semi analytical solution for three dimensional transient response of functionally graded annular plate on a two parameter viscoelastic foundation abstract the three dimensional transient analysis of functionally graded annular plates with arbitrary boundary conditions is carried out in this paper the material properties of the fgm plate are assumed to vary smoothly in an exponential law along the thickness direction the plate is assumed to rest on a two parameter viscoelastic foundation a semi analytical method which integrates the state space method ssm laplace transform and its inversion as well as the one dimensional differential quadrature method dqm is proposed to obtain the transient response of the plate the state space method is used to obtain the analytical solution in the thickness direction the differential quadrature method is employed to approximate the solution in the radial direction the laplace transform and the numerical inversion are used to obtain the solution in time domain numerical results show a good agreement between the response histories obtained by the present method and finite element method the effects of the boundary conditions at the edges the material graded index the winkler and shearing layer elastic coefficients and the damping coefficient are studied numerical examples show that the peak response decreases as the material graded index the winkler and shearing layer elastic coefficients and the damping coefficient increase the results obtained in this paper can serve as benchmark data in further research

three dimensional exact solution for the vibration of functionally graded rectangular plates abstract a three dimensional exact solution is presented for free and forced vibrations of simply supported functionally graded rectangular plates suitable displacement functions that identically satisfy boundary conditions are used to reduce equations governing steady state vibrations of a plate to a set of coupled ordinary differential equations which are then solved by employing the power series method the exact solution is valid for thick and thin plates and for arbitrary variation of material properties in the thickness direction results are presented for two constituent metal ceramic functionally graded rectangular plates that have a power law through the thickness variation of the volume fractions of the constituents the effective material properties at a point are estimated by either the mori tanaka or the self consistent schemes exact natural frequencies displacements and stresses are used to assess the accuracy of the classical plate theory the first order shear deformation theory and a third order shear deformation theory for functionally graded plates parametric studies are performed for varying ceramic volume fractions volume fraction profiles and length to thickness ratios results are also computed for a functionally graded plate that has a varying microstructure in the thickness direction using a combination of the mori tanaka and the self consistent methods forced vibrations of a plate with a sinusoidal spatial variation of the pressure applied on its top surface are scrutinized

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

three dimensional vibrations of thick circular and annular plates abstract the ritz method is applied in a three dimensional 3 d analysis to obtain accurate frequencies for thick circular and annular plates the method is formulated in a manner which allows one to have any combination of free or fixed plate boundaries admissible functions for the three displacement components are chosen as trigonometric functions in the circumferential co ordinate and algebraic polynomials in the radial and axial co ordinates upper bound convergence of the non dimensional frequencies to at least four significant figures is demonstrated comparisons of results are made with ones obtained by others using 2 d mindlin thick plate theory and with other 3 d solutions extensive and accurate four significant figure frequencies are presented for completely free circular plates having thickness to diameter ratios of 0 2 0 3 0 4 and 0 5 for poisson s ratios 0 0 3 and 0 499 frequencies are also given for thick annular plates having a thickness to outer diameter of 0 2 inside to outside diameter ratios of 0 1 0 5 and 0 9 and 0 3 all 3 d modes are included in the analyses e g flexural thickness shear in plane stretching and torsional the circular and annular plate frequency data given is exact to at least four digits thus being benchmark data against which results from 2 d thick plate theories or other approximate methods e g finite elements may be compared

three dimensional vibration analysis of circular and annular plates via the chebyshev ritz method abstract a three dimensional free vibration analysis of circular and annular plates is presented via the chebyshev ritz method the solution procedure is based on the linear small strain three dimensional elasticity theory selecting chebyshev polynomials which can be expressed in terms of cosine functions as the admissible functions a convenient governing eigenvalue equation can be derived through the ritz method according to the geometric properties of circular and annular plates the vibration is divided into three distinct categories axisymmetric vibration torsional vibration and circumferential vibration each vibration category can be further subdivided into the antisymmetric and symmetric ones in the thickness direction convergence and comparison study demonstrated the high accuracy and efficiency of the present method the present approach shows a distinct advantage over some other ritz solutions in that stable numerical operation can be guaranteed even when a large number of admissible functions is employed therefore not only lower order but also higher order eigenfrequencies can be obtained by using sufficient terms of the chebyshev polynomials finally some valuable results for annular plates with one or both edges clamped are given and discussed in detail

