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

exact characteristic equations for some of classical boundary conditions of vibrating moderately thick rectangular plates the dimensionless equations of motion are derived based on the mindlin plate theory to study the transverse vibration of thick rectangular plates without further usage of any approximate method the exact closed form characteristic equations are given within the validity of the mindlin plate theory for plates having two opposite sides simply supported the six distinct cases considered involve all possible combinations of classical boundary conditions at the other two sides of rectangular plates accurate eigenfrequency parameters are presented for a wide range of aspect ratio and thickness ratio for each case the three dimensional deformed mode shapes together with their associated contour plots obtained from the exact closed form eigenfunctions are also presented finally the effect of boundary conditions aspect ratios and thickness ratios on the eigenfrequency parameters and vibratory behavior of each distinct cases are studied in detail it is believed that in the present work the exact closed form characteristic equations and their associated eigenfunctions except for the plates with four edges simply supported for the rest of considered six cases are obtained for the first time

the calderon problem with partial data in this paper we improve an earlier result by bukhgeim and uhlmann 1 by showing that in dimension n 3 the knowledge of the cauchy data for the schr nodinger equation measured on possibly very small subsets of the boundary determines uniquely the potential we follow the general strategy of 1 but use a richer set of solutions to the dirichlet problem this implies a similar result for the problem of electrical impedance tomography which consists in determining the conductivity of a body by making voltage and current measurements at the boundary

modal analysis and shape optimization of rotating cantilever beams when a cantilever beam rotates about an axis perpendicular to its neutral axis its modal characteristics often vary significantly if the geometric shape and the material property of the beam are given the modal characteristic variations can be accurately estimated following a well established analysis procedure employing assumed mode method or finite element method in many practical design situations however some modal characteristics are usually specified as design requirements and the geometric shape that satisfies the requirements needs to be found in the present study certain modal characteristic requirements such as maximum or minimum slope natural frequency loci are specified and the geometric shapes that satisfy the requirements are obtained through an optimization procedure

numerical presentation of eigenvalue curve veering and mode localization in coupled pendulums to be 0 01 0 01 0 01 0 0 and 0 01 0 the e rst variations and the eigenvalues obtained by the classic method and the improved calculation are given in table 1 the relative errors of the variations are shown in fig 2 the result of the improved calculation is in the very good agreementwith the exact one apartfromthe third mode the e rst variations given by the improved calculation are even better than those with the second variations by the classic method a large modie cation of the truss is considered by multiplying a and b with a factor from 1 through 10 the relative errors of the e rst variations are shown in fig 3 the errors in the e rst mode increase from 0 0827 to 0 8410 whereas those of the classic method change from 0 4159 to 4 1834 the fourth mode shows the biggest difference as the largest error of the improved calculation is 0 0023 but 9 9982 for the classic method conclusions an improved calculation of eigenvalue variations has been presented the eigenvalue approximation from the e rst variation is a rayleigh quotient the variations are different from those in the classic method when there is a variation of b which is the inertiarelated matrix in a structural dynamics although there are more terms in the variations of eigenvalues no extra matrix operation is required thegivenexamplecone rmsthattheaccuracyoftheeigenvalue variations is much better than that obtained with the classic method

an element free galerkin approach for rigidflexible coupling dynamics in 2d state based on an improved element free galerkin efg method and the geometric nonlinear elastic theory an element free numerical approach for rigidflexible coupling dynamics of a rotating hubbeam system is implemented using the hamilton principle the coupled nonlinear integral differential governing equations are derived in which the dynamic stiffening effect is expressed by the longitudinal shrinking of the beam induced by the transverse displacement by the efg method where the global interpolating moving least squares imls and generalized moving least squares igmls were used for discretizing the longitudinal and transverse deformation variables respectively the spatially element free discretized dynamic equations of the system are obtained and the newmark scheme was selected as the time integration method for the numerical computation the superiority of the global interpolating property makes the ease for imposing both displacement and derivative boundary conditions the transverse bending vibration and structural dynamics of the flexible beam in non inertial system are analyzed in the numerical simulations and influence parameters of the efg method are also fully discussed simulation results verify the feasibility of the improved efg approach for rigidflexible coupling dynamics

particularities of newton s method in space frame force determination utilising eigenpair functions abstract redundant space frame dynamics are modelled through the structural eigenproblem which is formulated to account for the geometric stiffness due to self equilibrating membrane forces the resulting mathematical eigenvalues and eigenvectors respectively indicative of natural frequencies and modes of oscillation are then assumed to be continuous functions of a scalar factor upon a normalised set of forces in equilibrium newton s method or sensitivity analysis provides a means for minimising the difference between mathematical and physically observed eigenvalues whereupon the axial forces are inferred from the model issues of convergence and root uniqueness are anticipated eigenvalue coalescence in which eigenvalues transitorily coalesce to permute their arbitrarily numerical ordering is seen to define non smooth eigenvalue functions and hence encumber newton s method mode tracing strategies to overcome this are discussed the existence of various degrees of eigenvalue degeneracy owing to frame cyclic symmetry or otherwise is anticipated in terms of the influence upon newton s method if the degree of frame static redundancy is greater than one and there exist a number of linearly independent force distributions then the required force determination is a multidimensional newton method problems encountered in these manifold dimensions including those arising from frame spatial periodicity and the adversity of newton s method are overcome emphasis is placed upon minimising the dimensionality of newton s method through enforcement of equilibrium constraints illustrative numerical simulations are given and some applications of the method are proposed

