisted beam the variationally derived equations of motion are based on three dimensional elasticity and finite element modelling of the cross section this discretization procedure accommodates arbitrarily shaped cross sections of inhomogeneous anisotropic material properties that follow the pretwist rotation rate an harmonic solution form in both timetand axial co ordinate is introduced i e exp i k t resulting in a two parameter algebraic eigensystem by specifying the axial wavenumberk the eigenproblem permits real frequencies of propagating modes to be determined by specifying real frequency both real and complex axial wavenumbers can be extracted where real values pertain to propagating modes and the complex ones to edge vibrations or end modes due to pretwist the effect of extension torsion and flexural are coupled examples of homogeneous isotropic beams with rectangular and square cross sections are given to illustrate the method of analysis and the physical behavior

a spectral element method for fluid dynamics laminar flow in a channel expansion a spectral element method that combines the generality of the finite element method with the accuracy of spectral techniques is proposed for the numerical solution of the incompressible navier stokes equations in the spectral element discretization the computational domain is broken into a series of elements and the velocity in each element is represented as a high order lagrangian interpolant through chebyshev collocation points the hyperbolic piece of the governing equations is then treated with an explicit collocation scheme while the pressure and viscous contributions are treated implicitly with a projection operator derived from a variational principle the implementation of the technique is demonstrated on a one dimensional inflow outflow advection diffusion equation and the method is then applied to laminar two dimensional separated flow in a channel expansion comparisons are made with experiment and previous numerical work

input power to waveguides calculated by a finite element method this paper considers the power injected into waveguide structures from forces that are concentrated along the waveguide but are otherwise arbitrary the motion of the structure is described by a set of coupled linear one dimensional wave equations these equations are in this work devised by the waveguide finite element method which is a versatile tool for describing wave motion in general structures that have uniform properties along one direction two separate procedures are derived the first is based on spatial and frequency averaging of a modal solution the second procedure is based on a spatial fourier transform which by nature assumes the waveguide to be infinite it is shown that in the limit of zero damping the two methods are identical subsequently input power to a stiffener in a railway car structure is calculated and compared with an in situ measurement showing a fair agreement

flux explicit imex runge kutta schemes for hyperbolic to parabolic relaxation problems we consider the development of implicit explicit imex runge kutta r k schemes for hyperbolic systems of conservation laws with stiff diffusive relaxation the asymptotic behavior of such systems as the relaxation parameter vanishes is governed by a reduced parabolic system and it is desirable to have schemes that are able to capture the correct diffusive limit the hyperbolic part becomes stiff when the system relaxes towards the parabolic equation for this reason in previous works part of the hyperbolic terms are treated implicitly s jin l pareschi and g toscani siam j numer anal 35 1998 pp 2405 2439 s jin and l pareschi j comp phys 161 2000 pp 312 330 g naldi and l pareschi siam j numer anal 37 2000 pp 1246 1270 in particular in s boscarino l pareschi and g russo implicit explicit runge kutta schemes for hyperbolic systems and kinetic equations in the diffusion limit submitted the scheme relaxes to an implicit method for the limit diffusi

free vibration analysis of rotating cantilever plates linearized equations of motion for the free vibration analysis of rotating cantilever plates are derived two inplane stretch variables are introduced and approximated to obtain the ordinary differential equations of motion the use of the two in plane stretch variables enables one to obtain the equations of motion which include proper motion induced stiffness variation terms the equations of motion are transformed into dimensionless forms in which dimensionless parameters are identieed the effects of the dimensionless parameters on the modal characteristics of rotating cantilever plates are investigated through numerical study the eigenvalue loci veering and crossing along with the associated mode shape variations are also presented and discussed

natural vibration of pre twisted shear deformable beam systems subject to multiple kinds of initial stresses free vibration and buckling of pre twisted beams exhibit interesting coupling phenomena between compression moments and torque and have been the subject of extensive research due to their importance as models of wind turbines and helicopter rotor blades the paper investigates the influence of multiple kinds of initial stresses due to compression shears moments and torque on the natural vibration of pre twisted straight beam based on the timoshenko theory the derivation begins with the three dimensional green strain tensor the nonlinear part of the strain tensor is expressed as a product of displacement gradient to derive the strain energy due to initial stresses the frenet formulae in differential geometry are employed to treat the pre twist the strain energy due to elasticity and the linear kinetic energy are obtained in classical sense from the variational principle the governing equations and the associated natural boundary conditions are derived it is noted that the first mode increases together with the pre twisted angle but the second decreases seeming to close the first two modes together for natural frequencies and compressions the gaps close monotonically as the angle of twist increases for natural frequencies and buckling compressions however unlike natural frequencies and compressions the closeness is not monotonic for buckling shears moments and torques

a new asymptotic preserving scheme based on micro macro formulation for linear kinetic equations in the diffusion limit we propose a new numerical scheme for linear transport equations it is based on a decomposition of the distribution function into equilibrium and nonequilibrium parts we also use a projection technique that allows us to reformulate the kinetic equation into a coupled system of an evolution equation for the macroscopic density and a kinetic equation for the nonequilibrium part by using a suitable time semi implicit discretization our scheme is able to accurately approximate the solution in both kinetic and diffusion regimes it is asymptotic preserving in the following sense when the mean free path of the particles is small our scheme is asymptotically equivalent to a standard numerical scheme for the limit diffusion model a uniform stability property is proved for the simple telegraph model various boundary conditions are studied our method is validated in one dimensional cases by several numerical tests and comparisons with previous asymptotic preserving schemes

an asymptotic induced scheme for nonstationary transport equations in the diffusive limit an asymptotic induced scheme for nonstationary transport equations with the diffusion scaling is developed the scheme works uniformly for all ranges of mean free paths it is based on the asymptotic analysis of the diffusion limit of the transport equation a theoretical investigation of the behavior of the scheme in the diffusion limit is given and an approximation property is proven moreover numerical results for different physical situations are shown and the uniform convergence of the scheme is established numerically