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

three dimensional vibration analysis of cantilevered and completely free isosceles triangular plates the free vibration of cantilevered and completely free isosceles triangular plates based on exact three dimensional elasticity theory is investigated the actual plate domain is first mapped onto a basic cubic domain then the ritz method is applied to derive the eigenfrequency equation from the strain energy and the kinetic energy of the plate a set of chebyshev polynomial series multiplied by a boundary function chosen to satisfy the essential geometry boundary conditions of the plate is developed as the admissible functions of each displacement component the convergence and comparison studies show that rather accurate results can be obtained by using this approach the effects of thickness to width ratio and apex angle on eigenfrequencies of the plates are studied in detail sets of valuable results are presented which may serve as the benchmark values for future numerical techniques in thick plate vibration analysis data for the completely free isosceles triangular plates are presented for the first time

structural properties of the one dimensional drift diffusion models for semiconductors this paper is devoted to the analysis of the one dimensional current and voltage drift diffusion models for arbitrary types of semiconductor devices and under the assumption of vanishing generation recombination we show in the course of this paper that these models satisfy structural properties which are due to the particular form of the coupling of the involved systems these structural properties allow us to prove an existence and uniqueness result for the solutions of the current driven model together with monotonicity properties with respect to the total current i of the electron and hole current densities and of the electric field at the contacts we also prove analytic dependence of the solutions on i these results allow us to establish several qualitative properties of the current voltage characteristic in particular we give the nature of the possible bifurcation points of this curve we show that the voltage function is an analytic function of the total current and we characterize the asymptotic behavior of the currents for large voltages as a consequence we show that the currents never saturate as the voltage goes to 00 contrary to what was predicted by numerical simulations by m s mock compel 1 1982 pp 165 174 we also analyze the drift diffusion models under the assumption of quasi neutral approximation we show in particular that the reduced current driven model has at most one solution but that it does not always have a solution then we compare the full and the reduced voltage driven models and we show that in general the quasi neutral approximation is not accurate for large voltages even if no saturation phenomenon occurs finally we prove a local existence and uniqueness result for the current driven model in the case of small generation recombination terms

qualitative properties of steady state poisson nernst planck systems mathematical study we examine qualitative properties of solutions of self consistent poisson nernst planck systems including uniqueness in the case of vanishing permanent charge the predominant case studied our results unveil a rich structure inherent in these systems one that is determined by the boundary conditions and the signs of the oppositely charged carrier fluxes a particularly significant special case that of simple boundary conditions is shown to lead to uniqueness and to a complete characterization this case underlies the more complicated cases studied later a contraction mapping principle is included for completeness and allows for an arbitrary permanent charge distribution

in plane free vibration of functionally graded circular arches with temperature dependent properties under thermal environment analysis of in plane free vibration of functionally graded fg thin to moderately thick deep circular arches in thermal environments is presented based on first order shear deformation theory fsdt the material properties are assumed to be temperature dependent and graded in the thickness direction hamilton s principle is employed to derive the equations of motion and the related boundary conditions including the effects of initial thermal stresses the temperature is assumed to be uniform through the arch surface and varied through the thickness the initial thermal stresses are obtained by solving the thermoelastic equilibrium equations the differential quadrature method dqm as an efficient numerical tool is adopted to solve the thermoelastic equilibrium equations and the equations of motion the numerical solutions are validated by comparing to the solutions of the limited cases for isotropic arches as well as by examining the solutions convergence behavior parametric studies are also conducted to study the effects of the temperature rise boundary conditions and the material graded index on the frequency of the fg arches also the impact of geometrical parameters such as the thickness to mean radius ratio and the opening angle are examined

3 d free vibration analysis of annular plates on pasternak elastic foundation via p ritz method in this study a three dimensional 3 d free vibration analysis of thick annular plates resting on elastic foundation with different combinations of free soft simply supported hard simply supported and clamped boundary conditions at the inner and outer edges of the annular plate is presented on the basis of the polynomials ritz method the elastic foundation is considered as a pasternak model with adding a shear layer to the winkler model the analysis procedure is based on the linear small strain and 3 d elasticity theory in this analysis method a set of orthogonal polynomial series in cylindrical polar coordinate is used to extract eigenvalue equation yielding the natural frequencies and mode shapes for the annular plates the accuracy of these results is verified by appropriate convergence studies and checked with the available literature finite element method fem analysis and the mindlin theory furthermore the effect of the foundation stiffness parameters thickness radius ratio inner outer radius ratio and different combinations of boundary conditions on the ill conditioning of the mass matrix as well as on the vibration behavior of the annular plates is investigated finally the validity and the range of applicability of the results obtained on the basis of the mindlin and classical plate theories for a thin and moderately thick annular plate with different values of the winkler foundation stiffness are graphically presented through comparing them with those obtained by the present 3 d p ritz solution

nonlinear free vibration behavior of functionally graded plates in this paper an analytical solution is provided for the nonlinear free vibration behavior of plates made of functionally graded materials the material properties of the functionally graded plates are assumed to vary continuously through the thickness according to a power law distribution of the volume fraction of the constituents the fundamental equations for thin rectangular plates of functionally graded materials are obtained using the von karman theory for large transverse deflection and the solution is obtained in terms of mixed fourier series the effect of material properties boundary conditions and thermal loading on the dynamic behavior of the plates is determined and discussed the results reveal that nonlinear coupling effects play a major role in dictating the fundamental frequency of functionally graded plates