non linear free vibrations of a rotating flexible arm abstract the non linear moderately large amplitude flexural free vibrations of an arm clamped with a setting angle to a rigid rotating hub are studied the shear deformation and rotary inertia effects are assumed to be negligible but account is taken of axial inertia non linear curvature and the inextensibility condition the lagrangian approach in conjunction with the assumed modes method assuming constant hub rotation speed is used in a consistent manner to obtain the third order non linear uni modal temporal problem because of the strength of the non linearities in the temporal problem which includes elastic and inertial geometric stiffening as well as inertial softening terms a time transformation method is employed to obtain an approximate solution to the frequency amplitude relation of arm free oscillation results in non dimensional form are presented graphically for the effect of hub rotation speed blade setting angle and hub radius on the variation of the natural frequency with vibration amplitude

behavior of derivatives of eigenvalues and eigenvectors in curve veering and mode localization and their relation to close eigenvalues the problem to measure the phenomena of eigenvalue curve veering and mode localization is addressed in this paper the second derivative of an eigenvalue and the first derivative of an eigenvector are taken as the measures numerically showing curve veering and mode localization based on the measurement close eigenvalues as a key factor for the occurrence of the phenomena are defined two eigenvalues are considered to be close if their difference is small enough to cause the occurrence of the phenomena the curve veering and mode localization can be noted by comparison of the derivatives with a critical value and hence the associated eigenvalues are close weakly coupled springs are given as an example

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

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

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

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 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

an analytical numerical and experimental study of the axisymmetric vibrations of a short cylinder this paper presents a study of standing axisymmetric waves in homogeneous isotropic linear and elastic cylinders whose length and diameter are of the same order of magnitude it is analytically demonstrated that only materials with a poisson s ratio equal to zero can vibrate in pure radial and longitudinal axisymmetric modes and hence the universal frequencies independent of poisson s ratio and the corresponding universal aspect ratios can be accurately calculated the ritz method is applied to numerically determine the natural frequencies and the mode shapes of finite cylinders vibration of a cylinder in the neighbourhood of the universal point is analysed both free and forced vibrations are experimentally detected by using a laser speckle interferometer that allows the determination of the natural frequencies and the mode shapes from the numerical calculations it is confirmed that for materials with poisson s ratio not equal to zero no crossings occur between the curves of non dimensional frequency versus aspect ratio neither for antisymmetric modes themselves nor for symmetric modes there is a good agreement between the analytical solutions the numerical results and the experimental measurements

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

vibration of high speed rotating rings coupled to space fixed stiffnesses abstract this study investigates the vibration of high speed rotating rings coupled to space fixed discrete stiffnesses the ring radial and tangential deformations are defined using space fixed eulerian coordinates where material particles pass through fixed locations in space engineering strain is used in the strain energy expression the derived nonlinear equations from hamilton s principle are linearized about the steady non trivial configuration that results from constant ring rotation comparisons are made to other models in the literature that use different assumptions the governing equations are cast in terms of matrix differential operators that reveal the system s standard gyroscopic system structure the natural frequencies and vibration modes are calculated over a wide range of rotation speeds for axisymmetric free rings and a non axisymmetric ring with a space fixed discrete stiffness element

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

stability estimates for the calderon problem with partial data this is a follow up of a previous article where we proved local stability estimates for a potential in a schr odinger equation on an open bounded set in dimension n 3 from the dirichlet to neumann map with partial data the region under control was the penumbra delimited by a source of light outside of the convex hull of the open set these local estimates provided stability of log log type corresponding to the uniqueness results in calder on s inverse problem with partial data proved by kenig sj ostrand and uhlmann in this article we prove the corresponding global estimates in all dimensions higher than three the estimates are based on the construction of solutions of the schr odinger equation by complex geometrical optics developed in the anisotropic setting by dos santos ferreira kenig salo and uhlmann to solve the calder on problem in certain admissible geometries

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

generalized differential quadrature method for the free vibration of truncated conical panels abstract this paper presents an improved generalized differential quadrature gdq method for the investigation of the effects of boundary conditions on the free vibration characteristics of truncated conical panels the truncated conical panel is an important geometrical shape in the fields of aerospace marine and structural engineering however despite this importance few works in free vibration analysis have dealt with this particular geometry in this work the vibration characteristics of clamped and simply supported truncated conical shells are obtained for various circumferential wave numbers further the effects of the vertex and subtended angles on the frequency parameters are also examined in detail due to limited published results in the open literature results for a range of cases are compared with those generated from the commercial finite element solver mcneal schwendler corporation nastran and excellent agreement is observed

frequency coalescence and mode localization phenomena a geometric theory physical systems the natural frequencies of which depend parametrically on certain quantities may exhibit the phenomenon of frequency coalescence when two or more natural frequencies become equal or the phenomenon of avoided crossings when two or more frequencies approach rapidly and then avoid crossing each other in the process the natural modes undergo significant variations it is shown that both phenomena can be described in a unified manner from the singularities of the mapping from the complex parameter plane into the complex frequency plane in particular the formation of a saddle point in the frequency plane and a branch point in the parameter space is the basis for explaining the properties associated with these phenomena the question of sensitivity of the system response near such singularities is subsequently examined it is shown that the development of a branch point singularity in the complex parameter plane can cause large or even infinite sensitivity of the system about this point depending on the distance of the branch point from the real axis in the parameter space it is further shown that mode localization is also associated with the appearance of a branch point near the real axis of the complex parameter plane which causes the large sensitivity that characterizes the phenomenon the theory is applied to examples of conservative and dissipative systems undergoing free vibrations

optimal stability estimate in the inverse boundary value problem for periodic potentials with partial data abstract we consider the inverse boundary value problem for operators of the form q in an infinite domain r r 1 n n 3 with a periodic potential q for dirichlet to neumann data localized on a portion of the boundary of the form 1 r 1 with 1 being the complement either of a flat or spherical portion of we prove that a log type stability estimate holds