dynamic analysis of thin walled closed section beams the present paper considers the problem of dynamic behavior of thin walled beams of arbitrary closed cross section by means of an exact solution starting from benscoter s theory the differential equations of motion are derived by postulating the principle of the virtual work due to a variation of displacements in the case of simply supported thin walled beam a closed form solution for the coupled natural frequencies of free harmonic vibrations was derived the method is illustrated by examples and results are compared with analytical results analyzed by vlasov s theory as well as with fem results

vibration of pretwisted cantilever shallow conical shells abstract this paper presents a mathematical model to investigate the effects of initial twist on the vibratory characteristics of cantilever shallow conical shells the energy functional is minimized according to the ritz procedure to arrive at the governing eigenvalue equation a set of orthogonally generated two dimensional polynomials associated with a basic function which accounts for the boundary expressions and constraints is introduced to approximate the in plane and transverse displacement amplitude functions the complete procedure has been automated to compute the vibration frequencies and mode shapes for exemplary problems in the numerical experiments the convergence of eigenvalues is confirmed by increasing the degrees of polynomials employed in the admissible shape functions to enhance the existing literature a set of first known frequency parameters is presented the paper highlights the important effects of angle of twist on the vibration frequencies and mode shapes of conical shells the fundamental physical frequency decreases monotonically for a longer conical shell the result shows that an increase in the angle of twist does not ensure higher torsional stiffness for a conical shell which is in contradiction with previous observation for a pretwisted beam or plate the symmetry of modes is absent when the angle of twist is non zero

vibration of thin pre twisted helical beams abstract a helical beam has non zero curvature and tortuosity when there is a pre twist the frenet triad is not necessary coincident with the principal triad when an initially straight rod undergoing a large deformation it will be curved and twisted during each deformation sequence the purpose of the paper is to establish the governing equations and the associated natural boundary conditions for a pre twisted helical beam by variational principles and differential geometry although circular helix is taken as example the formulation is valid for inhomogeneous and non uniform parameters along the centerline that variable curvature and tortuosity can be treated without difficulties the method can be used to treat helical anisotropy if the pre twist rate of a ring is 0 5 we show a thick mobius ring for the first time the solution of the natural vibration problem is through chebyshev discretization and clenshaw curtis integration by means of the galerkin formulation

accurate numerical resolution of transients in initial boundary value problems for the heat equation if the initial and boundary data for a pde do not obey an infinite set of compatibility conditions singularities will arise in the solution at the corners of the initial time space domain for dissipative equations such as the 1 d heat equation or 1 d convection diffusion equations the impacts of these singularities are short lived however they can cause a very severe loss of numerical accuracy if we are interested in transient solutions the phenomenon has been described earlier from a theoretical standpoint here we illustrate it graphically and present a simple remedy which with only little extra cost and effort restores full numerical accuracy

a spectral tchebychev solution for three dimensional dynamics of curved beams under mixed boundary conditions abstract this paper presents the application of the spectral tchebychev st technique for solution of three dimensional dynamics of curved beams structures having variable and arbitrary cross section under mixed boundary conditions to accurately capture the vibrational behavior of curved structures a three dimensional 3d solution approach is required since these structures generally exhibit coupled motions in this study the integral boundary value problem ibvp governing the dynamics of the curved structures is found using extended hamilton s principle where the strain energy is expressed using 3d linear elasticity equation to solve the ibvp numerically the 3d spectral tchebychev 3d st approach is used to evaluate the integral and derivative operations defined by the ibvp and to render the complex geometry into an equivalent straight beam with rectangular cross section a series of coordinate transformations are applied to validate and assess the performance of the presented solution approach two case studies are performed i curved beam with rectangular cross section ii curved and pretwisted beam with airfoil cross section in both cases the results natural frequencies and mode shapes are also found using a finite element fe solution approach it is shown that the difference in predicted natural frequencies are less than 1 and the mode shapes are in excellent agreement based on the modal assurance criteria mac analyses however the presented spectral tchebychev solution approach significantly reduces the computational burden therefore it can be concluded that the presented solution approach can capture the 3d vibrational behavior of curved beams as accurately as an fe solution but for a fraction of the computational cost

asymptotic analysis of discrete schemes for non equilibrium radiation diffusion motivated by providing well behaved fully discrete schemes in practice this paper extends the asymptotic analysis on time integration methods for non equilibrium radiation diffusion in 2 to space discretizations therein studies were carried out on a two temperature model with larsen s flux limited diffusion operator both the implicitly balanced ib and linearly implicit li methods were shown asymptotic preserving in this paper we focus on asymptotic analysis for space discrete schemes in dimensions one and two first in construction of the schemes in contrast to traditional first order approximations asymmetric second order accurate spatial approximations are devised for flux limiters on boundary and discrete schemes with second order accuracy on global spatial domain are acquired consequently then by employing formal asymptotic analysis the first order asymptotic preserving property for these schemes and furthermore for the fully discrete schemes is shown finally with the help of manufactured solutions numerical tests are performed which demonstrate quantitatively the fully discrete schemes with ib time evolution indeed have the accuracy and asymptotic convergence as theory predicts hence are well qualified for both non equilibrium and equilibrium radiation diffusion provide ap fully discrete schemes for non equilibrium radiation diffusion propose second order accurate schemes by asymmetric approach for boundary flux limiter show first order ap property of spatially and fully discrete schemes with ib evolution devise subtle artificial solutions verify accuracy and ap property quantitatively ideas can be generalized to 3 dimensional problems and higher order implicit schemes

the identities of the algebraic invariants of the four dimensional riemann tensor this paper extends the investigation of the invariants of the riemann tensor to include the invariants that are of odd degree in the trace free ricci tensor it is shown that these invariants can be expressed in terms of 15 such invariants that are irreducible as a consequence it is possible to write down a complete set of invariants of the riemann tensor several syzygies for these invariants have been found and examples of these are given these syzygies suggest there may be several new syzygies of invariants with even degree in the trace free ricci tensor a large number of these have also been found and are discussed in the paper