exact closed form frequency equations for thick circular plates using a third order shear deformation theory abstract this paper presents for the first time exact closed form frequency equations and transverse displacement for thick circular plates with free soft simply supported hard simply supported and clamped boundary conditions based on reddy s third order shear deformation theory hamiltonian and minimum potential energy principles are used to extract the equations of dynamic equilibrium and natural boundary conditions of the plate the new formulation is verified by comparing the results with their counterparts reported in open literature natural frequencies of circular plates with different boundary conditions are tabulated in dimensionless form for various values of thickness radius ratios the results presented on the basis of exact closed form frequency equations are expected to serve as reliable benchmarks

three dimensional vibration analysis of a torus with circular cross section the free vibration characteristics of a torus with a circular cross section are studied by using the three dimensional small strain elasticity theory a set of three dimensional orthogonal coordinates system comprising the polar coordinate r at each circular cross section and the circumferential coordinate around the ring is developed each of the displacement components ur and w in the r and directions respectively is taken as a product of the chebyshev polynomials in the r direction and the trigonometric functions in the and directions eigenfrequencies and vibration mode shapes have been obtained via a three dimensional displacement based extremum energy principle upper bound convergence of the first seven eigenfrequencies accurate to at least six significant figures is obtained by using only a few terms of the admissible functions the eigenfrequency responses due to variation of the ratio of the radius of the ring centroidal axis to the cross sectional radius are investig

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

stability and accuracy of differential quadrature method in solving dynamic problems in this paper the differential quadrature method is used to solve dynamic problems governed by second order ordinary differential equations in time the legendre radau chebyshev chebyshev gauss lobatto and uniformly spaced sampling grid points are considered besides two approaches using the conventional and modified differential quadrature rules to impose the initial conditions are also investigated the stability and accuracy properties are studied by evaluating the spectral radii and truncation errors of the resultant numerical amplification matrices it is found that higher order accurate solutions can be obtained at the end of a time step if the gauss and radau sampling grid points are used however the conventional approach to impose the initial conditions in general only gives conditionally stable time step integration algorithms unconditionally stable algorithms can be obtained if the modified differential quadrature rule is used unfortunately the commonly used chebyshev gauss lobatto sampling grid points would not generate unconditionally stable algorithms

axisymmetric straining modes in the vibration of circular plates axisymmetric straining modes which are different from the axisymmetric flexural modes of vibrating circular plates and cannot be revealed by conventional plate theory based approaches are investigated in the present study mode shapes of an example problem with clamped and four different simply supported boundary conditions are presented to show what straining modes may look like the straining modes are classified into three types and a criterion is set up to predict the appearance of straining modes some observations about straining modes are obtained and discussions are made results for different poisson ratios are also shown

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

thermo elastic analysis of functionally graded circular plates resting on a gradient hybrid foundation extracting the new differential equation for gradient hybrid foundation analysis of thermo elastic behavior of fg circular plates on gradient hybrid foundation for the first time investigating the effects of the plate material gradient indices foundation parameters on thermo elastic behavior of fg circular plates deriving the state equations of the problem based on the 3d theory of thermo elasticity presenting a semi analytical solution for the problem state space method and 1d differential quadrature rule in this paper an attempt is made to investigate the thermo elastic behavior of functionally graded fg circular plates embedded on gradient hybrid foundation and subjected to non uniform asymmetric mechanical and uniform thermal loads the supporting medium is modeled as the horvath colasanti type foundation with variable coefficients in the radial and circumferential directions the thermal environment is assumed to be uniform over the bottom and top surfaces of the plate and varies along the thickness direction only the governing state equations are extracted in terms of displacements and temperature based on 3d theory of thermo elasticity and assuming the material properties of the plate except the poisson s ratio vary continuously throughout the thickness direction according to an exponential function these equations are solved using a semi analytical method and some numerical results are displayed to clarify the effects of material heterogeneity indices foundation stiffness coefficients foundation gradient indices loads ratio and temperature difference between the upper and lower surfaces of the plate on displacement and stress fields the results are reported for the first time and the new results can be used as a benchmark for researchers to validate their numerical and analytical methods in the future

fuzzy weighted averages and implementation of the extension principle abstract this paper addresses the computational aspect of the extension principle when the principle is applied to algebraic mappings and in particular to weighted average operations in risk and decision analysis a computational algorithm based on the cut representation of fuzzy sets and interval analysis is described the method provides a discrete but exact solution to extended algebraic operations in a very efficient and simple manner examples are given to illustrate the method and its relation to other discrete methods and the exact approach by non linear programming the algorithm has been implemented in a computer program which can handle very general extended algebraic operations on fuzzy numbers