numerical study of vibration localization in disordered cyclic structures a study of mode localization in disordered cyclic structures that have multi degree of freedom substructures in presented particular emphasis is placed on the transition of the natural modes from being extended throughout the structure to being localized on a single substructure a localization length scale is proposed as a measure of the spatial extent of a mode for the purpose of discussing the results of numerical experiments and comparing the localization of different modes different modes in the same mode group were found to have significantly different degrees of localization and similar modes in different mode groups were found to be related to each other via a scaling parameter results also indicate that the particular set of random disorder introduced into the finite structure can have a significant effect on the degree of localization

on nonlinear frequency veering and mode localization of a beam with geometric imperfection resting on elastic foundation this work presents an investigation on the effect of an initial geometric imperfection wavelength amplitude and degree of localization on the in plane nonlinear natural frequencies veering and mode localization of an elastic euler bernoulli beam resting on a winkler elastic foundation the beam is assumed to be pinned pinned with a linear torsional spring at one end the effect of the axial force induced by mid plane stretching is accounted for in the derivation of the mathematical model due to its known importance and significant effect on the nonlinear dynamic behavior of the beam as it was proved and presented in earlier investigations the governing partial differential equation is discretized using the assumed mode method and the resulting nonlinear temporal equation was solved using the harmonic balance method to obtain results for the nonlinear natural frequencies and mode shapes the results are presented in the form of characteristic curves which show the variations of the nonlinear natural frequencies of the first three modes of vibration for a selected range of physical parameters like torsional spring constant elastic foundation stiffness and amplitude and wavelength of a localized and non localized initial slack

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

wave propagation in two dimensional periodic lattices plane wave propagation in infinite two dimensional periodic lattices is investigated using floquet bloch principles frequency bandgaps and spatial filtering phenomena are examined in four representative planar lattice topologies hexagonal honeycomb kagome lattice triangular honeycomb and the square honeycomb these topologies exhibit dramatic differences in their long wavelength deformation properties long wavelength asymptotes to the dispersion curves based on homogenization theory are in good agreement with the numerical results for each of the four lattices the slenderness ratio of the constituent beams of the lattice or relative density has a significant influence on the band structure the techniques developed in this work can be used to design lattices with a desired band structure the observed spatial filtering effects due to anisotropy at high frequencies short wavelengths of wave propagation are consistent with the lattice symmetries

stability analysis for the flapwise motion of a cantilever beam with rotary oscillation abstract the flapwise motion of a cantilever beam with rotary oscillation is analyzed to investigate the dynamic stability of the beam the cantilever beam is regarded as a system subjected to parametric excitation because the angular speed of the cantilever beam varies harmonically to consider the stiffening effect due to the centrifugal force this study adopts the linear partial differential equation of flapwise motion which is derived by a modelling method using the stretch deformation instead of the conventional longitudinal deformation after the partial differential equation is discretized by the galerkin method the method of multiple scales is applied using this method the stability of the beam is analyzed for the variations of the oscillating frequency and the maximum angular speed in addition to verify the stability results the time responses of flapwise motion are computed by the generalized time integration method

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 system level model reduction technique for the efficient simulation of flexible multibody systems flexible multibody systems are governed by sets of non linear differential algebraic equations dae the number of degrees of freedom dofs required for accurate body flexibility modeling as well as the presence of the algebraic constraint equations limit the simulation speed body level model reduction and general purpose system level model reduction techniques do not result in optimal model dimension reduction and do not necessarily transform the dae set into a cheaper to solve set of ordinary differential equations as opposed to model reduction techniques such as global modal parameterization gmp which are based on describing the system motion by the contribution of its dominant configuration dependent system level modal patterns their use as a simulation tool has not been thoroughly investigated this paper investigates the influence of the modal content of the configuration dependent mode set on the simulation accuracy through numerical experiments by including the dynamically excited eigenmodes and static deformation patterns for dofs in which the system is externally loaded the system can be accurately represented by a very limited number of dofs phenomena such as mode veering and mode crossing in which the modal content of eigenmodes rapidly varies can be expected to be problematic for such a description which is confirmed with numerical experiments copyright 2010 john wiley sons ltd

dynamics of rectangular plates undergoing prescribed overall motion a set of linear equations of motion for rectangular plates undergoing prescribed overall motion is derived in this paper two in plane stretch variables with which the in plane strain energy of the plate can be expressed in an exact quadratic form are employed and approximated to derive the equations of motion the equations of motion include motion induced stiffness variation terms which are expressed as explicit functions of the prescribed overall motion the effects of the motion induced stiffness variation terms which are neglected in the conventional linear modelling method on the dynamic response of the plate are investigated the reliability and the accuracy of the equations of motion which are derived in the present work are examined through the numerical study

the vibration and stability of a friction guided translating string abstract eyelets capstans and cylindrical surfaces are often used in thread fiber and paper handling machinery to guide the axially moving element in addition to providing positional control these guides introduce dry friction forces that alter the vibration and stability characteristics of the system this paper examines the lateral response of a string that slides through an elastically supported dry friction guide exact expressions are derived for the linear response under free and forced conditions solutions for the eigenvalue spectrum exhibit unusual features including multiple divergence instabilities regions of flutter instability and regions of curve veering associated with mode localization a second order perturbation solution is derived to examine the behavior of the eigenvalue spectrum in regions of flutter instability and curve veering the analysis highlights the common features of these two phenomena and suggests ways to minimize vibration by adjusting various design variables the analysis also demonstrates that the eigenvalue loci in regions of flutter instability and curve veering are naturally described by a local hyperbolic approximation