finite element model for vibration analysis of pre twisted timoshenko beam abstract a new linearly pre twisted timoshenko beam finite element which has two nodes and four degrees of freedom per node is developed and subsequently used for coupled bending bending vibration analysis of pre twisted beams with uniform rectangular cross section first displacement functions based on two coupled displacement fields the polynomial coefficients are coupled through consideration of the differential equations of equilibrium are derived for pre twisted beams whose flexural displacements are coupled in two planes this approach helps to reduce the number of nodal variables next the stiffness and mass matrices of the finite element model are obtained by using the energy expressions finally the natural frequencies of pre twisted timoshenko beams are obtained and compared with previously published theoretical and experimental results to confirm the accuracy and efficiency of the present model excellent agreement is found with the previous studies also the new pre twisted timoshenko beam element has good convergence characteristics

exact free vibration analysis for membrane assemblies with general classical boundary conditions abstract this paper proposes exact dynamic stiffness formulations for membranes and their assemblies under any arbitrary classical boundary conditions first by taking exact solutions in one direction satisfying all possible opposite edge supports we can derive exact general solutions of the helmholtz equation for membrane vibration then generic force and displacement boundary conditions in the other direction are expressed in terms of the general solutions finally the dynamic stiffness matrices of rectangular membrane elements are formulated which can be assembled directly and allows applications of arbitrary boundary conditions as an accurate and efficient modal solution technique the wittrick williams ww algorithm is applied onto the global dynamic stiffness matrix of the final structure the most important issue of the ww algorithm j 0 count has been resolved with the analytical expressions derived for all possible cases the proposed dynamic stiffness method dsm is then applied to several examples including individual membranes and their assemblies high accuracy and exactness of the proposed method within the whole frequency range is demonstrated by comparison with the finite element method besides interesting findings have been observed on repeated eigenvalues with distinct mode shapes corresponding to certain aspect ratio and tension ratio where physical and mathematical understanding has been provided

space time algebra approach to curvature introducing the notions of vector and bivector differentiation into the dirac algebra considered as a clifford algebra makes possible an extremely concise and geometrically transparent treatment of the curvature tensor and its properties and of related topics such as lorentz invariants characteristic equations petrov types and principal null directions by explicit construction

pretwisted nonuniform beams with time dependent elastic boundary conditions the governing differential equations with the nonhomogeneous time dependent elastic boundary conditions for the coupled bending bending vibration of a pretwisted nonuniform beam are derived by hamilton s principle by taking a general change of dependent variable with shifting functions the original system is transformed to be a system composed of two nonhomogeneous governing differential equations and eight homogeneous boundary conditions consequently the method of separation ofvariables can beused to solvethetransformed problem the physical meanings of these shifting functions are explored the orthogonality condition for the eigenfunctions of a pretwistednonuniformbeamwithelasticboundaryconditionsisalsoderived thestiffnessmatrixforanonuniform beam with arbitrary pretwist is derived as the coefe cients of the matrix can be integrated analytically the exact stiffness matrix is therefore obtained the relation between the shifting functions and the stiffness matrix is derived the ine uence of the pretwist angle on the dynamic response of the beam is studied the vibration control of a pretwist beam with boundary inputs is investigated

exact dynamic stiffness elements based on one dimensional higher order theories for free vibration analysis of solid and thin walled structures in this paper an exact dynamic stiffness formulation using one dimensional 1d higher order theories is presented and subsequently used to investigate the free vibration characteristics of solid and thin walled structures higher order kinematic fields are developed using the carrera unified formulation which allows for straightforward implementation of any order theory without the need for ad hoc formulations classical beam theories euler bernoulli and timoshenko are also captured from the formulation as degenerate cases the principle of virtual displacements is used to derive the governing differential equations and the associated natural boundary conditions an exact dynamic stiffness matrix is then developed by relating the amplitudes of harmonically varying loads to those of the responses the explicit terms of the dynamic stiffness matrices are also presented the resulting dynamic stiffness matrix is used with particular reference to the wittrick williams algorithm to carry out the free vibration analysis of solid and thin walled structures the accuracy of the theory is confirmed both by published literature and by extensive finite element solutions using the commercial code msc nastran

micro macro schemes for kinetic equations including boundary layers we introduce a new micro macro decomposition of collisional kinetic equations in the specific case of the diffusion limit which naturally incorporates the incoming boundary conditions the idea is to write the distribution function f in all its domain as the sum of an equilibrium adapted to the boundary which is not the usual equilibrium associated with f and a remaining kinetic part this equilibrium is defined such that its incoming velocity moments coincide with the incoming velocity moments of the distribution function a consequence of this strategy is that no artificial boundary condition is needed in the micro macro models and the exact boundary condition on f is naturally transposed to the macro part of the model this method provides an asymptotic preserving numerical scheme that generates a very good approximation of the space boundary values at the diffusive limit without any mesh refinement in the boundary layers our numerical results are in very good agreement with the exact so c

finite element theory for curved and twisted beams based on exact solutions for three dimensional solids part 1 beam concept and geometrically exact nonlinear formulation a geometrically exact and completely consistent finite element theory for curved and twisted beams is proposed it is based on the kinematical hypothesis generally formulated for large deformation and accounts for all kinds of deformation of a three dimensional solid translational and rotational displacements of the cross sections warping of their plane and distortion of their contours the principle of virtual work is applied in a straightforward manner to all non zero six components of the strain and stress tensors expressions are given for tangent matrices of elastic inertia and external forces and specific techniques for discretization and updating are developed for the analysis of beams in inertial and non inertial frames finally the numerical properties of the finite element models are demonstrated through examples c 1998 elsevier science s a all rights reserved

vibrations of elastically restrained nonuniform beams with arbitrary pretwist the coupled governing differential equations with general elastic boundary conditions for coupled bending bending vibration of a pretwisted nonuniform beam are derived by using hamilton s principle the e eld transfer matrix for the general system is expressed in integration form as the elements of the matrix can be integrated analytically the exact e eld matrix is therefore obtained the transfer matrix method is presented to study the vibrations of any nonuniform cross sectional beam with arbitrary variation of pretwist angle the frequency equation is derived and expressed in terms of the transfer matrix several limiting cases are examined the corresponding results are compared with previous work in the literature finally the ine uence of elastically restrained boundary conditions and uniform and nonuniform pretwists on the natural frequencies is investigated