alternative state space formulations for magnetoelectric thermoelasticity with transverse isotropy and the application to bending analysis of nonhomogeneous plates abstract by introducing two displacement functions and two stress functions the governing equations of the linear theory of magneto electro thermo elasticity with transverse isotropy are simplified on selecting certain physical quantities as the basic unknowns two new state equations are established each of them is order reduced when compared with the one reported recently in literature leading to a higher numerical efficiency the material inhomogeneity along the axis of symmetry z direction can be taken into account and an approximate laminate model is employed to facilitate deriving analytical solutions the validity of new formulations is examined by considering a laminated magneto electro elastic rectangular plate and good agreement is obtained with existent results a plate with a functionally graded property is then analyzed the effect of magnetoelectric coupling in a batio3 cofe2o4 composite predicted from the micromechanics simulation is studied quantitatively

three dimensional vibration analysis of thick rectangular plates using chebyshev polynomial and ritz method this paper describes a method for free vibration analysis of rectangular plates with any thicknesses which range from thin moderately thick to very thick plates it utilises admissible functions comprising the chebyshev polynomials multiplied by a boundary function the analysis is based on a linear small strain three dimensional elasticity theory the proposed technique yields very accurate natural frequencies and mode shapes of rectangular plates with arbitrary boundary conditions a very simple and general programme has been compiled for the purpose for a plate with geometric symmetry the vibration modes can be classified into symmetric and antisymmetric ones in that direction in such a case the computational cost can be greatly reduced while maintaining the same level of accuracy convergence studies and comparison have been carried out taking square plates with four simply supported edges as examples it is shown that the present method enables rapid convergence stable numerical operation and very high computational accuracy parametric investigations on the vibration behaviour of rectangular plates with four clamped edges have also been performed in detail with respect to different thickness side ratios aspect ratios and poissons ratios these results may serve as benchmark solutions for validating approximate two dimensional theories and new computational techniques in future 2002 elsevier science ltd all rights reserved

three dimensional vibration analysis of rectangular thick plates on pasternak foundation the free vibration characteristics of rectangular thick plates resting on elastic foundations have been studied based on the three dimensional linear and small strain elasticity theory the foundation is described by the pasternak two parameter model the ritz method is used to derive the eigenvalue equation of the rectangular plate by augmenting the strain energy of the plate with the potential energy of the elastic foundation the chebyshev polynomials multiplied by a boundary function are selected as the admissible functions of the displacement functions in each direction the approach is suitable for rectangular plates with arbitrary boundary conditions convergence and comparison studies have been performed on square plates on elastic foundations with different boundary conditions it is shown that the present method has a rapid convergent rate stable numerical operation and very high accuracy parametric investigations on the dynamic behaviour of clamped square thick plates on elastic foundations have been carried out in detail with respect to different thickness span ratios and foundation parameters some results found for the first time have been given and some important conclusions have been drawn

on the existence of multiple steady state solutions in the theory of electrodiffusion part i the nonelectroneutral case part ii a constructive method for the electroneutral case

free vibration analyses of thin sector plates by the new version of differential quadrature method abstract the new version of differential quadrature dq method is extended to analyze the free vibration of thin sector plates with various sector angles and six combinations of boundary conditions detailed formulations are given various numerical examples are studied comparisons are made with existing analytical and or numerical data numerical results indicate that convergence can be achieved with increasing in number of grid points and accurate results could be obtained with 9 9 gird or even higher grid by using the extended dq method for the cases considered

free vibration studies of simply supported non homogeneous functionally graded magneto electro elastic finite cylindrical shells in this article free vibration studies on functionally graded materials fgm magneto electro elastic cylindrical shells have been carried out a series solution is assumed in circumferential and axial direction such that the three dimensional character of the solution is preserved the finite element model is derived based on constitutive equation of magneto electro elastic material accounting for coupling between elasticity electric and magnetic effect frequency behavior with the variation of power law index is analyzed and explained on the basis of constitutive material one of the aims of the study is to evaluate the influence of magnetic and piezoelectric effect on the structural frequency in addition influence of length to radius ratio and radius to thickness ratio on the frequency behaviour of such shells have been attempted

free vibration of circular and annular plates with variable thickness and different combinations of boundary conditions in this paper the first nine frequency parameters of circular and annular plates with variable thickness and combined boundary conditions are computed for different thickness to radius ratios several combined boundary conditions are considered for inner and outer edges these are free soft and hard simply supported and clamped boundary conditions three dimensional elasticity theory is used results of this paper are compared with works of other authors and the results of finite element method analysis which are in agreement data for thick circular and annular plates with linear and parabolic thickness variation and different combinations are presented for the first time

a radial basis function approach for the free vibration analysis of functionally graded plates using a refined theory abstract the free vibration analysis of functionally graded plates is performed by the multiquadric radial basis function method and a higher order shear deformation theory the multiquadric method is a truly meshless method allowing a fast and simple domain and boundary discretization we use an homogenization technique for material properties based on the mori tanaka scheme numerical tests show that the method is reliable and produces good results

three dimensional elasticity solutions for free vibrations of circular plates a polynomials ritz analysis this paper presents accurate three dimensional elasticity solutions for free vibration of circular plates the derivation of a linear frequency equation based on an exact three dimensional small strain linearly elastic principle is detailed the solution to this problem is made possible by using the ritz method with a set of orthogonal polynomial series to approximate the spatial displacements of the circular plate in cylindrical polar coordinates the perturbation of frequency responses due to the variations of boundary conditions and thickness is investigated first known frequency parameters and three dimensional deformed mode shapes are presented in vivid graphical forms the accuracy of these results are verified by appropriate convergence studies and when possible are checked with existing solutions

