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

robust model predictive control of constrained linear systems with bounded disturbances this paper provides a novel solution to the problem of robust model predictive control of constrained linear discrete time systems in the presence of bounded disturbances the optimal control problem that is solved online includes uniquely the initial state of the model employed in the problem as a decision variable the associated value function is zero in a disturbance invariant set that serves as the origin when bounded disturbances are present and permits a strong stability result namely robust exponential stability of the disturbance invariant set for the controlled system with bounded disturbances to be obtained the resultant online algorithm is a quadratic program of similar complexity to that required in conventional model predictive control

testing the minimal repair assumption in an imperfect repair model abstract models assuming minimal repair specify that on repair a failed system is returned to the working state while the effective age of the system is held constant that is the distribution of the time until the next failure of the repaired system is the same as for a system of the same age that has not yet failed these models are common in the literature of operations research and reliability and many probabilistic results as well as inferential procedures depend on the minimal repair assumption we propose two nonparametric tests of the assumption that imperfectly repaired systems are minimally repaired in some models the large sample theory for these tests is derived from the asymptotic joint distribution of a survival function estimator and the ordinary empirical survival function based on the initial failure times of new or perfectly repaired systems simulation results are also provided for the null hypothesis case and under other alternatives

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

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

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 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

equi normalization and exact scaling dynamics in homothetic tube model predictive control this paper develops an equi normalization process in order to verify the existence of and characterize the minimal robust positively invariant set generated by a number of a priori but suitably selected linear inequalities it also develops the exact scaling dynamics associated with this set the paper then proposes an improved homothetic tube model predictive control synthesis for linear systems subject to additive disturbances and polytopic constraints

nonparametric methods for imperfect repair models in the age dependent minimal repair model of block borges and savits bbs a system failing at age t undergoes one of two types of repair with probability p t a perfect repair is performed and the system is returned to the good as new state while with probability 1 p t a minimal repair is performed and the system is repaired but is only as good as a working system of age t whitaker and samaniego propose an estimator for the system life distribution f when data are collected under this model in the present article an appropriate probability model for the bbs process is developed and a counting process approach is used to extend the large sample theorems of whitaker and samaniego to the whole line applications of these results to confidence bands and an extension of the wilcoxon two sample test are examined

estimating the reliability of systems subject to imperfect repair abstract this study of statistical inference for repairable systems focuses on the development of estimation procedures for the life distribution f of a new system based on data on system lifetimes between consecutive repairs the brown proschan imperfect repair model postulates that at failure the system is repaired to a condition as good as new with probability p and is otherwise repaired to the condition just prior to failure in treating issues of statistical inference for this model the article first points out the lack of identifiability of the pair p f as an index of the distribution of interfailure times t 1 t 2 it is then shown that data pairs ti zi i 1 2 render the parameter pair p f identifiable where zi is a bernoulli variable that records the mode of repair perfect or imperfect following the ith failure under the assumption that data of the form ti zi are drawn via inverse sampling until the occurrence of the mth perfect repair the problem of estimating the

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

constraint admissible state sets for switched systems with average dwell time abstract the exact computational problem of constrained admissible average dwell time caadt contractive set and caadt invariant set for discrete time switched systems with and without persistent amplitude bounded additive disturbance is investigated in this paper the considered switching signal satisfies average dwell time adt and is discussed in terms of stage which is both length based and sequence based for the first time two more general criteria are established for checking the existence of the average dwell time adt contractive set and the adt invariant set of the considered system by assuming the value of stage length is taken from an arbitrary finite set a detailed discussion is included to identify a proper value for stage length by taking the computational complexity and the conservatism of the designed finite step computational algorithms of the caadt contractive set and the caadt invariant set into consideration some characteristics of the admissible caadt contractive set and caadt invariant set are derived an illustrative example illustrates the effectiveness of the developed results