dispersion relations of axisymmetric wave propagation in initially twisted bi material compounded cylinders abstract this paper investigates the dispersion relations of axisymmetric wave propagation in initially twisted bi material compound cylinders within the scope of the piecewise homogeneous body model utilizing 3d linearized wave propagation theory in an initially stressed body it is assumed that the constituents of the compound cylinder are isotropic and homogeneous the corresponding eigen value problem is formulated and the solution method for this problem as well as the algorithm for obtaining the numerical results is developed the numerical results illustrate the influence of the initial twisting of the compound cylinder on the dispersion of the axisymmetric wave propagation as presented and discussed in the present paper in particular it is established that as a result of the existence of the initial twisting at least in one constituent of the considered compound cylinder the axisymmetric longitudinal and torsional waves cannot propagate separately i e the new type axisymmetric waves which differ from the axisymmetric torsional and longitudinal waves must appear

free vibration analysis of a twisted beam using the dynamic stiffness method abstract an exact dynamics stiffness matrix is developed and subsequently used for free vibration analysis of a twisted beam whose flexural displacements are coupled in two planes first the governing differential equations of motion of the twisted beam undergoing free natural vibration are derived using hamilton s principle next the general solutions of these equations are obtained when the oscillatory motion of the beam is harmonic this is followed by application of boundary conditions for displacements and forces which essentially leads to the formation of the dynamics stiffness matrix of the twisted beam relating harmonically varying forces with harmonically varying displacements at its ends the resulting dynamic stiffness matrix is used in connection with the wittrick williams algorithm to compute natural frequencies and mode shapes of a twisted beam with cantilever end condition these are compared with previously published results to confirm the accuracy of the method and some conclusions are drawn

three dimensional free vibration of pretwisted beams a method for analyzing the free vibration of pretwisted structural members of arbitrary but uniform cross section is presented this method is based on three dimensional elasticity theory and three dimensional finite element formulation the equations of elasticity and the governing equations of motion are obtained using a rotating coordinate system that rotates along with the cross section the relationship between the fixed cartesian coordinate system and the rotating coordinate system is based on the pretwist angle rate this method can capture warping poisson effects and shear effects hamilton s principle is used to derive the equations of motion that in turn are used to obtain the natural frequencies and mode shapes results showing the relationship between the rate of pretwist and the natural frequencies of prismatic members with rectangular cross sections and different lengths are presented the results also show coupling between the two bending modes and coupling between the axial and torsional modes if the axis of rotation and the centroid of the cross section are not coincident coupling among all four basic modes and higher modes may occur this behavior is difficult or sometimes impossible to capture with simpler technical theories because the method is based on three dimensional elasticity theory it can accurately capture the behavior of long or short beams thin or thick sections arbitrary geometry and inhomogeneous laminated anisotropic materials

the determination of all syzygies for the dependent polynomial invariants of the riemann tensor i pure ricci and pure weyl invariants in this paper we shall consider all pure ricci and pure weyl scalar invariants of any degree in a four dimensional lorentzian space we present a general graph theoretic based reduction algorithm which decomposes using syzygies any pure invariant in terms of the independent base invariants r1 r2 r3 or w1 w2 e zakhary and j carminati j math phys 42 1474 2001

modal analysis of rotating composite cantilever plates a modelling method for the modal analysis of a rotating composite cantilever plate is presented in this paper a set of linear ordinary differential equations of motion for the plate is derived by using the assumed mode method two in plane stretch variables are employed and approximated to derive the equations of motion the equations of motion include the coupling terms between the in plane and the lateral motions as well as the motion induced stiffness variation terms dimensionless parameters are identified and the explicit mass and the stiffness matrices for the modal analysis are obtained with the dimensionless parameters the effects of the dimensionless angular velocity and the fiber orientation angles of rotating composite cantilever plates on their modal characteristics are investigated natural frequency loci veering and crossing along with associated mode shape variations are observed

uniformly accurate diffusive relaxation schemes for multiscale transport equations many transport equations such as the neutron transport radiative transfer and transport equations for waves in random media have a diffusive scaling that leads to the diffusion equations in many physical applications the scaling parameter mean free path may differ in several orders of magnitude from the rarefied regimes to the hydrodynamic diffusive regimes within one problem and it is desirable to develop a class of robust numerical schemes that can work uniformly with respect to this relaxation parameter in an earlier work jin pareschi and toscani siam j numer anal 35 1998 pp 2405 2439 we handled this numerical problem for discrete velocity kinetic models by reformulating the system into a form commonly used for a relaxation scheme for conservation laws jin and xin comm pure appl math 48 1995 pp 235 277 such a reformulation allows us to use the splitting technique for relaxation schemes to design a class of implicit yet explicitly implementable schemes that work with high resolution uniformly with respect to the relaxation parameter in this paper we show that such a numerical technique can be applied to a large class of transport equations with continuous velocities when one uses the even and odd parities of the transport equation

algebraic invariants of the riemann tensor in a four dimensional lorentzian space a set of 16 scalar invariants is given of the riemann tensor which is shown to contain complete minimal sets in the einstein maxwell and perfect fluid cases all previously known sets fail to be complete in the perfect fluid case

a spectral tchebychev solution technique for determining vibrational behavior of thick plates having arbitrary geometry abstract this paper presents a new approach referred to here as the two dimensional spectral tchebychev 2d st technique to predict the dynamics of thick plates having arbitrary geometries under different boundary conditions the integral boundary value problem governing the dynamics of plate like structures is obtained using the mindlin plate theory and following an energy based approach to solve the boundary value problem numerically a spectral tchebychev based solution technique is developed to simplify the calculation of integral and derivative operations and thus to increase the numerical efficiency of the solution approach a one to one coordinate mapping technique is used to map the arbitrary geometry onto an equivalent rectangular in plane shape of the plate the proposed solution technique is applied to various different plate problems to assess the accuracy and show the applicability of the technique in each case the convergence of the solution is analyzed and the predicted non dimensional natural frequencies are compared to those found in the literature or to those found using finite element modeling it is shown that the calculated natural frequencies converge exponentially with increasing number of tchebychev polynomials used and are in excellent agreement with those found in the literature and found form a finite elements solution therefore it is concluded that the presented spectral tchebychev solution technique can accurately and efficiently capture the dynamics of thick plates having arbitrary geometries furthermore the utility of the 2d st is demonstrated by comparing the results obtained using a three dimensional solution approach