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

a bifurcation analysis of the one dimensional steady state semiconductor device equations this paper considers the one dimensional steady state semiconductor device equations modeling a thyristor these equations can be considered as a singularly perturbed boundary value problem the reduced problem is considered in order to derive an approximation to the current voltage curve a bifurcation equation is obtained that completely determines the qualitative structure of the current voltage characteristic a numeric example shows that the developed theory applies to data of realistic magnitude

on free vibration of non homogeneous transversely isotropic magneto electro elastic plates two independent state equations are established for transversely isotropic magneto electro elastic media by introducing proper stress and displacement functions the free vibration problem of simply supported rectangular plates with general inhomogeneous functionally graded material properties along the thickness direction is then considered an approximate laminate model is employed to transform the state equations with variable coefficients to the ones with constant coefficients two different classes of vibrations are found in particular the frequency of the first class is only related to the elastic property of the plate while that of the second class is affected by the couplings among the elastic electric and magnetic fields numerical results are presented and some important issues are discussed

multiple steady states in one dimensional electrodiffusion with local electroneutrality this paper concerns itself with construction and study of multiple steady states occurring in one dimensional ambipolar electrodiffusion with local electroneutrality constant and equal charge carrier mobilities in the absence of generation recombination piecewise constant fixed change density with four sign alterations is assumed multiple solution branches are constructed via a numerical and asymptotic solution of a system of nonlinear equations resulting from an explicit integration of the appropriate boundary value problem the parameter range in which multiplicity occurs is determined with the aid of asymptotic procedures existence of the appropriate multiple solutions follows from the newton kantorovich theorem

finite element analysis of three dimensional vibrations of thick circular and annular plates abstract three dimensional vibrations of thick circular and annular plates are analyzed by a finite element method which with a properly assumed set of displacement field is different from the traditional 3 d finite element analysis and is reduced to a sequence of 2 d analyses one for each circumferential wave number the present approach has several unique features 1 it can obtain vibration frequencies which are comparable to or as accurate as those by other three dimensional approaches whenever comparisons between them are possible and yet the formulation of the present method is simpler and its application is straightforward 2 different simply supported boundary conditions can be exactly imposed with the present approach the latter feature may be quite difficult if not impossible for other methods in the present analysis vibration frequencies of a circular and an annular plate under different combinations of boundary conditions wave numbers and finite element meshes are calculated vibration characteristics are examined and some typical mode shapes are shown graphically then the results of some example problems by the present method are compared to those available in the literature to show its validity and accuracy

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

studies on dynamic behavior of functionally graded cylindrical shells with pzt layers under moving loads based on the first order shear deformation theory fsdt the hamilton s principle and the maxwell equation this paper presents the coupling equations to govern the electric potential and the displacements of the functionally graded cylindrical shell with surface bonded pzt piezoelectric layer and subjected to moving loads the frequencies equations are obtained by using displacement functions and one electric potential function the modal analysis technique and newmark s integration method are used to calculate the displacements and sensory electric potential of the shell subjected to moving loads the effects of the moving velocities of the loads volume fraction exponents of functionally graded materials fgms and temperature environment on the dynamic responses of shells are investigated an analytical approximate equation is obtained to describe the relationship between critical velocities of moving loads and natural frequencies of shells the present approach is validated by comparing the natural frequencies with the result presented by ng et al in addition numerical results show the relationship between the displacements and sensory electric potential of the shell the present work shows that some meaningful and interesting results presented in this paper are helpful for the application and the design of smart sensory structures

rapid analysis of variable stiffness beams and plates legendre polynomial triple product formulation copyright 2017 john wiley sons ltd numerical integration techniques are commonly employed to formulate the system matrices encountered in the analysis of variable stiffness beams and plates using a ritz based approach computing these integrals accurately is often computationally costly herein a novel alternative is presented the recursive analytical polynomial integral definition rapid formulation the rapid formulation offers a significant improvement in the speed of analysis achieved by reducing the number of numerical integrations that are performed by an order of magnitude a common legendre polynomial basis is employed for both trial functions and stiffness load variations leading to a common form for the integrals encountered the legendre polynomial basis possesses algebraic recursion relations that allow these integrals to be reformulated as triple products with known analytical solutions defined compactly using the wigner 3j coefficient the satisfaction of boundary conditions calculation of derivatives and transformation to other bases is achieved through combinations of matrix multiplication with each matrix representing a unique boundary condition or physical effect therefore permitting application of the rapid approach to a variety of problems indicative performance studies demonstrate the advantage of the rapid formulation when compared to direct analysis using matlab s integral and integral2 copyright 2017 john wiley sons ltd

