three dimensional free vibration of thick functionally graded annular plates in thermal environment the free vibration analysis of functionally graded fg thick annular plates subjected to thermal environment is studied based on the 3d elasticity theory the material properties are assumed to be temperature dependent and graded in the thickness direction considering the thermal environment effects and using hamilton s principle the equations of motion are derived the effects of the initial thermal stresses are considered accurately by obtaining them from the 3d thermoelastic equilibrium equations the differential quadrature method dqm as an efficient and accurate numerical tool is used to solve both the thermoelastic equilibrium and free vibration equations very fast rate of convergence of the method is demonstrated also the formulation is validated by comparing the results with those obtained based on the first order shear deformation theory and also with those available in the literature for the limit cases i e annular plates without thermal effects the effects of temperature rise material and geometrical parameters on the natural frequencies are investigated the new results can be used as benchmark solutions for future researches

nonlinear vibration of a coating fgm substrate cylindrical panel subjected to a temperature gradient this paper deals with the linear and nonlinear vibration analysis of a three layer coating fgm substrate cylindrical panel with general boundary conditions and subjected to a temperature gradient across the thickness due to steady heat conduction the theoretical formulation is based on geometric nonlinearity in von karman sense and the first order shear deformation theory which accounts for the effects of transverse shear strains and rotary inertia a nonlinear pre vibration analysis is conducted to determine the thermally induced deformation and pre stress state of the cylindrical panel due to the bending and stretching coupling effect being introduced by the graded layer the nonlinear governing differential equations of motion are obtained by adding an incremental dynamic state to the pre vibration state a numerical method that makes use of differential quadrature approximation together with iterative algorithms is employed to model the linear and nonlinear vibration behavior of the cylindrical panels numerical results are presented in both tabular and graphical forms showing that the linear and nonlinear vibration frequencies are significantly influenced by vibration amplitude temperature change out of plane boundary support and the values of a b a h and r a the effects of the in plane displacement constraints and the volume fraction index of the intermediate fgm thin layer are not very prominent

vibration of two dimensional imperfect functionally graded 2d fg porous nano micro beams abstract this study presents analysis on the vibration behavior of the two dimensional functionally graded 2d fg nano and microbeams which are made of two kinds of porous materials for the first time based on timoshenko beam theory the material of the nano and microbeams is modeled as 2d fgms according to the power law the eringen s nonlocal elasticity and the modified couple stress theories are used respectively in case of nano and microbeams the boundary conditions are considered as clamped cc simply supported ss clamped simply supported cs and cantilever cf the governing equations are solved using the generalized differential quadrature method gdqm the effects of fg power indexes along length and thickness are studied along each other and also exclusively the parametric studies are presented for functionally graded along thickness fg functionally graded along length afg and 2d fg porous and perfect micro nanobeams under different boundary conditions

solution of the poisson equation by differential quadrature the method of differential quadrature is demonstrated by solving the two dimensional poisson equation the results for three test problems are compared with the exact analytical solutions and the numerical solutions obtained by others for the galerkin the control volume and the five point finite difference methods the method of differential quadrature leads to more accurate results for comparable levels of computational effort

free vibration analysis of functionally graded plates using the element free kp ritz method a free vibration analysis of metal and ceramic functionally graded plates that uses the element free kp ritz method is presented the material properties of the plates are assumed to vary continuously through their thickness according to a power law distribution of the volume fractions of the plate constituents the first order shear deformation plate theory is employed to account for the transverse shear strain and rotary inertia and mesh free kernel particle functions are used to approximate the two dimensional displacement fields the eigen equation is obtained by applying the ritz procedure to the energy functional of the system convergence studies are performed to examine the stability of the proposed method and comparisons of the solutions derived with those reported in the literature are provided to verify its accuracy four types of functionally graded rectangular and skew plates al al2o3 al zro2 ti 6al 4v aluminum oxide and sus304 si3n4 are included in the study and the effects of the volume fraction boundary conditions and length to thickness ratio on their frequency characteristics are discussed in detail

random vibration of the functionally graded laminates in thermal environments this work deals with the random free vibration of functionally graded laminates with general boundary conditions and subjected to a temperature change taking into account the randomness in a number of independent input variables such as young s modulus poisson s ratio and thermal expansion coefficient of each constituent material based on third order shear deformation theory the mixed type formulation and a semi analytical approach are employed to derive the standard eigenvalue problem in terms of deflection mid plane rotations and stress function a mean centered first order perturbation technique is adopted to obtain the second order statistics of vibration frequencies a detailed parametric study is conducted and extensive numerical results are presented in both tabular and graphical forms for laminated plates that contain functionally graded material which is made of aluminum and zirconia showing the effects of scattering in thermo elastic material constants temperature change edge support condition side to thickness ratio and plate aspect ratio on the stochastic characteristics of natural frequencies

nonlinear free vibrations of composite plates abstract the evolution of the natural mode method nmm for finite element analysis of complex composite structures continues in the present study by applying its principles and formulating the kinematically consistent matrix of a model three node multilayered triangular element both translational and rotational inertia are included in the mass matrix which is conceived using kinematical and geometrical arguments consistent with the assumed natural rigid body and straining modes of the element linear eigenfrequencies are validated with experimental and finite element solutions subsequently the large amplitude nonlinear undamped free vibration of composite plates is investigated a computational scheme is conceived whereby the structure is initially displaced by conducting a full geometrically nonlinear static analysis and subsequently set to transient nonlinear free oscillations by removing the static loading in this regard we discuss the two structured eulerian convective computational schemes employed namely the ariban scheme accumulation of rigid body and natural modes for static nonlinear analysis and the cubic hermitian scheme cuherm for large displacement transient deformation numerical examples demonstrate the efficiency of the formulation and the potential of the natural mode method to deal vigorously with intricate nonlinear time dependent phenomena as well as its potential to provide answers for larger and more complex structures the study also indicates the efficiency and tailoring flexibility offered by advanced composite structural systems

an eight node curvilinear differential quadrature formulation for reissner mindlin plates a first endeavour to exploit the differential quadrature dq method as a simple accurate and efficient numerical technique for the bending of quadrilateral reissner mindlin plates with curvilinear boundaries is made the curvilinear quadrilateral is mapped onto a square domain by using the geometric coordinate transformation this geometric mapping technique is employed to transform the governing differential equations and boundary conditions of the problem from the physical domain onto the computational domain the dq procedures are then applied to discretise the transformed set of differential equations and boundary conditions into a set of linear algebraic equations the numerical solutions to the problem are obtained by solving this set of linear algebraic equations examples illustrating the accuracy and convergence of the dq method for reissner mindlin plates with curvilinear boundaries are presented the great development potential of the dq method as an alternative to other approximate techniques for solving problems related to engineering sciences and structural mechanics is exploited in the present study

on the free vibration analysis of circular plates with stepped thickness over a concentric region by the differential quadrature element method it can be seen the dqem retains all advantages of the differential quadrature method extends the applicability range of the dq method and is more convenient for treating various boundary conditions