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

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

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

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

theoretical explanation of observed decreasing failure rate pooled data on the times of successive failures of the air conditioning system of a fleet of jet airplanes seemed to indicate that the life distribution had a decreasing failure rate more refined analysis showed that the failure distribution for each airplane separately was exponential but with a different failure rate using the theorem that a mixture of distributions each having a non increasing failure rate e g a mixture of exponential distributions itself has a non increasing failure rate the apparent decreasing failure rate of the pooled air conditioning life distribution was satisfactorily explained the present study has implications in other areas where an observed decreasing failure rate may well be the result of mixing exponential distributions having different parameters

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

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

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

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

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

optimized robust control invariance for linear discrete time systems theoretical foundations this paper introduces the concept of optimized robust control invariance for discrete time linear time invariant systems subject to additive and bounded state disturbances a novel characterization of two families of robust control invariant sets is given the existence of a constraint admissible member of these families can be checked by solving a single and tractable convex programming problem in the generic linear convex case and a standard linear quadratic program when the constraints are polyhedral or polytopic the solution of the same optimization problem yields the corresponding feedback control law that is in general set valued a procedure for selection of a point valued nonlinear control law is provided

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

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

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

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

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

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

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

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

change of life distribution via a hazard transformation an inequality with application to minimal repair we introduce a general transformation of hazard rates and discuss the corresponding change of a life length distribution minimal repair transformations are shown to be special cases of this framework which builds on general results concerning likelihood ratios for point processes and in particular on the girsanov theorem for point processes we then study the role of the available information and the consequent definition of state in the change of distributions by using the general notion of f minimal repair where f stands for the information which identifies the state of the considered device we show that the black box minimal repair modeling leads to a stochastically longer total life length than the more realistic one based on internal state information thus the former forms a potential source of bias in minimal repair modeling

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

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

a one step approach to computing a polytopic robust positively invariant set a procedure and theoretical results are presented for the problem of determining a minimal robust positively invariant rpi set for a linear discrete time system subject to unknown bounded disturbances the procedure computes via the solving of a single lp a polytopic rpi set that is minimal with respect to the family of rpi sets generated from a finite number of inequalities with pre defined normal vectors

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

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

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

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

invariant approximations of the minimal robust positively invariant set this note provides results on approximating the minimal robust positively invariant mrpi set also known as the 0 reachable set of an asymptotically stable discrete time linear time invariant system it is assumed that the disturbance is bounded persistent and acts additively on the state and that the constraints on the disturbance are polyhedral results are given that allow for the computation of a robust positively invariant outer approximation of the mrpi set conditions are also given that allow one to a priori specify the accuracy of this approximation

choosing the resampling scheme when bootstrapping a case study in reliability abstract often when dealing with complex data structures there is no unique way to bootstrap if the data can be viewed as u 1 u n iid from some distribution p then one can bootstrap by resampling the u s alternately one can resample in a more model based way that is by making use of the structure of the model p a typical example of this is linear regression in which the data is y i x i i 1 n one can resample the pairs y i x i or one can resample the residuals from a fitted model this phenomenon arises over quite a wide spectrum of problems and in many cases the different methods of bootstrapping can give substantially different results it seems hopeless to come up with a general theory that compares the different ways of bootstrapping in this article we study in some detail a certain model that arises in reliability theory in which there are two natural ways to bootstrap this model is described as follows available for testing is a sample of n iid systems each having t

survey paper set invariance in control the properties of positively invariant sets are involved in many different problems in control theory such as constrained control robustness analysis synthesis and optimization in this paper we provide an overview of the literature concerning positively invariant sets and their application to the analysis and synthesis of control systems

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

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

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

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

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

switched systems with average dwell time computation of the robust positive invariant set abstract in this paper computational results of robust positive invariant rpi sets for switched systems with amplitude bounded persistent additive disturbance and average dwell time adt switching are developed towards this end new idea for facilitating the analysis of the adt switching signal is conceptualized by a series of predefined stages and sufficient conditions for the existence of an adt rpi set of the considered systems are established by utilizing the structure characteristics at each stage of the adt switching signal an exact computational algorithm of the adt rpi set of the considered system is developed the effectiveness of the proposed algorithms are illustrated by a numerical example

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

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

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

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