axisymmetric dynamic response of a circular plate on an elastic foundation circulate plates on elastic foundations are used in footings and raft foundations of various structures in addition tubesheets used in various shell and tube type heat exchangers can be modelled as circular plates on elastic foundations this paper presents an analysis and numerical results for the axisymmetric free and forced vibration of a circular plate on an elastic foundation

3 d vibration analysis of generalized super elliptical plates using chebyshev ritz method the three dimensional free vibration of generalized super elliptical plates is analysed based on the exact small strain and linear elasticity theory the ritz method is applied to derive the frequency equation the triplicate chebyshev polynomial series form the backbones of the admissible functions as modified by a characteristic boundary function to ensure the satisfaction of geometric boundary conditions of the plate utilizing the symmetry of the plate under consideration eight distinct vibration modes can be classified and individually solved while maintaining the same level of accuracy the accuracy of the present method has been examined by the convergence and comparison studies the effect of geometric parameters on vibration behaviour of the generalized super elliptical plates with free and fixed perimeters have been studied for different powers thickness ratios and aspect ratios

perceptual reasoning for perceptual computing in 1996 zadeh proposed the paradigm of computing with words cww a specific architecture for making subjective judgments using cww was proposed by mendel in 2001 it is called a perceptual computer per c and because words can mean different things to different people it uses interval type 2 fuzzy set it2 fs models for all words the per c has three elements the encoder which transforms linguistic perceptions into it2 fss that activate a cww engine the decoder which maps the output of a cww engine back into a word and the cww engine although di fferent kinds of cww engines are possible this paper only focuses on cww engines that are rule based and the computations that map its input it2 fss into its output it2 fs five assumptions are made for a rule based cww engine the most important of which is the result of combining fired rules must lead to a footprint of uncertainty fou that resembles the three kinds of fou that have previously been shown to model words interior left shoulder and right shoulder fous requiring this means that the output fou from a rule based cww engine will look similar in shape to an fou in a codebook i e a vocabulary of words and their respective fous for an application so that the decoder can therefore sensibly establish the word most similar to the cww engine output fou because existing approximate reasoning methods do not satisfy this assumption a new kind of rule based cww engine is proposed one that is called perceptual reasoning and is proved to always satisfy this assumption additionally because all it2 fss in the rules as well as those that excite the rules are either an interior left shoulder or right shoulder fou it is possible to carry out the sup min calculations that are required by the inference engine and those calculations are also in this paper the results in this paper let us implement a rule based cww engine for the per c

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

a reconstruction decoder for computing with words the word decoder is a very important approach for decoding in the perceptual computer it maps the computing with words cwws engine output which is a fuzzy set into a word in a codebook so that it can be understood however the word decoder suffers from significant information loss i e the fuzzy set model of the mapped word may be quite different from the fuzzy set output by the cww engine especially when the codebook is small in this paper we propose a reconstruction decoder which represents the cww engine output as a combination of two successive codebook words with minimum information loss by solving a constrained optimization problem the reconstruction decoder preserves the shape information of the cww engine output in a simple form without sacrificing much accuracy it can be viewed as a generalized word decoder and is also implicitly a rank decoder moreover it is equivalent to the 2 tuple representation under certain conditions the effectiveness of the reconstruction decoder is verified by three experiments

semi analytical analysis for multi directional functionally graded plates 3 d elasticity solutions semi analytical 3 d elasticity solutions are presented for orthotropic multi directional functionally graded plates using the differential quadrature method dqm based on the state space formalism material properties are assumed to vary not only through the thickness but also in the in plane directions following an exponential law the graded in plane domain is solved numerically via the dqm while exact solutions are sought for the thickness domain using the state space method convergence studies are performed and the present hybrid semi analytical method is validated by comparing numerical results with the exact solutions for a conventional unidirectional functionally graded plate finally effects of material gradient indices on the displacement and stress fields of the plates are investigated and discussed copyright 2009 john wiley sons ltd

three dimensional vibration analysis of functionally graded material sandwich plates abstract free vibration of functionally graded material sandwich rectangular plates with simply supported and clamped edges is studied based on the three dimensional linear theory of elasticity two common types of fgm sandwich plates namely the sandwich with fgm facesheet and homogeneous core and the sandwich with homogeneous facesheet and fgm core 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 rapid convergence is observed in this study the natural frequencies of simply supported power law fgm sandwich plates are compared with results from different two dimensional plate theories parametric study is performed for varying volume fraction layer thickness ratios thickness length ratios and aspect ratios of the sandwich plates