free vibration of fgm cylindrical shells with holes under various boundary conditions free vibration analysis of functionally graded material fgm cylindrical shells with holes was studied in this paper the variational equation was founded firstly and the unified displacement mode shape function of the shells with various boundary conditions was put forward then the general analytical expressions of natural frequency and mode shape solutions given by functional variation and characteristic value analysis which can be applied to fgm cylindrical shells with holes of arbitrary functionally graded distribution along the thickness direction and different boundary conditions non dimensional frequencies of shell with holes of different shape number location were given in the end of this paper

a dqem for transverse vibration analysis of multiple cracked non uniform timoshenko beams with general boundary conditions in this paper a differential quadrature element method dqem for free transverse vibration analysis of multiple cracked non uniform timoshenko beams with general boundary conditions is proposed governing equations the compatibility conditions at the damaged cross sections and implementation of the external boundary conditions are derived and formulated by the differential quadrature analogue the accuracy convergence and versatility of the proposed method are confirmed by the exact solution of the uniform beam which has been presented by other authors and 2d finite element method fem numerical results for non uniform beam after the validation of the presented method the effect of quantity depth and location of the cracks on the frequency values of vibrations are investigated the achieved results show that the existence of the crack leads to a decrease in the frequencies of the vibrations through decrease in the stiffness of the beam meanwhile the compatibility conditions at the damaged section is considered as a discontinuity in slope and vertical displacement where the effect of the discontinuity in the slope is more considerable as many authors have neglected the discontinuity in the vertical displacement as it will be shown consideration of the discontinuity in the vertical displacement causes more decrease in the frequencies

on the use of the domain decomposition method for vibration of symmetric laminates having discontinuities at the same edge abstract a free vibration analysis of symmetrically laminated plates with mixed edge boundary conditions is presented a highly efficient and accurate domain decomposition method is employed to establish the model the original domain is first assumed to be an assemblage of small subdomains with the admissible functions of each subdomain represented by sets of orthogonal polynomials these polynomials are generated by using the gram schmidt procedure the continuity matrices resulting from the geometric compatibilities between the subdomains are used to couple the eigenvectors of adjacent subdomains the stiffness and mass matrices of each subdomain after pre and post multiplying by the respective continuity matrices are assembled to form the global stiffness and mass matrices to demonstrate this method the free vibrations of symmetrically laminated plates of various types of mixed edge boundaries are calculated

a new approach to the differential quadrature method for fourth order equations a generalized and more complete methodology for treating boundary conditions in the differential quadrature method dqm is presented this improved approach eliminates the deficiencies of the type grid arrangement which represents an approximation by applying the boundary conditions exactly two kinds of basis functions chebyshev and lagrange are used for concept demonstration it is found that the new approach cures most deficiencies of the current dqm 1997 by john wiley sons ltd

nonlinear free and forced vibration analysis of thin circular functionally graded plates in this paper a semi analytical approach for nonlinear free and forced axisymmetric vibration of a thin circular functionally graded plate is developed the plate thickness is constant functionally graded material fgm properties vary through the thickness of the plate for harmonic vibrations by using assumed time mode method and kantorovich time averaging technique the governing equations are solved steady state free and forced vibration analysis is investigated in detail and corresponding results at uniform ambient temperature are illustrated some of these results in special cases are verified by comparing with those in the literature the results show that the free vibration frequencies are dependent on vibration amplitudes and that the volume fraction index has a significant influence on the nonlinear response characteristics of the plate

finite element theory for curved and twisted beams based on exact solutions for three dimensional solids part 2 anisotropic and advanced beam models consistent finite element formulations for beams made of anisotropic materials and taking into account non classic inhomogeneous torsion have been developed the formulations are based on a kinematical hypothesis that includes exact solutions for three dimensional solids under terminal loading they describe warping of the cross sections in and out of their planes as well as their rigid displacements and rotations their large deformation and geometrically exact description by finite rotations are considered for the cases of monoclinic orthotropic and transversely isotropic materials exact solutions for the solid made from a monoclinic material have been deduced c 1998 elsevier science s a all rights reserved

free vibration of plates by the high accuracy quadrature element method in this paper a highly accurate and rapidly converging hybrid approach is presented for the quadrature element method qem solution of plate free vibration problems the hybrid qem essentially consists of a collocation method in conjunction with a galerkin finite element technique to combine the high accuracy of the differential quadrature method dqm for the efficient solution of differential equations with the generality of the finite element formulation this results in superior accuracy with fewer degrees of freedom than conventional fem or fdm a series of numerical tests is conducted to assess the performance of the quadrature plate element in free vibration problems anisotropic and stepped thickness plates are investigated as well as mixed boundary conditions and point supports at the edges in all cases the results obtained are quite accurate

recognizable closures and submonoids of free partially commutative monoids abstract the main result of this paper is the presentation of two sufficient conditions for the closure x of x and the closure x of x respectively in any free partially commutative monoid for any regular language x to be recognizable several previously obtained sufficient conditions for x to be recognizable can be seen to imply one of those two conditions

an extension of kleene s and ochman ski s theorems to infinite traces abstract as was noted by mazurkiewicz traces constitute a convenient tool for describing finite behaviour of concurrent systems extending in a natural way mazurkiewicz s original definition infinite traces have recently been introduced enabling one to deal with infinite behaviour of nonterminating concurrent systems in this paper we examine the basic families of recognizable sets and of rational sets of infinite traces the seminal kleene characterization of recognizable subsets of the free monoid and its subsequent extensions to infinite words due to buchi and to finite traces due to ochmanski are the cornerstones of the corresponding theories the main result of our paper is an extension of these characterizations to the domain of infinite traces using recognizing and weakly recognizing morphisms as well as a generalization of the schutzenberger product of monoids we prove various closure properties of recognizable trace languages moreover we establish normal form representations for recognizable and rational sets of infinite traces

recognizable subsets of some partially abelian monoids we show that in a free partially abelian monoid generated by a finite alphabet a the subset x of a containing all the words equivalent to a product of words of x is rational if x is a finite set of words each word containing at least one occurrence of any letter of a we suppose that the graph the vertices of which are letters of a and the edges of which correspond to noncommuting pairs of letters is connected

differential quadrature method for nonlinear vibration of orthotropic plates with finite deformation and transverse shear effect based on the reddy s theory of plates with the effect of higher order shear deformations the governing equations for nonlinear vibration of orthotropic plates with finite deformations are presented the nonlinear free vibration is analyzed by the differential quadrature method the differential quadrature approach suggested by wang and bert is extended to handle the multiple boundary conditions of the plate a new technique is also further extended to simplify nonlinear computations and the harmonic balance method is used in deriving the equation of motion the numerical convergence and comparison studies are carried out to validate the present solutions the results show that the presented differential quadrature method is fairly reliable and valid influences of geometric and material parameters transverse shear deformations and rotation inertia as well as vibration amplitudes on the nonlinear free vibration characteristics of orthotropic plates are studied