dynamics of flexible beams undergoing overall motions abstract a modelling method for straight beams undergoing large overall motions as well as small elastic deformations is presented in this paper different from the classical linear cartesian modelling method which employs three cartesian deformation variables the present modelling method uses a non cartesian variable along with two cartesian variables to describe the elastic deformation a quadratic form of the strain energy expressed with the hybrid set of deformation variables is used to obtain the generalized active forces and a geometric constraint equation relating the non cartesian variable and cartesian variables is used to obtain the generalized inertia forces in the equations of motion the present modelling method not only provides accurate simulation results but also clarifies the limit of validity of the classical linear cartesian modelling method

determining conductivity by boundary measurements a p calderon pose la question est il possible de determiner la conductivite thermique d un objet a partir de mesures statiques de la temperature et du flux de chaleur a la limite on demontre que ces mesures determinent de facon unique la conductivite thermique et toutes ses derivees a la limite

multi parameter perturbation methods for the eigensolution sensitivity analysis of nearly resonant non defective multi degree of freedom systems the dynamic behavior of structural systems may be strongly characterized by the occurrence of multiple internal resonances for particular combinations of the mechanical parameters the linear models governing these resonant or nearly resonant systems tend to exhibit high sensitivity of the eigenvalues and eigenvectors to small parameter modifications this pathological condition is recognized as a source of relevant phenomena such as frequency veering and mode localization or hybridization the paper presents the generalization of uniformly valid perturbation methods to perform eigensolution sensitivity analyses in multi degree of freedom hamiltonian systems with a generic number of close eigenvalues the leading idea is to treat systematically nearly resonant systems as multi parameter perturbations of a perfectly resonant non defective though a priori unknown reference system given a single nearly resonant system a multi parameter perturbation method is presented to achieve a two fold objective first identify a close resonant system suited to serve as a starting point for sensitivity analyses inverse problem second to approximate asymptotically the eigensolution of all the nearly resonant systems which may arise from its generic perturbation direct problem the conditions of existence and uniqueness of the inverse problem solution are discussed the direct problem solution is analyzed with a focus on the eigensolution sensitivity to parameter perturbations with different physical meanings such as a slight geometric disorder or weak elastic coupling in periodic structures finally the procedure is verified on a prototypical structural system describing the section dynamics of a suspended bridge

analysis of in plane wave propagation in hexagonal and re entrant lattices plane wave propagation in hexagonal and re entrant lattices is investigated through the application of bloch s theorem two dimensional dispersion relations are estimated and analyzed to illustrate peculiar properties of re entrant configurations and investigate the directional behavior of hexagonal lattices for varying construction angles special attention is devoted to the determination of phase and group wave velocities velocity plots are obtained for varying frequency and direction of wave propagation to analyze the dispersion characteristics of the lattices and further investigate their directional characteristics

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

linear vibration characteristics of cable buoy systems abstract a theoretical model for the linear vibration of a cable tensioned by a subsurface buoy is developed the equilibrium of the cable buoy system subject to drag is evaluated using an approximate closed form solution whose range of validity is confirmed through comparison with numerical solutions the three dimensional equations of cable buoy motion are linearized about this equilibrium and then used to assess vibration characteristics the characteristic equations for the natural frequencies of both in plane and out of plane vibration modes are derived the in plane natural frequency spectrum exhibits the curve veering phenomena due to asymmetry of the associated mode shapes parameter studies reveal the dependencies of the in plane and out of plane vibration modes on the cable tension the buoy mass and the current velocity

dynamic analysis of flexible beams undergoing overall motion employing linear strain measures a modeling method for the dynamic analysis of a eexible beam undergoing free overall motion is proposed the overall motion is measured at a reference frame that is a rigid cross section of the beam the elastic deformation is measured with respect to the reference frame and is expressed with deformation variables including a stretch variable theuseof astretch variable leadsto asimplelinear strain measure and acorrespondingquadraticstrain energy expression in spite of the simplicity motion induced stiffness variation effects which are often critically important to the dynamic analysis of e exible structures undergoing overall motion can be captured accurately by the modeling method to demonstrate the accuracy of the modeling method test problems are presented and solved the present modeling method proves to be as accurate as a nonlinear e nite element modeling method applicable ranges of the present modeling method are investigated through dimensional analysis and numerical study

three dimensional vibration of rectangular plates variance of simple support conditions and influence of in plane inertia plate models developed on the basis of the three dimensional elasticity theory are crucial to the correct solutions in dynamics problems in a three dimensional setting there exist numerous possible definitions of boundary conditions this paper attempts to identify the variance of three dimensional simple support conditions existing in practice the hard simple support condition assumes vanishing normal stresses at the edges and zero transverse and tangential displacement at the peripheries the soft simple support on the other hand imposes zero transverse displacement with vanishing normal and shear stresses at the boundaries to quantify the relative effects of each boundary condition on the vibratory responses of thick plates a global three dimensional ritz formulation is employed for analysis this technique uses sets of finite polynomial series in cartesian co ordinates to approximate the global normal mode variations of the plate these separable one dimensional polynomials are orthogonally generated within the plate domain such that all the essential edge conditions are identically satisfied the accuracy of the proposed three dimensional ritz method is assured from the convergence and comparison studies numerical experiments have been conducted to study firstly the effects of geometric parameters on the overall normal mode characteristics of simply supported plates and secondly the effects of in plane inertia on the vibration frequencies of plates with different thicknesses the three dimensional deformed mode shapes for selected cases have also been computed these have served to describe more vividly the normal mode characteristics of different types of simply supported rectangular plates