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

aggregation using the linguistic weighted average and interval type 2 fuzzy sets the focus of this paper is the linguistic weighted average lwa where the weights are always words modeled as interval type 2 fuzzy sets it2 fss and the attributes may also but do not have to be words modeled as it2 fss consequently the output of the lwa is an it2 fs the lwa can be viewed as a generalization of the fuzzy weighted average fwa where the type 1 fuzzy inputs are replaced by it2 fss this paper presents the theory algorithms and an application of the lwa it is shown that finding the lwa can be decomposed into finding two fwas since the lwa can model more uncertainties it should have wide applications in distributed and hierarchical decision making

dynamic stability analysis of functionally graded cylindrical shells under periodic axial loading abstract in this paper a formulation for the dynamic stability analysis of functionally graded shells under harmonic axial loading is presented a profile for the volume fraction is assumed and a normal mode expansion of the equations of motion yields a system of mathieu hill equations the stability of which is analyzed by the bolotin s method the present study examines the effects of the volume fraction of the material constituents and their distribution on the parametric response in particular the positions and sizes of the instability regions

elasticity solutions for free vibrations of annular plates from three dimensional analysis abstract this article examines the vibrational characteristics of annular plates by using the three dimensional elasticity theory it aims to raise the quality of the investigation beyond that provided by the two dimensional plate theories by resorting to a full three dimensional analysis a polynomials ritz model based on sets of orthogonally generated polynomial functions to approximate the spatial displacements of the plates in cylindrical polar coordinates is presented the model is then used to extract the full vibration spectrum of natural frequencies and mode shapes the vibration responses due to the variations of boundary conditions and thickness are investigated frequency parameters and three dimensional deformed mode shapes are presented in vivid graphical forms the accuracy of the method is validated through appropriate convergence and comparison studies

natural vibration of circular and annular thin plates by hamiltonian approach abstract the present paper deals with the natural vibration of thin circular and annular plates using hamiltonian approach it is based on the conservation principle of mixed energy and is constructed in a new symplectic space a set of hamiltonian dual equations with derivatives with respect to the radial coordinate on one side of the equations and to the angular coordinate on the other side are obtained by using the variational principle of mixed energy the separation of variables is employed to solve hamiltonian dual equations of eigenvalue problem analytical frequency equations are obtained based on different cases of boundary conditions the natural frequencies are the roots of the frequency equations and corresponding mode functions are in terms of the dual variables q1 r three basic edge constraint cases for circular plates and nine edge constraint cases for annular plates are calculated and the results are compared well with existing ones

semi analytical solution for three dimensional vibration of functionally graded circular plates based on the three dimensional theory of elasticity and assuming that the mechanical properties of the materials vary continuously in the thickness direction and have the same exponent law variations the three dimensional free and forced vibration analysis of functionally graded circular plate with various boundary conditions is achieved in this paper a semi analytical method which makes use of the state space method and the one dimensional differential quadrature method is used to obtain the vibration frequencies and dynamic responses of circular plates the analytical solution in the thickness direction can be acquired using the state space method and approximate solution in the radial direction can be obtained using the one dimensional differential quadrature method numerical results are given to demonstrate the accuracy and superiority of the presented method the influences of the material property graded index the circumferential wave number and the forced frequencies on the dynamic behavior for different functionally graded circular plates are also studied

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

a higher order shear deformation theory for the vibration of thick plates abstract several first order shear deformation theories for thick plates have been formulated during the past half century e g by reissner hencky mindlin and ambartsumyan the mindlin theory has been widely used for vibration analysis it is well known that consideration of shear flexibility corrects the flexural frequencies by reducing them however it has been found that first order shear deformation theories result in over correction in the present work a higher order theory is presented which provides additional freedom to the displacements through the plate thickness and essentially eliminates the over correction a complete theory is developed including energy functionals equations of motion and boundary conditions comparisons of frequencies arising from classical thin plate theory mindlin theory and the present theory are made for completely free rectangular plates of moderate and large thickness completely free boundaries rather than simply supported ones are chosen because they are more consistent with physical models in the theories used

free vibration analysis of functionally graded conical cylindrical shell and annular plate structures with a four parameter power law distribution based on the first order shear deformation theory fsdt this paper focuses on the dynamic behavior of moderately thick functionally graded conical cylindrical shells and annular plates the last two structures are obtained as special cases of the conical shell formulation the treatment is developed within the theory of linear elasticity when materials are assumed to be isotropic and inhomogeneous through the thickness direction the two constituent functionally graded shell consists of ceramic and metal these constituents are graded through the thickness from one surface of the shell to the other a generalization of the power law distribution presented in literature is proposed two different four parameter power law distributions are considered for the ceramic volume fraction some material profiles through the functionally graded shell thickness are illustrated by varying the four parameters of power law distributions for the first power law distribution the bottom surface of the structure is ceramic rich whereas the top surface can be metal rich ceramic rich or made of a mixture of the two constituents and on the contrary for the second one symmetric and asymmetric volume fraction profiles are presented in this paper the homogeneous isotropic material can be inferred as a special case of functionally graded materials fgm the governing equations of motion are expressed as functions of five kinematic parameters by using the constitutive and kinematic relationships the solution is given in terms of generalized displacement components of the points lying on the middle surface of the shell the discretization of the system equations by means of the generalized differential quadrature gdq method leads to a standard linear eigenvalue problem where two independent variables are involved without using the fourier modal expansion methodology numerical results concerning six types of shell structures illustrate the influence of the power law exponent of the power law distribution and of the choice of the four parameters on the mechanical behaviour of shell structures considered