three dimensional elasticity solutions to some orthotropic plate problems abstract this paper presents a three dimensional analysis of rectangular orthotropic plates by employing the differential quadrature dq method the derivation of the governing equations from the governing equations and the stress strain relationship of the three dimensional elasticity model is detailed the constrained conditions of the orthotropic plate edges are given the governing equations and boundary conditions are first normalized and discretized according to the dq procedure example problems pertaining to the bending buckling and free vibration of orthotropic plates with generic boundary conditions are selected to illustrate the simplicity and applicability of the dq method the convergence characteristics of the dq method are first obtained based on numerical studies after which the dq solutions are compared where possible with exact solutions it is found that the dq method yields accurate results for the plate problems under investigation

on the equivalence of generalized differential quadrature and highest order finite difference scheme abstract it is shown in this paper that the global method of generalized differential quadrature gdq is equivalent to the highest order finite difference scheme which is the extension of low order finite difference schemes the effect of grid point distribution on the accuracy of numerical results is studied by two numerical examples the results showed that the ability to alter the grid point distribution in the gdq method is an important feature to obtain accurate numerical solutions in certain problems

static analysis of structures by the quadrature element method qem abstract the differential quadrature method dqm is an alternative discrete approach to solving directly the governing equations of engineering and mathematical physics since the dqm does not require the derivation of the weak forms of the governing equations like the fem it can greatly reduce formulation efforts in higher order approximation the dqm has been applied in the past to the analyses of various single structural components such as bars beams membranes and plates all of the component analyses yielded good to excellent results however previous studies were limited to simple geometries and simple boundary conditions due to the limitation of using global basis functions in the present study a domain decomposition technique for the dqm is proposed to analyse truss and frame structures where the whole structural domain is represented by a collection of simple element subdomains connected together at specific nodal points this method is named the quadrature element method qem

on recognizable subsets of free partially commutative monoids on montre que dans un mono de partiellement commutatif libre engendre par un alphabet fini a le sous ensemble x de a forme des mots equivalents a un des mots de x est reconnaissable si x est reconnaissable et si tout facteur iterant de x a un graphe de non commutation connexe

vibration analysis of functionally graded annular plates with mixed boundary conditions in thermal environment abstract the free vibration analysis of functionally graded annular plates with mixed boundary conditions in thermal environment is carried out by the 3d elasticity theory and the chebyshev ritz method the material properties are assumed to be temperature dependent and graded in the thickness direction the mixed boundary conditions which include upper and lower surfaces partially fixed inner side partially fixed and outer side partially fixed are considered respectively the accuracy of the present approach for solving the free vibration of the plates with different boundary conditions is validated by comparing the present numerical results with the results available the effects of the different mixed boundary conditions the temperature rise the material graded index and the geometrical parameters on the eigen frequencies are studied

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

on the performance of three iterative methods for solution of gdq algebraic equations abstract in this paper the three conventional iterative methods namely j oe or jacobi gauss seidel g s and sor methods are extended to solve the gdq algebraic equations the performances of these three iterative methods for the gdq and second order finite difference fd algebraic equations are comparatively studied by their application to solve the two dimensional poisson equation it was found that sor method gives the fastest convergence rate for both gdq and fd algebraic equations however the effect of relaxation factor for gdq algebraic equations is reduced the high efficiency and accuracy of gdq over second order fd scheme are also shown in the paper furthermore the performance of j oe and sor methods was validated by their application to a complicated problem that is numerical simulation of natural convection in the annulus between two concentric cylinders it was found that for this complicated case jacobi and gauss seidel methods cannot get converged solution and the efficiency of sor method is reduced to be around three times faster than the j oe method

semi analytical finite elements in the higher order theory of beams abstract the paper presents semi analytical finite elements leading to the development of a higher order theory for beams an analysis of existing beam theories reveals their semi analytical character the semi analytical finite element sfe method proposed assumes the cross section of a solid beam to be an assemblage of certain semi analytical elements the sfe method is based on independent approximations of three dimensional fields of displacements and stresses the method reflects the multi level nature of beams where conventional finite elements are transferred to the level of beam equations for heuristic considerations a mathematical formulation of the linear theory of a solid beam involves the equations of compatibility equilibrium and constitutive relationships i e the elastic law as well as static and kinematic boundary conditions compatibility conditions are derived directly by using finite element approximations while equilibrium equations constitutive equations and boundary conditions may be derived by applying stationarity of a modified hellinger reissner functional this derivation may be also defined by straightforward application of a generalised virtual work formulation the equations of a beam are formulated in terms of generalised variables integral resultants of stresses and strains as well as of nodal displacements the definition of generalised variables is assigned to the nodes of the finite element mesh bending warping and other higher order deformation modes are described automatically finally the set of governing equations includes mixed algebraic differential operators their explicit expressions depend on one of the element types isoparametric subparametric or superparametric the versatility of sfe is demonstrated in practical applications involving well known solutions the classical euler bernoulli and timoshenko theories are derived using a single one dimensional element the beams with a thin walled cross section are described as an assemblage of semi analytical elements on the basis of a higher order theory the conventional semi analytically based finite elements sabfe are derived their basic relations are also presented some numerical examples of the applications to thin walled beams illustrate the basic features possible extensions of sfe to dynamics geometric non linearity and shells are briefly discussed

static analysis of frame structures by the differential quadrature element method in this paper a new version of differential quadrature method dqm is proposed and then extended to analyse frame structures the new method called the differential quadrature element method dqem retains all advantages of the earlier version of the differential quadrature method and overcomes some critical shortcomings existing in the original dqm the proposed method is however different from the quadrature element method qem proposed earlier by striz et al the methodology is explained in details herein via a differential quadrature beam element and some numerical examples are given to show the efficiency of the present method 1997 by john wiley sons ltd

static analysis of mindlin plates the differential quadrature element method dqem abstract the differential quadrature method dqm is a new numerical method for fast solving linear and nonlinear differential equations based on global basis functions in the present study a discrete approximate method based on the dqm the differential quadrature element method dqem is developed for the axisymmetric static analysis of moderately thick circular and annular plates described by the mindlin shear deformable theory the basic idea of the dqem is 1 to divide the whole variable domain into several sub domains elements 2 to form discretized element governing equations by applying the dqm to each element and 3 to assemble all the discretized element governing equations into the overall characteristic equations with the consideration of displacement and stress compatibility conditions between adjacent elements the annular and circular mindlin plate elements of differential quadrature dq are established the convergence characteristics of the proposed method are carefully investigated from the view points of element refinement and element grid refinement and some general regulations and suggestions on element division and element grid selection are provided a number of numerical examples are calculated and the results are compared with the corresponding exact solutions which exhibits high accuracy simplicity and applicability of the present method