a finite element for vibration analysis of twisted blades based on beam theory on presente une methode d elements finis de discretisation en segments de poutre d aubes tournantes pretordues en employant la methode de deplacement de matrice on developpe les proprietes de rigidite et de masse on obtient de maniere systematique la matrice de rigidite structurale et l effet du mouvement de rotation du rotor sur la matrice de rigidite a partir des fonctions potentielles et d energie cinetique

diffusion approximation and computation of the critical size this paper is devoted to the mathematical definition of the extrapolation length which appears in the diffusion approximation to obtain this result we describe the spectral properties of the transport equation and we show how the diffusion approximation is related to the computation of the critical size the paper also contains some simple numerical examples and some new results for the milne problem introduction the computation of the critical size and the diffusion approximation for the transport equation have been closely related and this is due to the following facts first the computation of the critical size is much easier for the diffusion approximation than for the original transport equation second for the critical size one can consider a host media x nxq with x0 given and 17 a positive number the problem of the critical size is then reduced to the computation of the parameter zj it turns out that when the transport operator is almost conservative the critical value of the parameter 17 is large and it is exactly for this range of value that the diffusion approximation is accurate on the other hand the physical boundary condition for the diffusion approxi mation is of the form

development of an exact dynamic stiffness matrix for free vibration analysis of a twisted timoshenko beam abstract an exact dynamic stiffness matrix for a twisted timoshenko beam is developed in this paper in order to investigate its free vibration characteristics first the governing differential equations of motion and the associated natural boundary conditions of a twisted timoshenko beam undergoing free natural vibration are derived using hamilton s principle the inclusion of a given pretwist together with the effects of shear deformation and rotatory inertia gives rise in free vibration to four coupled second order partial differential equations of motion involving bending displacements and bending rotations in two planes for harmonic oscillation these four partial differential equations are combined into an eighth order ordinary differential equation which is identically satisfied by all components of bending displacements and bending rotations this difficult task has become possible only with the help of symbolic computation next the exact solution of the differential equation is obtained in completely general form in terms of eight arbitrary constants this is followed by application of boundary conditions for displacements and forces the procedure leads to the formation of the dynamics stiffness matrix of the twisted timoshenko beam relating harmonically varying forces with harmonically varying displacements at its ends the resulting dynamic stiffness matrix is used with particular reference to the wittrick williams algorithm to compute the natural frequencies and mode shapes of a twisted timoshenko beam with cantilever end condition the exact results from the present theory are compared with numerically simulated results using simpler theories and some conclusions are drawn

high order asymptotic preserving nodal discontinuous galerkin imex schemes for the bgk equation in this paper we develop high order asymptotic preserving ap schemes for the bgk equation in a hyperbolic scaling which leads to the macroscopic models such as the euler and compressible navier stokes equations in the asymptotic limit our approaches are based on the so called micro macro formulation of the kinetic equation which involves a natural decomposition of the problem to the equilibrium and the non equilibrium parts the proposed methods are formulated for the bgk equation with constant or spatially variant knudsen number the new ingredients for the proposed methods to achieve high order accuracy are the following we introduce discontinuous galerkin dg discretization of arbitrary order of accuracy with nodal lagrangian basis functions in space we employ a high order globally stiffly accurate implicit explicit imex runge kutta rk scheme as time discretization two versions of the schemes are proposed scheme i is a direct formulation based on the micro macro decomposition of the bgk equation while scheme ii motivated by the asymptotic analysis for the continuous problem utilizes certain properties of the projection operator compared with scheme i scheme ii not only has better computational efficiency the computational cost is reduced by half roughly but also allows the establishment of a formal asymptotic analysis specifically it is demonstrated that when 0 e 1 scheme ii up to o e 2 becomes a local dg discretization with an explicit rk method for the macroscopic compressible navier stokes equations a method in a similar spirit to the ones in bassi and rebay 1997 3 cockburn and shu 1998 16 numerical results are presented for a wide range of knudsen number to illustrate the effectiveness and high order accuracy of the methods

three dimensional dynamics of rotating structures under mixed boundary conditions abstract this paper presents the spectral tchebychev st technique for solution of three dimensional 3d dynamics of rotating structures in particular structures that exhibit coupled dynamic response require a 3d modeling approach to capture their dynamic behavior rotational motions further complicate this behavior inducing coriolis centrifugal softening and nonlinear stress stiffening effects therefore a 3d solution approach is needed to accurately capture the rotational dynamics the presented 3d st technique provides a fast converging and precise solution approach for rotational dynamics of structures with complex geometries and mixed boundary conditions specifically unlike finite elements techniques the presented technique uses a series expansion approach considering distributed parameter system equations the integral boundary value problem for rotating structures is discretized using the spectral tchebychev approach to simplify the domain of the structures cross sectional and rotational transformations are applied to problems with curved cross section and pretwisted geometry the nonlinear terms included in the integral boundary value problem are linearized around an equilibrium solution using the quasi static method as a result mass damping and stiffness matrices as well as a forcing vector are obtained for a given rotating structure several case studies are then performed to demonstrate the application and effectiveness of the 3d st solution for each problem the natural frequencies and modes shapes from the 3d st solution are compared to those from the literature when available and to those from a commercial finite elements software the case studies include rotating spinning parallelepipeds under free and mixed boundary conditions and a cantilevered pretwisted beam i e rotating blade with an airfoil geometry rotating on a hub it is seen that the natural frequencies and mode shapes from the 3d st technique differ from those from the finite elements model by less than 1 percent for any rotational speed however 3d st approach significantly reduces the computational burden it is concluded that the 3d st technique can be used to obtain the 3d dynamics of rotating structures including those with mixed boundary conditions and complex geometry in a precise and numerically efficient fashion