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

stochastic modeling and vibration analysis of rotating beams considering geometric random fields abstract geometric parameters such as the thickness and width of a beam are random for various reasons including manufacturing tolerance and operation wear due to these random parameter properties the vibration characteristics of the structure are also random in this paper we derive equations of motion to conduct stochastic vibration analysis of a rotating beam using the assumed mode method and stochastic spectral method the accuracy of the proposed method is first verified by comparing analysis results to those obtained with monte carlo simulation mcs the efficiency of the proposed method is then compared to that of mcs finally probability densities of various modal and transient response characteristics of rotating beams are obtained with the proposed method

on the non linear vibrations of an inextensible rotating arm with setting angle and flexible hub abstract this work is concerned with the development of a dynamic model for a slender flexible arm undergoing relatively large planar flexural deformations and clamped with a setting angle to a compliant rotating hub the model is derived assuming an inextensible euler bernoulli beam but takes into account the axial inertia and nonlinear curvature two coordinate transformations were used to obtain the inertial position vector of a typical material point along the beam span the inextensibility constraint is used to relate the axial and transverse displacements as well as velocities of the material point in the beam body coordinate system the displacement and velocity vectors obtained are used in the system kinetic energy and exact curvature to eliminate dependence of the system lagrangian on the beam axial deflection and velocity the assumed mode method is used to discretize the system lagrangian and to derive directly the nonlinear equivalent temporal solutions to the problem the resulting dynamic model is a set of four strongly coupled nonlinear ordinary differential equations which in the present work is solved only numerically examples of the results of the numerical solutions for the effects of setting angle and defined physical parameter ratios on the system dynamic response characteristics for a sinusoidal hub torque profile are presented and discussed

stability estimates for the radon transform with restricted data and applications in this article we prove a stability estimate going from the radon transform of a function with limited angle distance data to the l p norm of the function itself under some conditions on the support of the function we apply this theorem to obtain stability estimates for an inverse boundary value problem with partial data

the role of non linear theories in transient dynamic analysis of flexible structures abstract transient dynamic analysis of flexible structures undergoing large motions is considered for rotating structures it is explicitly shown that appropriate account of the influence of centrifugal force on the bending stiffness requires the use of a geometrically non linear at least second order beam theory use of a first order linearized linear beam theory results in a spurious loss of bending stiffness for a rotating plane beam a set of linear partial differential equations of motion that includes all inertia effects coriolis centrifugal acceleration of revolution and coupling between extensional and flexural deformations is derived from the fully non linear beam theory by consistent linearization the analysis is subsequently extended to the more general case of a plate accomodating shear deformation and undergoing a general three dimensional rotating motion the discretization process of the resulting linear equations of motion for the beam and the plate is also discussed

effects of mode localization on input output directional properties of structures abstract the singular value decomposition svd is employed to study the effects of localization phenomena on input output relationships and power and energy transmission ratios of structures for weakly and strongly coupled systems existence of strong localization of singular vectors and abrupt veering of singular value loci are shown occurrence of strong localization causes abrupt changes in input output directional properties in contrast to eigenvalues singular values do not veer away by introducing a disorder in weakly coupled systems in particular the use of singular values and vectors is computationally advantageous in considering multiple load cases while eigenvalue based analyses give information about the resonance frequencies and vibration modes of a structure singular values of the structure are related to the forced response characteristics and give the dynamic behavior in the frequency domain representative examples in structural dynamics are presented

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

transverse vibrations of a rotating uniform cantilever beam with tip mass as predicted by using beam characteristic orthogonal polynomials in the rayleigh ritz method abstract natural frequencies and mode shapes of a rotating uniform cantilever beam with a tip mass are studied by using beam characteristic orthogonal polynomials in the rayleigh ritz method the set of orthogonal polynomials which satisfy the geometrical boundary conditions are generated by using the gram schmidt process the results are compared with those obtained by the myklestad method the extended galerkin method and finite element methods the variation of natural frequencies with the speed of rotation is plotted for several parameter combinations such as setting angle tip mass moment of inertia of tip mass etc mode shapes at different rotational speeds are also plotted use of orthogonal polynomials for the deflection shapes enables the computation of higher natural frequencies of any order to be accomplished without facing any numerical difficulties which is not the case when arbitrary polynomial expressions are used

limiting carleman weights and anisotropic inverse problems in this article we consider the anisotropic calderon problem and related inverse problems the approach is based on limiting carleman weights introduced in kenig et al ann math 165 567 591 2007 in the euclidean case we characterize those riemannian manifolds which admit limiting carleman weights and give a complex geometrical optics construction for a class of such manifolds this is used to prove uniqueness results for anisotropic inverse problems via the attenuated geodesic ray transform earlier results in dimension n 3 were restricted to real analytic metrics

dynamic analysis of a rotating cantilever beam by using the finite element method a finite element analysis for a rotating cantilever beam is presented in this study based on a dynamic modelling method using the stretch deformation instead of the conventional axial deformation three linear partial differential equations are derived from hamilton s principle two of the linear differential equations are coupled through the stretch and chordwise deformations the other equation is an uncoupled one for the flapwise deformation from these partial differential equations and the associated boundary conditions are derived two weak forms one is for the chordwise motion and the other is for the flapwise motion the weak forms are spatially discretized with newly defined two node beam elements with the discretized equations the behaviours of the natural frequencies are investigated for the variation of the rotating speed in addition the time responses and distributions of the deformations and stresses are computed when the rotating speed is prescribed the effects of the rotating speed profile on the vibrations of the beam are also investigated

free vibration analysis of rotating thick plates abstract a finite element formulation for vibration analysis of rotating thick plates is developed mindlin plate theory combined with second order strain displacement assumptions are applied for plate modeling kane dynamic method is employed for the derivation of nonlinear governing equations of motion which include coriolis effects and the couplings between in plane and out of plane deformations the nonlinear equations of motion are linearized using the conventional quasi static method and frequency results are obtained the effects of different parameters including aspect ratio thickness ratio hub radius ratio and rotation speed on dimensionless natural frequencies are investigated and discussed in addition the differences between linear and nonlinear approaches toward in plane vibration analysis of rotating plates are studied tune speeds are observed for the in plane vibration frequencies the results are in good agreement with those of other theories and experiments

the attenuated ray transform on simple surfaces we show that the attenuated geodesic ray transform on two dimensional simple surfaces is injective moreover we give a stability estimate and develop a reconstruction procedure