vibration characteristics and transient response of shear deformable functionally graded plates in thermal environments free and forced vibration analyses for initially stressed functionally graded plates in thermal environment are presented material properties are assumed to be temperature dependent and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents theoretical formulations are based on reddy s higher order shear deformation plate theory and include the thermal effects due to uniform temperature variation the plate is assumed to be clamped on two opposite edges with the remaining two others either free simply supported or clamped one dimensional differential quadrature technique galerkin approach and the modal superposition method are used to determine the transient response of the plate subjected to lateral dynamic loads comprehensive numerical results for silicon nitride stainless steel rectangular plates are presented in dimensionless tabular and graphical forms the roles played by the constituent volume fraction index temperature rise shape and duration of dynamic loads initial membrane stresses as well as the character of boundary conditions are studied the results reveal that when thermal effects are considered functionally graded plates with material properties intermediate to those of isotropic ones do not necessarily have intermediate natural frequencies and dynamic responses

application of differential quadrature to transport processes the methodology and numerical solution of problems concerning transport processes via the method of differential quadrature are presented application of the method is demonstrated by solving a simple one dimensional time dependent transient diffusion process involving an irreversible reaction without any flux across the end boundary in addition the same technique is used for the first time to the authors knowledge to solve a steady state problem for this purpose a convection diffusion problem involving an irreversible reaction is considered the demonstration is carried out in two ways 1 using the bellman et al technique which employs approximation formulas for higher order partial derivatives derived by iterating the linear quadrature approximation for the first order partial derivative and 2 using individual quadratures to approximate the partial derivatives of first as well as higher orders as suggested by mingle both approaches give the same results however the latter saves an appreciable amount of iterative computing effort despite the fact that it requires separate weighting coefficients for each individual quadrature since the technique of differential quadrature can produce solutions with sufficient accuracy even when using as few as three discrete points both the programming task and computational effort are alleviated considerably for these reasons the differential quadrature approach appears to be very practical in solving a variety of problems related to transport phenomena

permutation rewriting and algorithmic verification we propose a natural subclass of regular languages alphabetic pattern constraints apc which is effectively closed under permutation rewriting i e under iterative application of rules of the form ab ba it is well known that regular languages do not have this closure property in general our result can be applied for example to regular model checking for verifying properties of parametrized linear networks of regular processes and for modeling and verifying properties of asynchronous distributed systems we also consider the complexity of testing membership in apc and show that the question is complete for pspace when the input is an nfa and complete for nlogspace when it is a dfa moreover we show that both the inclusion problem and the question of closure under permutation rewriting are pspace complete when we restrict to the class apc

three dimensional vibration analysis of functionally graded material plates in thermal environment free vibration of functionally graded material rectangular plates with simply supported and clamped edges in the thermal environment is studied based on the three dimensional linear theory of elasticity simply supported and clamped fgm plates with temperature dependent material properties subjected to uniform temperature rise linear temperature rise and nonlinear temperature rise are considered the three displacements of the plates are expanded by a series of chebyshev polynomials multiplied by appropriate functions to satisfy the essential boundary conditions the natural frequencies are obtained by ritz method the numerical results of the present approach are compared with the results of other researchers for the validation parametric study is performed for supported conditions temperature fields volume fraction indices of fgm plates

on optimal selection of interior points for applying discretized boundary conditions in dq vibration analysis of beams and plates the direct implementation of derivative boundary conditions at edge points was demonstrated to be simple flexible and computationally efficient in the vibration analysis of beams and plates by using the differential quadrature dq method in the approach the discretized governing equations at certain interior points need to be replaced by the discretized boundary conditions naturally one may have questions as to whether the replacement points can be selected arbitrarily and how to choose the optimal replacement points this paper tries to answer these questions and its focus is to investigate systematically the effect of the replacement location on the accuracy of the numerical solution from the error distribution analysis of derivative approximation it is found that the optimal position for the replacement is the interior point just adjacent to the boundary this conclusion is confirmed by the numerical experiments of free vibration analysis for beams and plates with various boundary conditions

comparison of discrete singular convolution and generalized differential quadrature for the vibration analysis of rectangular plates this paper presents a comprehensive comparison study between the discrete singular convolution dsc and the well known global method of generalized differential quadrature gdq for vibration analysis so as to enhance the understanding of the dsc algorithm the dsc method is implemented through lagrange s delta sequence kernel dsc lk which utilizes local lagrange polynomials to calculate weighting coefficients whereas the gdq requires global ones moreover it is shown that the treatments of boundary conditions and the use of grid systems are different in the two methods comparison study is carried out on 21 rectangular plates of different combinations of simply supported s clamped c and transversely supported with nonuniform elastic rotational restraint e edges and five rectangular plates of mixed supporting edges some of which with a range of aspect ratios and rotational spring coefficients all the results of the dsc lk agree very well with both those in the literature and newly computed gdq results furthermore it is observed that the dsc lk performs much better for plates vibrating at higher order eigenfrequencies unlike the gdq the dsc lk is numerically stable for problems which require a large number of grid points

three dimensional analysis for transient coupled thermoelastic response of a functionally graded rectangular plate abstract the generalized coupled thermoelasticity based on the lord shulman theory is considered to study the transient thermoelastic response of functionally graded rectangular plates the state equations of functionally graded rectangular plate subjected to time dependent thermal loads were established by using of state space approach in which three displacement components three stress components the temperature and the heat flux were chosen as state variables by giving simply supported boundary conditions and assuming that the material properties of the plate have an exponential law distribution along the thickness coordinate the equations were solved by the numerical laplace transformations and shooting methods for transient thermal responses of a three dimensional functionally graded rectangular plate due to a thermal shock on its top surface effects of the volume fraction distributions of material constituents on the thermal responses including the temperature change the displacement and the stresses distributions were investigated

two new approximate methods for analyzing free vibration of structural components two approximate methods which have not previously been used for structural dynamics problems are applied to the free vibration analysis of various structural components the first method is a new version of the complementary energy method it is shown to be considerably more accurate than the conventional rayleigh and rayleigh schmidt methods when applied to spatially one dimensional free vibration problems prismatic and tapered bars prismatic beams and axisymmetric motion of circular membranes the second method is the differential quadrature method introduced by bellman and his associates it is applied successfully here to all of the problems mentioned plus square membranes and circular and square plates

rectangular thick plates on winkler foundation differential quadrature element solution abstract this paper deals with the static analysis of homogenous isotropic rectangular plates on winkler foundation on the basis of first order shear deformation theory an improved differential quadrature dq method called the differential quadrature element method dqem has been developed for this analysis the plates considered are subjected to a patch load or a concentrated line load which are not solvable by the global dq method the convergence and comparison studies are carried out to establish the reliability of the dqem results then the numerical results for different boundary conditions i e ssss cccc s s s s and sfsf are presented showing the parametric effects of dimensions of loading area line relative thickness ratio and elastic foundation modulus on the deflection bending and twisting moments and shear forces at selected locations most of these data are new and due to the high accuracy of the dq solution they can be useful for benchmarking future work

differential quadrature element method a new approach for free vibration analysis of polar mindlin plates having discontinuities this paper presents the numerical development of the differential quadrature element method dqem for free vibration analysis of the shear deformable plates in polar coordinates this is an improvement on the global differential quadrature method dqm the formulations of the dqem for polar plate vibration element are derived in detail the convergence characteristics of the dqem for solving the free vibration of polar plates are carefully examined the reliability and flexibility of the dqem are illustrated by solving several selected example polar plates having discontinuities which are not solvable directly by the dqm the accuracy of the dqem is evaluated and verified by comparing the present numerical results with the existing exact or approximate solutions or the fem solutions computed using the software package ansys version 5 3