dynamic stiffness matrix of a rectangular plate for the general case the dynamic stiffness matrix of a rectangular plate for the most general case is developed by solving the bi harmonic equation and finally casting the solution in terms of the force displacement relationship of the freely vibrating plate essentially the frequency dependent dynamic stiffness matrix of the plate when all its sides are free is derived making it possible to achieve exact solution for free vibration of plates or plate assemblies with any boundary conditions previous research on the dynamic stiffness formulation of a plate was restricted to the special case when the two opposite sides of the plate are simply supported this restriction is quite severe and made the general purpose application of the dynamic stiffness method impossible the theory developed in this paper overcomes this long lasting restriction the research carried out here is basically fundamental in that the bi harmonic equation which governs the free vibratory motion of a plate in harmonic oscillation is solved in an exact sense leading to the development of the dynamic stiffness method it is significant that the ingeniously sought solution presented in this paper is completely general covering all possible cases of elastic deformations of the plate the wittrick williams algorithm is applied to the ensuing dynamic stiffness matrix to provide solutions for some representative problems a carefully selected sample of mode shapes is also presented

on a cell entropy inequality for discontinuous galerkin methods we prove a cell entropy inequality for a class of high order dis continuous galerkin finite element methods approximating conservation laws which implies convergence for the one dimensional scalar convex case

moment closure hierarchies for kinetic theories this paper presents a systematicnonperturbative derivation of a hierarchy of closed systems of moment equations corresponding to any classical kinetic theory the first member of the hierarchy is the euler system which is based on maxwellian velocity distributions while the second member is based on nonisotropic gaussian velocity distributions the closure proceeds in two steps the first ensures that every member of the hierarchy is hyperbolic has an entropy and formally recovers the euler limit the second involves modifying the collisional terms so that members of the hierarchy beyound the second also recover the correct navier stokes behavior this is achieved through the introduction of a generalization of the bgk collision operator the simplest such system in three spatial dimensions is a 14 moment closure which also recovers the behavior of the grad 13 moment system when the velocity distributions lie near local maxwellians the closure procedure can be applied to a general class of kinetic theories

implicit explicit runge kutta schemes for hyperbolic systems and kinetic equations in the diffusion limit we consider implicit explicit imex runge kutta r k schemes for hyperbolic systems with stiff relaxation in the so called diffusion limit in such a regime the system relaxes towards a convection diffusion equation the first objective of this paper is to show that traditional partitioned imex r k schemes will relax to an explicit scheme for the limit equation with no need of modification of the original system of course the explicit scheme obtained in the limit suffers from the classical parabolic stability restriction on the time step the main goal of this paper is to present an approach based on imex r k schemes that in the diffusion limit relaxes to an imex r k scheme for the convection diffusion equation in which the diffusion is treated implicitly this is achieved by a novel reformulation of the problem and subsequent application of imex r k schemes to it an analysis of such schemes to the reformulated problem shows that the schemes reduce to imex r k schemes for the limit equation unde

three dimensional vibration analysis of curved and twisted beams with irregular shapes of cross sections by sub parametric quadrature element method abstract this paper presents a novel three dimensional 3d sub parametric quadrature element sp qe method for solving the coupled dynamic behavior of curved and pre twisted beamlike structures with irregular shapes of cross section the technique is an extension of the existing quadrature element method qem with regular shapes by mapping the irregular solid into a regular cube detailed formulations are worked out beams with rectangular circular elliptical and airfoil cross sections various curvature and pre twist rates and different boundary conditions are investigated either serendipity elements or lagrange elements are considered in the mapped regular domain convergence studies are carried out to show the computational performance of the proposed elements results are compared either with the existing 3d spectral tchebychev 3d st solutions or with the finite element data it is shown that the proposed method can yield accurate solutions with small number of degrees of freedom consistent or lumped mass matrix affects little on the accuracy of solutions therefore the element with lumped mass matrix can be efficiently used in dynamic analysis of solids with regular and irregular shapes

the axial torsional vibration of pretwisted beams we investigate the coupled axial torsional vibration of pretwisted beams the equations of motion governing the extension torsion and cross sectional warping of pretwisted beams are derived from hamiltons principle and the common assumptions used to simplify the equations are carefully examined through scaling analysis inconsistencies in previous works such as the neglect of spatial and time derivatives of torsion in the lagrangian functional are remedied giving rise to fourth order terms in the equations of motion that are significant for higher harmonics furthermore scaling analysis of the governing equations yields a set of objective criteria for checking the validity of the frequently misused assumption that the warping function under pretwist is locally identical to that of a prismatic beam we show that this simplification is responsible for the common poor prediction of axial resonance frequencies for pretwisted beams

generalized variational principle on nonlinear theory of naturally curved and twisted beams the nonlinear behavior for naturally curved and twisted beams undergoing large displacements and rotations but small strains has been investigated in this paper an incomplete generalized variational functional for the beams with complete constrained boundaries at two ends is established by means of the lagrange multiplier method a set of equilibrium equations which takes into account the effects of transverse shear deformations as well as torsion related warping has been derived from the stationary conditions of the functional the various elastic couplings of bending twisting and or extension twisting are also included in this analysis the present theory can also be easily extended to other various incomplete constrained boundaries in case of small displacement the equilibrium equations obtained by the present theory reduce to the well known results in literature

the linearized three dimensional beam theory of naturally curved and twisted beams the strain vectors formulation this paper presents the equations of the linearized geometrically exact three dimensional beam theory of naturally curved and twisted beams a new finite element formulation for the linearized theory is proposed in which the strain vectors are the only unknown functions the linear form of the consistency condition that the equilibrium and the constitutive internal force and moment vectors are equal is enforced to be satisfied at chosen points an arbitrary curved and twisted axis of the beam is taken into account which demands proper consideration of the non linearity of spatial rotations the accuracy and the efficiency of the derived numerical algorithm are demonstrated by comparing present numerical results with various analytical and numerical results

identities of the scalars of the four dimensional riemannian manifold a general algorithm is presented for the calculation of identities relating scalars constructed from appropriate contractions of the riemann tensor ricci tensor and curvature scalar the algorithm is applied to determining the identities among the quartic scalars