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

three dimensional elasticity solutions to vibration of cantilevered skewed trapezoids an accurate three dimensional elasticity model for determining the free vibration response of skewed trapezoidal plates is presented the method is formulated on the basis of a linear small strain three dimensional elasticity theory with the ritz minimization procedure the solution method uses sets of uniquely defined one and twodimensional polynomial functions to approximate the trial displacements in the thickness and surface directions respectively these functions are orthogonally generated and have been proven to be highly efficient and numerically stable the proposed technique yields natural frequencies and mode shapes for a wide range of cantilevered skewed trapezoidal plates of arbitrary planform the accuracy of these results whenever possible is validated through comparison with the analytical and experimental data parametric investigations on the vibration behavior of cantilevered trapezoidal plates with respect to different thickness ratios skew angles and chord ratios have been carried out for the first time the presence of surface parallel symmetric thickness modes for these plates is demonstrated in vivid three dimensional mode shape plots

equilibrium and modal analyses of rotating multibeam structures employing multiple reference frames a single reference frame is frequently employed to derive equations of motion in structural dynamic analysis for simple structures like a single beam and a single plate the method of employing a single reference frame usually provides well converged and accurate results for equilibrium and modal analyses however for structures having more general configurations such as multibeam structures use of a single reference frame often results in slow convergence and even erroneous analysis results in the present study a modeling method employing multiple reference frames for dynamic equilibrium and modal analyses of rotating structures is presented the superiority of the proposed modeling method over the single reference frame modeling method is verified with numerical examples

computing green currents via the heat kernel let x be a compact kahler manifold for an analytic cycle y x of complex codimension k the poincare duality assigns a class in the de rham cohomology which can be represented by a harmonic k k form y a green current gy connects both objects by the equality ddgy y y thus we can reconstruct y and its harmonic projection y from this equation because y is the locus where ddgy is not smooth while y is determined by its values on the dense open set x y furthermore the above equality tells us that y and y differ only by some exact current green currents for varieties of arbitrary dimension were systematically developed by h gillet and c soule in 3 these currents play a central role in arakelov theory see 10 and 7 on the one hand the existence of green currents follows more or less formally from the hodge decomposition for currents to do intersection theory on the other hand we need currents which behave well green forms and green currents of logarithmic type are examples of these currents see 2 and 3 here we present a method to find a canonical green current gy which depends only on the kahler manifold x and the cycle y this current gy is given by k k forms with l coefficients which are smooth on x y we start with repeating some basic results on kahler manifolds in 1 which can be found in the textbooks 5 or 11 furthermore we recall the main properties of the heat kernel before we consider the heat flow of dirac currents in section 2 obtaining a green operator for these currents in 3 we define the canonical harmonic green current and show that its harmonic projection is zero in section 4 we apply the heat kernel to intersections of properly intersecting cycles this is needed to derive a formula for the product of green currents in 5 however we have to restrict to cycles that intersect properly hence our results are weaker than those of 3 as we used a different approach we decided to present them here in section 6 we give examples which we found by a good guess 6 1 or because we know all eigen functions of the laplace operator 6 2 or from the explicit formula of the heat kernel 6 3 the last example shows how our techniques can be extended to non compact kahler manifolds for which a heat kernel exists we conclude in section 7 with some questions and remarks acknowledgment the author wishes to thank w gubler j kramer and u kuhn for many discussions which contributed to this paper the comments of the referee helped to clarify the exposition

free vibration analysis of rotating beams by a variable order finite element method the free vibration of rotating beams is analyzed by means of a finite element method of variable order this method entails displacement functions that are a complete power series of a variable number of terms the terms are arranged so that the generalized coordinates are composed of displacements and slopes at the element extremities and additionally displacements at certain points within the element the displacement is assumed to be analytic within an element and thus can be approximated to any degree of accuracy desired by a complete power series numerical results are presented for uniform beams with zero and nonzero hub radii tapered beams and a nonuniform beam with discontinuities since the present method reduces to a conventional beam finite element method for a cubic displacement function the results are compared and found to be superior to the conventional results in terms of accuracy for a given number of degrees of freedom indeed essentially exact eigenvalues and eigenvectors are obtained with this technique which is far more rapidly convergent than other approaches in the literature

eigenvalue curve veering in stressed structures an experimental study there have been extensive research works on the veering phenomenon in dynamic systems as eigenvalues change under parametric variation converging loci are commonly seen to veer away suddenly in a small region of the graph such that the modes swap trajectories all of the modal properties are swapped in the process leading to some curious behaviour in the transition zone theoretical studies of this behaviour have been reported for half a century but despite this heritage explicit references to experimental results are scarce in this paper detailed experimental and numerical investigations on veering are reported the parameter varied is the internal pre load of a redundant frame an fe model is presented and stress stiffening approximations are employed to obtain a tangent stiffness for a nonlinear static solution which is then used in a linear dynamic analysis experimental results are given and the behaviour is found to correspond well with the analytical results in particular the mode shape variation is found to be consistent and the implications of this finding with regard to modal correlation and model validation are noted analyses of the mode shapes in terms of eigenvector rotations are presented and are found to form a valuable tool for the interpretation of experimental results