a new differential quadrature methodology for beam analysis and the associated differential quadrature element method this paper presents a computationally efficient and an accurate new methodology in differential quadrature analysis of beam elements the methodology would overcome the difficulties in boundary conditions implementations of fourth order differential equations encountered in such problems the methodology benefited from defining the second order derivatives along the boundaries as independent degrees of freedom would enable the differential quadrature method to exactly satisfy some types of boundary conditions where by most other conventional algorithms have to be satisfied approximately the weighting coefficients employed are not exclusive and any accurate and efficient method such as the generalized differential quadrature method may be used to produce the methods weighting coefficients by solving some typical stability deflection and frequency analysis beam problems and by comparing the results with those of exact solutions and or those of other methodologies accuracy convergency and efficiency of the methodology is asserted in order to generalize its application to large scale beam structures and to the cases with the discontinuity in loading conditions and geometry a new one dimensional differential quadrature element method formulation is presented and implemented

nonlinear oscillations bifurcations and chaos of functionally graded materials plate abstract an analysis on the nonlinear dynamics of a simply supported functionally graded materials fgms rectangular plate subjected to the transversal and in plane excitations is presented in a thermal environment for the first time material properties are assumed to be temperature dependent based on reddy s third order plate theory the nonlinear governing equations of motion for the fgm plates are derived using hamilton s principle galerkin s method is utilized to discretize the governing partial equations to a two degree of freedom nonlinear system including the quadratic and cubic nonlinear terms under combined parametric and external excitations the resonant case considered here is 1 1 internal resonance and principal parametric resonance the asymptotic perturbation method is utilized to obtain four dimensional nonlinear averaged equation the numerical method is used to find the nonlinear dynamic responses of the fgm rectangular plate it was found that periodic quasi periodic solutions and chaotic motions exist for the fgm rectangular plates under certain conditions it is believed that the forcing excitations f1 and f2 can change the form of motions for the fgm rectangular plate

nonlinear transient response of functionally graded plates with general imperfections in thermal environments this paper deals with the nonlinear transient response of simply supported imperfect functionally graded plates in thermal environments an imperfection function is used to model general forms of initial geometric imperfections including sine type global type and localized type imperfections it is assumed that the plate is subjected to a temperature field uniform over the plate surface but varying along the thickness direction due to steady state heat conduction the theoretical formulations are based on the higher order shear deformation plate theory and von karman type nonlinear kinematics the asymptotic solution is obtained by using an improved perturbation approach galerkin technique and runge kutta iteration process the material properties of the plate are temperature dependent and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents numerical illustrations are given in both tabular and graphical forms it is shown that imperfection mode and magnitude have significant effects on the nonlinear transient response of functionally graded plates the influences of imperfection location temperature field and volume fraction index are also studied

three dimensional asymptotic approach to inhomogeneous and laminated piezoelectric plates an asymptotic theory is developed for anisotropic inhomogeneous and laminated piezoelectric plates on the basis of three dimensional linear piezoelectricity the inhomogeneity is assumed in the thickness direction and includes the important piezoelectric laminates as a special case through asymptotic expansions the resulting two dimensional differential equations are of the same form for each order with different nonhomogeneous terms being determined systematically by preceding order solutions the governing equations of the leading order when degenerated to pure elasticity are shown to be the same as those for equivalent classical thin elastic plates the proposed methodology is illustrated by considering a rectangular piezoelectric plate subject to both mechanical and electric loadings with its edges simply supported and grounded a three dimensional solution for the fully electromechanically coupled problem is obtained by successively solving the two dimensional field equations from the leading order to higher orders excellent agreement is observed with established results and new results are presented from which significant physical insights are discussed

application of a new differential quadrature methodology for free vibration analysis of plates a new methodology is introduced in the differential quadrature dq analysis of plate problems the proposed approach is distinct from other dq methods by employing the multiple boundary conditions in a different manner for structural and plate problems the methodology employs the displacement within the domain as the only degree of freedom whereas along the boundaries the displacements as well as the second derivatives of the displacements with respect to the co ordinate variable normal to the boundary in the computational domain are considered as the degrees of freedom for the problem employing such a procedure would facilitate the boundary conditions to be implemented exactly and conveniently in order to demonstrate the capability of the new methodology all cases of free vibration analysis of rectangular isotropic plates in which the conventional dq methods have had some sort of difficulty to arrive at a converged or accurate solution are carried out excellent convergence behaviour and accuracy in comparison with exact results and or results obtained by other approximate methods were obtained the analogous dq formulation for a general rectangular plate is derived and for each individual boundary condition the general format for imposing the given conditions is devised it must be emphasized that the computational efforts of this new methodology are not more than for the conventional differential quadrature methods copyright 2002 john wiley sons ltd

non axisymmetric bending of thin annular plates due to circumferentially distributed moments abstract the non linear deformation of a thin annular plate subjected to circumferentially distributed bending moments is studied a von karman plate model is adopted to formulate the equations of motion free free boundary conditions have been applied at both inner and outer edges the matrix formulation of the differential quadrature method is used to discretise and solve the governing equations linear analysis predicts that the annular disk deforms axisymmetrically into a spherical dome however the proposed non linear analysis shows that a symmetry breaking bifurcation may occur after which the linear solution becomes unstable and the plate transitions into a non axisymmetric cylindrical deformation this is the case when at least one of two parameters reaches a critical value these parameters are the non dimensionalised ratio between applied moment and bending stiffness and the ratio between inner and outer radius furthermore it is noted that free free boundary conditions and circumferentially distributed bending moments do not break the circular symmetry of the annular disk hence the principal axes of curvature in the deformed configuration do not have a preferred orientation therefore the present work describes a shell possessing infinite identical equilibria having different yet no favoured direction and hence links to previous researches on neutrally stable structures

differential quadrature element method for static analysis of reissner mindlin polar plates abstract in this paper a new numerical technique the differential quadrature element method dqem has been developed for static analysis of the two dimensional polar reissner mindlin plate in the polar coordinate system by integrating the domain decomposition method ddm with the differential quadrature method dqm the detailed formulations for the sectorial dqem plate bending element and the compatibility conditions between each element are presented the convergence properties and the accuracy of the dqem for bending of thick polar plates are investigated through a number of numerical computations consequently the dqem has been successfully applied to analyze several annular sector plates with discontinuous loading and boundary conditions and cutouts to illustrate the simplicity and flexibility of this method for solving reissner mindlin plates in polar coordinate system which are not solvable directly using the differential quadrature method the numerical results are verified by the existing exact solutions or the fem solutions obtained using the software package ansys version 5 3