a contribution to the exact modal solution of in plane beam structures abstract the exact vibration modes and natural frequencies of planar structures and mechanisms comprised euler bernoulli beams are obtained by solving a transcendental non linear eigenvalue problem stated by the dynamic stiffness matrix dsm to solve this kind of problem the most employed technique is the wittrick williams algorithm developed in the early seventies by formulating a new type of eigenvalue problem which preserves the internal degrees of freedom for all members in the model the present study offers an alternative to the use of this algorithm the new proposed eigenvalue problem presents no poles so the roots of the problem can be found by any suitable iterative numerical method by avoiding a standard formulation for the dsm the local mode shapes are directly calculated and any extension to the beam theory can be easily incorporated it is shown that the method here adopted leads to exact solutions as confirmed by various examples extensions of the formulation are also given where rotary inertia end release skewed edges and rigid offsets are all included

a global continuum ritz formulation for flexural vibration of pretwisted trapezoidal plates with one edge built in abstract the development of a continuum ritz model for twisted plate vibration on the basis of minimization of the energy functional is presented this method involves the use of a set of orthogonally generated pb 2 shape functions to approximate the transverse and in plane deflections in this paper a two dimensional recurrence formula is proposed to generate this set of functions during the orthogonalization process a basic function is introduced to each transverse and in plane displacement to ensure the automatic satisfaction of the essential boundary conditions the whole process can be easily implemented numerically and the accuracy of the method can be achieved by increasing the number of terms used in the polynomial functions following the above procedures a governing eigenvalue equation is derived this equation is solved to determine the vibration response of trapezoidal plates with initial twist in order to verify the validity and reliability of this method in addition to the convergence study the present results are compared with the available values from the literature where possible

free vibration analysis of functionally graded curved panels using a higher order finite element formulation free vibration analysis of functionally graded curved panels is carried out using a higher order formulation a c0 finite element formulation is used to carry out the analysis the element consists of nine degrees of freedom per node with higher order terms in the taylor s series expansion which represents the higher order transverse cross sectional deformation modes the formulation includes sanders approximation for doubly curved shells considering the effects of rotary inertia and transverse shear a realistic parabolic distribution of transverse shear strains through the shell thickness is assumed and the use of shear correction factor is avoided material properties are assumed to be temperature independent and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents heat conduction between ceramic and metal constituents is neglected the accuracy of the formulation is validated by comparing the results with those available in the literature effects of panel geometry parameters and boundary conditions are studied

high order asymptotic preserving dg imex schemes for discrete velocity kinetic equations in a diffusive scaling in this paper we develop a family of high order asymptotic preserving schemes for some discrete velocity kinetic equations under a diffusive scaling that in the asymptotic limit lead to macroscopic models such as the heat equation the porous media equation the advection diffusion equation and the viscous burgers equation our approach is based on the micro macro reformulation of the kinetic equation which involves a natural decomposition of the equation to the equilibrium and non equilibrium parts to achieve high order accuracy and uniform stability as well as to capture the correct asymptotic limit two new ingredients are employed in the proposed methods discontinuous galerkin dg spatial discretization of arbitrary order of accuracy with suitable numerical fluxes high order globally stiffly accurate implicit explicit imex runge kutta scheme in time equipped with a properly chosen implicit explicit strategy formal asymptotic analysis shows that the proposed scheme in the limit of e 0 is a consistent high order discretization for the limiting equation numerical results are presented to demonstrate the stability and high order accuracy of the proposed schemes together with their performance in the limit our methods are also tested for the continuous velocity one group transport equation in slab geometry and for several examples with spatially varying parameters

optimal vibration control of curved beams using distributed parameter models abstract the design of linear quadratic optimal controller using spectral factorization method is studied for vibration suppression of curved beam structures modeled as distributed parameter models the equations of motion for active control of the in plane vibration of a curved beam are developed firstly considering its shear deformation and rotary inertia and then the state space model of the curved beam is established directly using the partial differential equations of motion the functional gains for the distributed parameter model of curved beam are calculated by extending the spectral factorization method moreover the response of the closed loop control system is derived explicitly in frequency domain finally the suppression of the vibration at the free end of a cantilevered curved beam by point control moment is studied through numerical case studies in which the benefit of the presented method is shown by comparison with a constant gain velocity feedback control law and the performance of the presented method on avoidance of control spillover is demonstrated

analysis of asymptotic preserving dg imex schemes for linear kinetic transport equations in a diffusive scaling in this paper some theoretical aspects will be addressed for the asymptotic preserving discontinuous galerkin implicit explicit dg imex schemes recently proposed in j jang f li j m qiu and t xiong high order asymptotic preserving dg imex schemes for discrete velocity kinetic equations in a diffusive scaling http arxiv org abs 1306 0227 2013 submitted for kinetic transport equations under a diffusive scaling we will focus on the methods that are based on discontinuous galerkin dg spatial discretizations with the p k polynomial space and a first order implicit explicit imex temporal discretization and apply them to two linear models the telegraph equation and the one group transport equation in slab geometry in particular we will establish uniform numerical stability with respect to knudsen number varepsilon using energy methods as well as error estimates for any given varepsilon when varepsilon rightarrow 0 a rigorous asymptotic analysis of the schemes is also obta

a smooth transition model between kinetic and diffusion equations this paper presents a model which provides a smooth transition between a kinetic and a diffusion domain the idea is to use a buffer zone in which both diffusion and kinetic equations will be solved the solution of the original kinetic equation will be recovered as the sum of the solutions of these two equations we use an artificial connecting function which makes the equation on each domain degenerate at the end of the buffer zone thus no boundary condition is needed at the transition point this model avoids the delicate issue of finding the interface condition or iteration in a typical domain decomposition method that couples a kinetic equation with hydrodynamic equations a new asymptotic preserving method for this model is introduced and numerical examples are used to validate this new model and the new numerical method

fluid dynamic limits of kinetic equations i formal derivations the connection between kinetic theory and the macroscopic equations of fluid dynamics is described in particular our results concerning the incompressible navier stokes equations are based on a formal derivation in which limiting moments are carefully balanced rather than on a classical expansion such as those of hilbert or chapman enskog the moment formalism shows that the limit leading to the incompressible navier stokes equations like that leading to the compressible euler equations is a natural one in kinetic theory and is contrasted with the systematics leading to the compressible navier stokes equations some indications of the validity of these limits are given more specifically the connection between the diperna lions renormalized solution of the classical boltzmann equation and the leray solution of the navier stokes equations is discussed