plurisubharmonic functions in calibrated geometry and q convexity let m be a kahler manifold an integrable function varphi on m is called q plurisubharmonic if the current dd c varphi wedge omega q 1 is positive we prove that varphi is q plurisubharmonic if and only if varphi is subharmonic on all q dimensional complex subvarieties we prove that a q plurisubharmonic function is q convex and admits a local approximation by smooth q plurisubharmonic functions for any closed subvariety z subset m dim mathbb c z leq q 1 there exists a strictly q plurisubharmonic function in a neighbourhood of z this result is known for q convex functions this theorem is used to give a new proof of sibony s lemma on integrability of positive closed p p forms which are integrable outside of a complex subvariety of codimension p 1

geometric non linear substructuring for dynamics of flexible mechanical systems a substructure synthesis formulation is presented that permits use of established flexible multibody dynamic analysis computer codes to account for structural geometric non linear effects large relative displacement is permitted between points within bodies that undergo small strain elastic deformation components are divided into substructures on each of which the theory of linear elasticity relative to a body reference frame is adequate to describe deformation and its coupling with system motion normal vibration and static correction deformation modes are used to account for elastic deformation within each substructure compatibility conditions are derived and imposed as constraint equations at boundary points between substructures system equations of motion that include geometric non linear effects of large rotation in terms of generalized co ordinates of a reference frame for each substructure and a set of deformation modes that are defined within the substructure are assembled the method is implemented in an industry standard flexible multibody dynamics code with minimal modification use of the formulation is illustrated on the classical problem of a spinning beam with geometric stiffening and on a space structure that experiences large deformation

dynamic modelling and stability analysis of axially oscillating cantilever beams dynamic stability of an axially oscillating cantilever beam is investigated in this paper equations of motion for the axially oscillating beam are derived and transformed into dimensionless forms the equations include harmonically oscillating parameters which are related to the motion induced stiffness variation stability diagrams of the first and the second order approximate solutions are obtained by using the multiple scale perturbation method the stability diagrams show that there exist significant difference between the first and the second order approximate solutions it is also found that relatively large unstable regions exist around the first bending natural frequency twice the first bending natural frequency and twice the second being natural frequency the validity of the stability diagram is verified by direct numerical integrations of the equations of motion of the system

mode localization and eigenvalue loci veering phenomena in disordered structures an investigation of the effects of disorder on the modes of vibration of nearly periodic structures is presented it is shown that in structures with close eigenvalues small structural irregularities result in both strong localization of the mode shapes and abrupt veering away or mutual repulsion of the loci of the eigenvalues when these are plotted against a parameter representing the disorder in the system perturbation methods for the eigenvalue problem are applied to predict the occurrence of strong localization and eigenvalue loci veering which are shown to be two manifestations of the same phenomenon also perturbation methods that handle the dramatic effects of small disorder are developed to analyze eigenvalue loci veering and strong localization two representative disordered nearly periodic structures are studied a mistuned assembly of coupled oscillators and a multi span beam with irregular spacing of the supports

comments on curve veering in eigenvalue problems abstract the dependence of eigenvalues on a system parameter is frequently illustrated by a family of loci when two loci approach each other they often cross or abruptly diverge the latter case called curve veering has been observed in approximate solutions associated with discretized models the influence of discretization in producing curve veering has raised doubt on the validity of many approximate solutions the existence of curve veering in continuous models is illustrated by presenting the exact solution of an elementary eigenvalue problem veering is then examined in a general eigenvalue problem criteria are established to distinguish veerings from crossings in both continuous and discretized models the application of the criteria is illustrated by examples

determining a magnetic schrodinger operator from partial cauchy data in this paper we show in dimension n 3 that knowledge of the cauchy data for the schrodinger equation in the presence of a magnetic potential measured on possibly very small subsets of the boundary determines uniquely the magnetic field and the electric potential we follow the general strategy of 7 using a richer set of solutions to the dirichlet problem that has been used in previous works on this problem

dynamics of a slender beam with an attached mass under combination parametric and internal resonances part ii periodic and chaotic responses abstract the governing second order temporal differential equation of a slender beam with an attached mass at an arbitrary position under vertical base excitation which retains the cubic non linearities of geometric and inertial type is reduced to a set of first order differential equations by the method of normal forms for combination parametric and internal resonances of 3 1 these equations are used to find the periodic quasi periodic and chaotic responses of the system for various bifurcating parameters namely damping amplitude and frequency of base motion attached mass and its location bifurcation set mixed mode oscillation period doubling quasi periodic orbits and different routes to chaos namely alternate periodic chaotic transition torus breakdown and intermittency have been studied for the above mentioned bifurcating parameters using phase portrait poincare section time and power spectra

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

dynamic modeling and stability analysis of an axially oscillating beam undergoing periodic impulsive force a dynamic modeling method of an axially oscillating beam undergoing periodic impulsive force is proposed in the present work an element specific modeling method using a stretch deformation variable is employed to derive the linear equations of motion the stiffness variation effect induced by the periodic impulsive force as well as the axially oscillating motion is included in the linear equations of motion the accuracy of the proposed modeling method is verified by comparing its numerical solutions to those of a nonlinear finite element code the effects of the impulse magnitude the oscillating frequency the oscillating speed amplitude and the modal damping ratio on the dynamic stability of the beam are investigated with the modeling method

hermitian matrices depending on three parameters coalescing eigenvalues abstract we consider hermitian matrix valued functions depending on three parameters that vary in a bounded surface of r 3 we study how to detect when such functions have coalescing eigenvalues inside this surface our criterion to locate these singularities is based on a construction suggested by stone 20 for generic coalescings any such singularity is related to a particular accumulation of a certain phase or lack thereof as we cover the surface