three dimensional asymptotic nonlocal elasticity theory for the free vibration analysis of embedded single walled carbon nanotubes abstract within the framework of three dimensional 3d nonlocal elasticity theory the authors develop an asymptotic theory to investigate the free vibration characteristics of simply supported single walled carbon nanotubes swcnts non embedded or embedded in an elastic medium using the multiple time scale method eringen s nonlocal constitutive relations are adopted to account for the small length scale effect in the formulation the interactions between the swcnt and its surrounding medium are modeled as a two parameter pasternak foundation model after performing a series of mathematical processes including nondimensionalization asymptotic expansion and successive integration etc the authors obtain recurrent sets of motion equations for various order problems the nonlocal classical shell theory cst is derived as a first order approximation of the current 3d nonlocal elasticity problem and the equations of motion for higher order problems retain the same differential operators as those of the nonlocal cst although with different nonhomogeneous terms the current asymptotic solutions for the natural frequency parameters of non embedded or embedded swcnts and their corresponding through thickness modal stress and displacement component distributions are obtained to assess the accuracy of various nonlocal shell and beam theories available in the literature

nonlinear dynamics of initially imperfect functionally graded circular cylindrical shell under complex loads abstract the nonlinear vibration of a simply supported fgm cylindrical shell with small initial geometric imperfection under complex loads is studied the effects of radial harmonic excitation compressive in plane force combined with supersonic aerodynamic and thermal loads are considered the small initial geometric imperfection of the cylindrical shell is characterized in the form of the sine type trigonometric functions the effective material properties of this fgm cylindrical shell are graded in the radial direction according to a simple power law in terms of the volume fractions based on reddy s third order shear deformation theory von karman type nonlinear kinematics and hamilton s principle the nonlinear partial differential equation that controls the shell dynamics is derived both axial symmetric and driven modes of the cylindrical shell deflection pattern are included furthermore the equations of motion can be reduced into a set of coupled nonlinear ordinary differential equations by applying galerkin s method in the study of the nonlinear dynamics responses of small initial geometric imperfect fgm cylindrical shell under complex loads the 4th order runge kutta method is used to obtain time history phase portraits bifurcation diagrams and poincare maps with different parameters the effects of external loads geometric imperfections and volume fractions on the nonlinear dynamics of the system are discussed

application of a series type method to vibration of orthotropic rectangular plates with mixed boundary conditions the object of this paper is to show an application of a series type method to the free vibration of an orthotropic rectangular plate with mixed boundary conditions the rectangular plate considered is elastically constrained or clamped along a few parts of its edge and simply supported on the remainder a frequency equation is derived to accommodate rectangular orthotropy of the plate by the extension of a previously developed method and subsequent algebraic manipulation leads to the improved equation yielding natural frequencies of the plate with very good accuracy the method is demonstrated for numerical examples where one two or three parts are constrained along the boundary of the square plate and the effects of varying constraint and orthotropic parameters on the natural frequencies and mode shapes are studied

solving initial value problems by differential quadrature method part 1 first order equations in this paper the differential quadrature method is used to solve first order initial value problems the initial condition is given at the beginning of a time interval the time derivative at a sampling grid point within the time interval can be expressed as a weighted linear sum of the given initial condition and the function values at the sampling grid points within the time interval the order of accuracy and the stability property of the quadrature solutions depend on the locations of the sampling grid points it is shown that the order of accuracy of the quadrature solutions at the end of a time interval can be improved to 2n 1 or 2n if the n sampling grid points are chosen carefully in fact the approximate solutions are equivalent to the generalized pade approximations the resultant algorithms are therefore unconditionally stable with controllable numerical dissipation the corresponding sampling grid points are found to be given by the roots of the modified shifted legendre polynomials from the numerical examples the accuracy of the quadrature solutions obtained by using the proposed sampling grid points is found to be better than those obtained by the commonly used uniformly spaced or chebyshev gauss lobatto sampling grid points copyright 2001 john wiley sons ltd

on the use of the substructure method for vibration analysis of rectangular plates with discontinuous boundary conditions abstract a substructure method is presented for analysis of the free vibration of a rectangular plate with mixed edge boundary conditions the method involves the partitioning of the entire plate domain into appropriate elements to approximate the deflection function of each element by a set of admissible orthogonal polynomials the continuity conditions along the interconnecting boundaries provide the coupling between the coefficients of each element summing the strain and kinetic energies of each element and minimizing the resulting rayleigh quotient with respect to the unknown coefficients leads to the governing eigenvalue equation for the entire plate several plate problems are solved to demonstrate the applicability and accuracy of the present method where possible the results obtained are verified by comparisons with existing published values from the literature

buckling and free vibration analysis of thick rectangular plates resting on elastic foundation using mixed finite element and differential quadrature method abstract in this article a combination of the finite element fe and differential quadrature dq methods is used to solve the eigenvalue buckling and free vibration equations of rectangular thick plates resting on elastic foundations the elastic foundation is described by the pasternak two parameter model the three dimensional linear and small strain theory of elasticity and energy principle are employed to derive the governing equations the in plane domain is discretized using two dimensional finite elements the spatial derivatives of equations in the thickness direction are discretized in strong form using dqm buckling and free vibration of rectangular thick plates of various thicknesses to width and aspect ratios with pasternak elastic foundation are investigated using the proposed fe dq method the results obtained by the mixed method have been verified by the few analytical solutions in the literature it is concluded that the mixed fe dq method has good convergancy behavior and acceptable accuracy can be obtained by the method with a reasonable degrees of freedom

implementation of clamped and simply supported boundary conditions in the gdq free vibration analysis of beams and plates abstract in this paper a new methodology for implementing the clamped and simply supported boundary conditions is presented for the free vibration analysis of beams and plates using the generalized differential quadrature gdq method the proposed approach directly substitutes the boundary conditions into the governing equations and is referred to as sbcge approach the sbcge approach is presented to overcome the drawbacks of previous approaches in treating the boundary conditions a comparison of the sbcge approach with the method of modifying weighting coefficient matrices mwcm is made by their application to the vibration analysis of beams and plates with combinations of simply supported and clamped boundary conditions some details of the gdq method are also described in the paper

analysis of vibrating thick rectangular plates with mixed boundary constraints using differential quadrature element method a free vibration analysis of moderately thick rectangular plates with mixed boundary conditions is presented on the basis of the first order shear deformation plate theory the differential quadrature element method a highly efficient and accurate hybrid approach has been employed to establish the numerical model the complex plate domain is first decomposed into small simple continuous sub domains elements and the differential quadrature method is then applied to each continuous sub domain to solve the problems compatibility conditions are developed for the conjunction nodes on the interface boundaries of elements in order to connect the elements convergence and comparison studies are carried out to establish the reliability of the solutions the first eight frequency parameters are predicted for various types of thick rectangular plates with mixed edge constraints

new results on the star problem in trace monoids we prove that if it is decidable whether x is recognizable for a recognizable subset x of a free partially commutative monoid then it is decidable whether a recognizable subset of a free partially commutative monoid possesses the finite power property we prove that if any trace of a set x is connected we can decide whether x possesses the finite power property finally we also show that if x is a finite set containing at most four traces or at most two connected traces it is decidable whether x is recognizable