modal characteristic of a rotating rectangular cantilever plate modal characteristics of a rotating cantilever plate are investigated in the present work a dynamic modelling method for rectangular plates undergoing prescribed overall motion is employed to derive the equations of motion the general equations are particularized for the modal analysis of a rotating cantilever plate and dimensionless parameters are identified through dimensional analysis the effects of the dimensionless parameters on the modal characteristics of the rotating plate are investigated incidentally eigenvalue loci veering and crossing phenomena along with the corresponding modeshape variations are exhibited and discussed

analysis of an asymptotic preserving scheme for linear kinetic equations in the diffusion limit we present a mathematical analysis of the asymptotic preserving scheme proposed in m lemou and l mieussens siam j sci comput 31 2008 pp 334 368 for linear transport equations in kinetic and diffusive regimes we prove that the scheme is uniformly stable and accurate with respect to the mean free path of the particles this property is satisfied under an explicitly given cfl condition this condition tends to a parabolic cfl condition for small mean free paths and is close to a convection cfl condition for large mean free paths our analysis is based on very simple energy estimates

a completely solvable model of the nonlinear boltzmann equation abstract in one space and one time dimension a model of the nonlinear boltzmann equation is presented that is exactly solvable for all initial conditions furthermore this model has the following desirable properties i conservation of the number of particles ii energy conservation iii nonlinearity iv positivity of distribution functions and v unique equilibrium state for any given density which is approached as t for most physically interesting initial conditions some of the simple properties of this model are studied

curvature based beam elements for the analysis of timoshenko and shear deformable curved beams abstract curved beam elements with six degrees of freedom and two three four and five node timoshenko straight beam elements with four five six and seven degrees of freedom respectively are proposed to eliminate stiffness locking when applied to the dynamic analysis of the beams the elements are based on curvature assumptions so that they can represent the bending energy accurately and the shear strain energy is incorporated into the formulation by way of the equilibrium equation eigenvalue problems of timoshenko and shear deformable curved beams are analyzed by using the elements the results of the eigen analysis show that the curvature based beam elements are free of locking and are efficient

out of plane free vibrations of curved beams with variable curvature abstract the differential equations governing out of plane free vibrations of the elastic horizontally curved beams with variable curvature are derived and solved numerically to obtain natural frequencies and mode shapes for parabolic sinusoidal and elliptic beams with hinged hinged hinged clamped and clamped clamped end constraints in which the effects of the rotatory and torsional inertias and shear deformation are included experimental measures of frequencies for several laboratory scale parabolic models serve to validate the theoretical results

a spectral tchebychev technique for solving linear and nonlinear beam equations abstract this paper presents a spectral tchebychev technique for solving linear and nonlinear beam problems the technique uses tchebychev polynomials as spatial basis functions and applies galerkin s method to obtain the spatially discretized equations of motion unlike alternative techniques that require different admissible functions for each different set of boundary conditions the spectral tchebychev technique incorporates the boundary conditions into the derivation and thereby enables the utilization of the solution for any linear boundary conditions without re derivation furthermore the proposed technique produces symmetric system matrices for self adjoint problems in this work the spectral tchebychev solutions for euler bernoulli and timoshenko beams are derived the convergence and accuracy characteristics of the spectral tchebychev technique is studied by solving eigenvalue problems with different boundary conditions it is found that the convergence is exponential and a small number of polynomials is sufficient to obtain machine precision accuracy the application of the technique is demonstrated by solving 1 eigenvalue problems for tapered timoshenko beams with different boundary conditions taper ratios and beam lengths 2 an euler bernoulli beam problem with spatially and temporally varying forcing elastic boundary and damping 3 large deflection nonlinear euler bernoulli beam problems with different boundary conditions and 4 a micro beam problem with nonlinear electrostatic excitation the results obtained from the spectral tchebychev solutions are seen to be in excellent agreement with those presented in the literature

boltzmann equation micro macro decompositions and positivity of shock profiles we introduce an elementary energy method for the boltzmann equation based on a decomposition of the equation into macroscopic and microscopic components the decomposition is useful for the study of time asymptotic stability of nonlinear waves the wave location is determined by the macroscopic equation the microscopic component has an equilibrating property the coupling of macroscopic and microscopic components gives rise naturally to the dissipations similar to those obtained by the chapman enskog expansion our main result is the establishment of the positivity of shock profiles for the boltzmann equation this is shown by the time asymptotic approach and the maximal principle for the collision operator

free in plane vibration of general curved beams using finite element method the governing differential equations for the free in plane vibration of uniform and non uniform curved beams with variable curvatures including the effects of the axis extensibility shear deformation and the rotary inertia are derived using the extended hamilton principle these equations were then solved numerically utilizing the galerkin finite element method and the curvilinear integral taken along the central line of the curvilinear beam based on the proposed finite element formulation one can easily study curved beams having different geometrical and boundary conditions furthermore those curved beams excluding the effects of the axis extensibility shear deformation and the rotary inertia are modeled and then solved utilizing the finite element method using a new non isoparametric element the results for the natural frequencies modal shapes and the deformed configurations are presented for different types of the curved beams with various geometrical properties and boundary conditions and in order to illustrate the validity and accuracy of the presented methodology they are compared with those published in literature

error analysis of imex runge kutta methods derived from differential algebraic systems in this paper we present an error analysis of the imex runge kutta methods when applied to stiff problems containing a nonstiff term and a stiff term characterized by a small stiffness parameter varepsilon in this analysis we expand the global error in powers of varepsilon and show that the coefficients of the error are the global errors of the imex runge kutta method applied to a differential algebraic system interesting convergence results of these errors and of the remainder of the expansion allow us to determine sharp error bounds for stiff problems as a representative example of stiff problems we have chosen the van der pol equation we illustrate that the theoretical prediction is confirmed by the numerical test specifically an order reduction phenomenon is observed when the problem becomes increasingly stiff in particular making several assumptions we try to improve global error estimates of several imex runge kutta methods existing in the literature