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

explanation on the importance of narrow band random excitation characters in the response of a cantilever beam a detailed theoretical investigation into the first and second mode response of a parametrically excited slender cantilever beam where the narrow band random excitation characters are taken into consideration is presented the method of multiple scales is used to determine a uniform first order expansion of the solution of the nonlinear integro differential equations the first order moment frequency and force response data curves of a specimen beam tested by other investigators are obtained further comparisons have been made and results show that whether the first order moment frequency response data curves or the first order moment force response data curves of the first two modes are all in agreement with other investigators experimental results furthermore the stochastic jump and bifurcation have been investigated for the first modal parametric principal resonance by using the stationary joint probability of amplitude and phase results show that stochastic jump occurs mainly in the region of triple valued solution for the frequency response domain if the bandwidth is a variable and others keep constant the basic phenomena indicate that the most probable motion is around the higher branch when the bandwidth is smaller whereas the most probable motion gradually approaches the lower one when the bandwidth becomes higher if the excitation central frequency f is a variable and others keep constant the basic phenomena imply that the higher is f the more probable is the jump from the higher branch to the lower one once f exceeds an certain value for the force response domain there is a region of excitation acceleration a within which the joint probability density has two peaks an upper peak and a lower peak results show that the upper peak decreases while the lower peak increases as the value of a decreases

semi analytic solutions for the free in plane vibrations of confocal annular elliptic plates with elastically restrained edges abstract a two dimensional analytical model is developed to describe the free extensional vibrations of thin elastic plates of elliptical planform with or without a confocal cutout under general elastically restrained edge conditions based on the navier displacement equation of motion for a state of plane stress the model has been simplified by invoking the helmholtz decomposition theorem and the method of separation of variables in elliptic coordinates is used to solve the resulting uncoupled governing equations in terms of products of even and odd angular and radial mathieu functions extensive numerical results are presented in an orderly fashion for the first three anti symmetric symmetric natural frequencies of elliptical plates of selected geometries under different combinations of classical clamped and free and flexible boundary conditions also the occurrences of frequency veering between various modes of the same symmetry group and interchange of the associated mode shapes in the veering region are noted and discussed moreover selected 2d deformed mode shapes are presented in vivid graphical form the accuracy of solutions is checked through appropriate convergence studies and the validity of results is established with the aid of a commercial finite element package as well as by comparison with the data in the existing literature the set of data reported herein is believed to be the first rigorous attempt to obtain the in plane vibration frequencies of solid and annular thin elastic elliptical plates for a wide range of plate eccentricities

dynamics of a slender beam with an attached mass under combination parametric and internal resonances part i steady state response the non linear behaviour of a slender beam with an attached mass at an arbitrary position under vertical base excitation is investigated with combination parametric and internal resonances the governing equation which retains the cubic non linearities of geometric and inertial type is discretized by using galerkin s method and the resulting second order temporal differential equation is then reduced by the method of multiple scales to a set of first order non linear differential equations steady state response and its stability are obtained numerically from these reduced equations super and sub critical hopf bifurcations in the trivial as well as non trivial branches and the saddle node or fold type bifurcations in the non trivial branches of the response curves are found the effect of damping amplitude as well as frequency of base excitation the mass ratio and the location of the concentrated mass on the non linear response of the system having internal resonance of 3 1 is studied at length hysteresis saturation and blue sky catastrophe phenomena with bistability interval in the response curves are observed for a wide range of bifurcating parameters

transverse vibration of trapezoidal plates of variable thickness unsymmetric trapezoids abstract a set of simple two dimensional polynomial functions is employed as the admissible displacement function in the rayleigh ritz energy approach for the free transverse vibration analysis of symmetric trapezoidal plates with linearly varying thickness the admissible function consists the product of i a two dimensional polynomial function and ii a basic function the basic function is defined by the product of the equations of the prescribed continuous piecewise boundary shape each raised to the power of 0 1 or 2 corresponding to a free simply supported or clamped edge respectively the set of functions generated ensures the satisfaction of all the kinematic boundary conditions at the outset the proposed method is applied to solve several symmetric trapezoidal plates with different combinations of boundary conditions and variable thickness the results for some cases are compared with the available published values from the open literature these new results may serve as benchmark data for the development of other numerical methods

use of moving distributed mass element for the dynamic analysis of a flat plate undergoing a moving distributed load this paper presents the theory regarding a moving distributed mass element so that the dynamic responses of a rectangular plate subjected to a moving distributed mass with the effects of inertia force coriolis force and centrifugal force considered can be easily determined in which the property matrices of the moving distributed mass element are derived by means of the principle of superposition and the definition of shape functions and the overall property matrices of the entire vibrating system are determined from the combination of the last element property matrices of the moving distributed mass element and those of the plate itself since the property matrices of the moving distributed mass element have something to do with the instantaneous position and the distribution of the moving mass they are time dependent and so are the overall property matrices of the entire vibrating system based on the last concept the equations of motion for a rectangular plate subjected to a moving distributed mass are established and solved to yield the dynamic responses of the entire vibrating system numerical results reveal that the factors such as the contact area between the moving distributed mass and the plate moving load speed inertia force coriolis force and centrifugal force affect the vibration characteristics of the plate to some degree copyright 2006 john wiley sons ltd