imposition of boundary conditions by modifying the weighting coefficient matrices in the differential quadrature method one of the important issues in the implementation of the differential quadrature method is the imposition of the given boundary conditions there may be multiple boundary conditions involving higher order derivatives at the boundary points the boundary conditions can be imposed by modifying the weighting coefficient matrices directly however the existing method is not robust and is known to have many limitations in this paper a systematic procedure is proposed to construct the modified weighting coefficient matrices to overcome these limitations the given boundary conditions are imposed exactly furthermore it is found that the numerical results depend only on those sampling grid points where the differential quadrature analogous equations of the governing differential equations are established the other sampling grid points with no associated boundary conditions are not essential copyright 2002 john wiley sons ltd

application of generalized differential quadrature method to structural problems summary this paper presents the first endeavour to exploit a generalized differential quadrature method as an accurate efficient and simple numerical technique for structural analysis firstly drawbacks existing in the method of differential quadrature dq are evaluated and discussed then an improved and simpler generalized differential quadrature method gdq is introduced to overcome the existing drawback and to simplify the procedure for determining the weighting coefficients subsequently the generalized differential quadrature is systematically employed to solve problems in structural analysis numerical examples have shown the superb accuracy efficiency convenience and the great potential of this method numerical approximation methods for solving partial differential equations have been widely used in various engineering fields classical techniques such as finite element and finite difference methods are well developed and well known these methods can provide very accurate results by using a large number of grid points however in a large number of cases reasonably approximate solutions are desired at only a few specific points in the physical domain in order to get results even at or around a point of interest with acceptable accuracy conventional finite element and finite difference methods still require the use of a large number of grid points consequently the requirement for computer capacity is often unnecessarily large in such cases in seeking an alternate numerical method using fewer grid points to find results with acceptable accuracy the method of differential quadrature dq was introduced by bellman et a the method of dq is a global approximate method this method is based on the ideas that the derivative of a function with respect to a co ordinate direction can be expressed as a weighted linear sum of all the function values at all mesh points along that direction and that a continuous function can be approximated by a higher order polynomial in the overall domain the dq method differs from the finite element method fem in two aspects firstly the fem uses lower order polynomials to approximate a function on a local element level while the dq method approximates a function on the global area using higher order polynomials secondly the dq method directly approximates the derivatives of a function at a point while the fem approximates a function over a local element and the derivatives can then be derived from the approximate function in this aspect the dq method is more similar to the finite difference method fdm however the fdm is also a local approximation method based on lower order polynomial approximation in fact it can be shown that the fdm is just a special case of the dq method where it is applied locally on the range xi xi l owing to the higher order

thermally induced dynamic instability of laminated composite conical shells abstract thermally induced dynamic instability of laminated composite conical shells is investigated by means of a perturbation method the laminated composite conical shells are subjected to static and periodic thermal loads the linear instability approach is adopted in the present study a set of initial membrane stresses due to the elevated temperature field is assumed to exist just before the instability occurs the formulation begins with three dimensional equations of motion in terms of incremental stresses perturbed from the state of neutral equilibrium after proper nondimensionalization asymptotic expansion and successive integration we obtain recursive sets of differential equations at various levels the method of multiple scales is used to eliminate the secular terms and make an asymptotic expansion feasible using the method of differential quadrature and bolotin s method and imposing the orthonormality and solvability conditions on the present asymptotic formulation we determine the boundary frequencies of dynamic instability regions for various orders in a consistent and hierarchical manner the principal instability regions of cross ply conical shells with simply supported simply supported boundary conditions are studied to demonstrate the performance of the present asymptotic theory

asynchronous automata versus asynchronous cellular automata in this paper we compare and study some properties of two mathematical models of concurrent systems asynchronous automata zielonka 1987 and asynchronous cellular automata zielonka 1989 first we show that these models are polynomially related exhibiting polynomial time reductions between them subsequently we prove that in spite of that the classes of asynchronous automata and of asynchronous cellular automata recognizing a given trace language are in general deeply different in fact we exhibit a recognizable trace language t with the following properties there exists a unique minimum asynchronous automaton accepting t does not exist a unique minimum asynchronous cellular automaton but there are infinitely many minimal i e unreducible nonisomorphic asynchronous cellular automata accepting t we characterize the class of concurrent alphabets for which every recognizable trace language admits a minimum finite state asynchronous cellular automaton as the class of alphabets with full concurrency relation finally extending a result of bruschi et al 1988 we show that for every concurrent alphabet with nontransitive dependency relation there exists a trace language accepted by infinitely many minimal nonisomorphic asynchronous automata

differential quadrature and partial differential equations some numerical results abstract the differential quadrature method is used to solve partial differential equations arising in chemical reactor design the results are compared with the finite difference approach although only 9th order quadrature is used or only 9 grid points are calculated as compared to the calculation of 480 grid points in difference methods a reasonably good accuracy is obtained with differential quadrature

vibration analysis of symmetrically laminated plates based on fsdt using the moving least squares differential quadrature method in this paper we adopt the first order shear deformation theory in the moving least squares differential quadrature mlsdq procedure for predicting the free vibration behavior of moderately thick symmetrically laminated composite plates the transverse deflection and two rotations of the laminate are independently approximated with the moving least squares mls approximation the weighting coefficients used in the mlsdq approximation are obtained through the fast computation of the mls shape functions and their partial derivatives the natural frequencies of vibration are computed for various laminated plates and compared with the available published results through numerical experiments the capability and efficiency of the mlsdq method for eigenvalue problems are demonstrated and the numerical accuracy and convergence are thoughtfully examined effects of the size of support order of completeness of the basis functions and node irregularity on the numerical accuracy are also investigated

linear and geometrically nonlinear bending of isotropic and multilayered composite plates by the natural mode method abstract in the present study we apply the natural mode method and formulate an appropriate linear and geometrically nonlinear theory which is implemented on a model three node multilayered triangular facet element which incorporates the effect of transverse shear deformation and is intended for the nonlinear analysis of large and complex isotropic and composite structures in this context we discuss the derivation of the elastic and geometrical elemental stiffnesses which are based on appropriate kinematic as well as physical idealizations which constitute basic elements of the method of intelligent physical lumping subsequently we present the ariban scheme accumulation of the rigid body and natural modes for geometrically nonlinear analysis it is emphasized that both the triangular facet element and the nonlinear algorithm are developed for the analysis of large and complex structures for which higher order formal finite elements cannot provide answers inexpensivelly in addition the structure of the algorithm and its matrix language are ideally suited for modern parallel computers we conclude our study with numerical examples for isotropic and composite plates all the numerical experiments show the accuracy and potential of the developed methodology for extensive structural engineering computations

application of differential quadrature to static analysis of structural components the numerical technique of differential quadrature for the solution of linear and non linear partial differential equations first introduced by bellman and his associates is applied to the equations governing the deflection and buckling behaviour of one and two dimensional structural components separate transformations are used for higher order derivatives as suggested by mingle thus extending the method to treat fourth order equations and to include multiple boundary conditions in the respective co ordinate directions results are obtained for various boundary and loading conditions and are compared with existing exact and numerical solutions by other methods the application of differential quadrature to this class of problems is seen to lead to accurate results with relatively small computational effort

forced vibrations of functionally graded plates in the three dimensional setting the approach by siu and bert and by leissa that was originally developed for isotropic plates is extended to the problem of forced damped vibrations of functionally graded simply supported rectangular plates in the three dimensional setting contrary to classical normal mode analysis in this study the forced vibration response is determined without prior solving the free vibration problem the solution is obtained by the rayleigh ritz method extended to include the damping term and the work done by the external excitation numerical results are presented for a two phase graded material with a power law variation of the volume fraction of the constituents through the thickness as a byproduct the natural frequencies and the static solution are also determined the dynamic response as well as exact natural frequencies of homogeneous plate are used to assess the accuracy of the present formulation a parametric study with respect to varying volume fraction of the constituents and thickness ratio is conducted the analysis is applied to predict the dynamic response of a functionally graded plate subjected to a harmonically exciting force on its top surface

temperature dependent vibration analysis of functionally graded rectangular plates abstract a theoretical method is developed to investigate vibration characteristics of initially stressed functionally graded rectangular plates made up of metal and ceramic in thermal environment the temperature is assumed to be constant in the plane of the plate and to vary in the thickness direction only two types of thermal condition are considered the first type is that one value of the temperature is imposed on the upper surface and the other or same value on the lower surface the second is that the heat flows from the upper surface to the lower one held at a prescribed temperature material properties are assumed to be temperature dependent and vary continuously through the thickness according to a power law distribution in terms of the volume fraction of the constituents the third order shear deformation plate theory to account for rotary inertia and transverse shear strains is adopted to formulate the theoretical model the rayleigh ritz procedure is applied to obtain the frequency equation the analysis is based on an expansion of the displacements in the double fourier series that satisfy the boundary conditions the effect of material compositions plate geometry and temperature fields on the vibration characteristics is examined the present theoretical results are verified by comparing with those in literature

string matching problems over free partially commutative monoids abstract this paper studies two string matching problems over free partially commutative monoids we analyze these two problems in detail and present two efficient polynomial time algorithms for solving them

three dimensional analysis of transient thermal stresses in functionally graded plates an analytical solution is presented for three dimensional thermomechanical deformations of a simply supported functionally graded fg rectangular plate subjected to time dependent thermal loads on its top and or bottom surfaces material properties are taken to be analytical functions of the thickness coordinate the uncoupled quasi static linear thermoelasticity theory is adopted in which the change in temperature if any due to deformations is neglected a temperature function that identically satisfies thermal boundary conditions at the edges and the laplace transformation technique are used to reduce equations governing the transient heat conduction to an ordinary differential equation ode in the thickness coordinate which is solved by the power series method next the elasticity problem for the simply supported plate for each instantaneous temperature distribution is analyzed by using displacement functions that identically satisfy boundary conditions at the edges the resulting coupled odes with variable coefficients are also solved by the power series method the analytical solution is applicable to a plate of arbitrary thickness results are given for two constituent metal ceramic fg rectangular plates with a power law through the thickness variation of the volume fraction of the constituents the effective elastic moduli at a point are determined by either the mori tanaka or the self consistent scheme the transient temperature displacements and thermal stresses at several critical locations are presented for plates subjected to either time dependent temperature or heat flux prescribed on the top surface results are also given for various volume fractions of the two constituents volume fraction profiles and the two homogenization schemes 2003 elsevier ltd all rights reserved

an exact analytical approach to the free vibration analysis of rectangular plates with mixed boundary conditions abstract a comprehensive analytical technique is developed for the free vibration analysis of rectangular plates with discontinuities along the boundaries for illustrative purposes a solution is obtained for plates with edges partially clamped and partially simply supported and plates with edges partially and partially simply supported a vast array of first mode eigenvalues is provided for these families of plates solutions to the equations are obtained by exploiting a mathematical technique described by the author during an earlier publication it is shown that eigenvalue matrices are easily generated for a wide range of plates with discontinuities in boundary conditions

free vibration of generally supported rectangular kirchhoff plates state space based differential quadrature method the title problem is investigated using the differential quadrature method based on the state space formalism the plates with mixed boundary conditions may cross over one way internal rigid line supports that impose zero transverse displacement constraints differential quadrature procedure is applied in the direction of line supports while exact solution is sought in the transfer domain perpendicular to the line supports using the state space method to avoid numerical instability in the transfer matrix method joint coupling matrices are introduced mainly according to the continuity conditions at line joints natural frequencies of rectangular kirchhoff plates with general boundary conditions are calculated and compared with the results from other methods effects of location of internal line supports and the mixed boundary conditions on the frequency parameters are discussed copyright 2006 john wiley sons ltd

dynamic analysis of a spinning timoshenko beam by the differential quadrature method thedynamiccharacteristicsofaspinningtimoshenkobeamareinvestigatedbyusingthedifferentialquadrature method dqm the beam is subject to any combination of free simply supported clamped and elastically supported boundary conditions the weighting matrices in the differential quadrature formulation are modie ed to incorporate classical boundary conditions of the beam whereas boundary conditions of elastic supports are incorporated into the discretized equations numerical results of the spinning timoshenko beam obtained by the dqm are compared with the exact solutions orresults obtained by the e nite element method the results show the high accuracy and efe ciency of the differential quadrature method nomenclature a cross sectional area of beam c b damping matrix of elastic supports cxx cyy damping coefe cients e young s modulus g shear modulus g gyroscopic matrix i transverse moment of inertia jp polar mass moment of inertia k stiffness matrix k b stiffness matrix of elastic supports kxx kyy spring constants l

maximal serializability of iterated transactions abstract the serializability condition is usually considered in order to maintain the consistency of a database in the presence of conflicting accesses to the database performed by concurrent transactions this serializability condition is considered herein as a general synchronization problem among transactions or processes which can be iterated infinitely often the behaviour of such a system of transactions is represented by an infinite word over the alphabet of the operations performed by the transactions then a characterization of the prefixes of such behaviours is given and it is shown that satisfying the serializability condition so called correct behaviours is given and it is shown that the set of all correct behaviours can be controlled by a finite automaton as an example the classical dining philosophers problem is shown to be entirely modelled and solved as a serializability problem

an adaptive differential quadrature element method for large deformation contact problems involving curved beams with a finite number of contact points abstract contact problems involving large deformation of curved beams are difficult to analyze due to uncertainty of contact positions and strong nonlinearity a nonlinear large deformation model of curved beams is formulated in arc length coordinates a new adaptive differential quadrature element method adqem is proposed to predict contact positions of a curved beam with a finite number of contact points where a dragging method and continuity conditions are combined to determine the contact positions simulation results show that the adqem greatly improves efficiency and accuracy of the large deformation contact problem of the curved beam the number of iterations in the present method does not greatly increase with the number of contact points