perceptual reasoning for perceptual computing a similarity based approach perceptual reasoning pr is an approximate reasoning method that can be used as a computing with words cww engine in perceptual computing there can be different approaches to implement pr e g firing interval based pr fi pr which has been proposed in j m mendel and d wu ieee trans fuzzy syst vol 16 no 6 pp 1550 1564 dec 2008 and similarity based pr s pr which is proposed in this paper both approaches satisfy the requirement on a cww engine that the result of combining fired rules should lead to a footprint of uncertainty fou that resembles the three kinds of fous in a cww codebook a comparative study shows that s pr leads to output fous that resemble word fous which are obtained from subject data much more closely than fi pr hence s pr is a better choice for a cww engine than fi pr

novel weighted averages versus normalized sums in computing with words in this paper some properties of novel weighted averages that are related to the concepts of possibility theory are examined it is shown that novel weighted averages have certain interpretations in terms of addition of interactive interval or fuzzy constraints to do this alternative forms of novel weighted averages are provided in particular an alternative form of novel weighted averages represented by the extension principle is determined it is shown that when fuzzy set models of words are obtained by collecting data from subjects in a computing with words setting interactive addition of fuzzy sets is not a well defined method and the optimization problems related to it may have no solutions although interactive addition is recommended in the literature for solving multicriteria decision making problems and for dealing with uncertain probabilities on the other hand novel weighted averages perform a specific normalization that guarantees that they always exist

on computing normalized interval type 2 fuzzy sets this paper explains how to compute normalized interval type 2 fuzzy sets in closed form and explains how the results reduce to well known results for type 1 fuzzy sets and interval sets such normalized interval type 2 fuzzy sets may be needed in linguistic probability computa tions or multiple criteria decision analysis under uncertainty index terms fuzzy weighted average fwa interval type 2 fuzzy sets it2 fss interval weighted average iwa linguistic probability linguistic weighted average lwa normalized interval type 2 fuzzy sets

three dimensional free vibration of thick circular plates on pasternak foundation abstract this paper describes a study of the three dimensional vibration characteristics of thick circular plates resting on elastic foundation the analysis is based on the three dimensional small strain linear and exact elasticity theory the foundation is described by the pasternak model the ritz method is used to derive the frequency equation of the plate foundation system by augmenting the strain energy of the plate with the elastic potential energy of the foundation a set of chebyshev polynomials multiplied by a boundary function is adopted as the admissible functions of the displacement components in each direction for plates with free edges the effect of foundation medium beyond the edge of the plate has been considered by introducing the generalized shearing force concept in the analysis the convergence and comparison studies demonstrate the correctness and accuracy of the present method it is shown that the present method has rapid convergent rate stable numerical operation and very high accuracy parametric investigations on the dynamic behavior of thick circular plates resting on elastic foundation have been carried out with respect to various thickness radius ratios foundation stiffness parameters and boundary conditions results known for the first time have been reported and discussed in detail some significant conclusions have been drawn

closed form solution for free vibration of piezoelectric coupled annular plates using levinson plate theory abstract free vibration analysis of annular moderately thick plates integrated with piezoelectric layers is investigated in this study for different combinations of soft simply supported hard simply supported and clamped boundary conditions at the inner and outer edges of the annular plate on the basis of the levinson plate theory lpt the distribution of electric potential along the thickness direction in the piezoelectric layer is assumed as a sinusoidal function so that the maxwell static electricity equation is approximately satisfied the differential equations of motion are solved analytically for various boundary conditions of the plate in this study the closed form solution for characteristic equations displacement components of the plate and electric potential are derived for the first time in the literature to demonstrate the accuracy of the present solution comparison studies is first carried out with the available data in the literature and then natural frequencies of the piezoelectric coupled annular plate are presented for different thickness radius ratios inner outer radius ratios thickness of piezoelectric material of piezoelectric and boundary conditions present analytical model provides design reference for piezoelectric material application such as sensors actuators and ultrasonic motors

effects of fgm materials on the parametric resonance of plate structures abstract the parametric resonance of functionally graded rectangular plates under harmonic in plane loading is presented the objective here is to study the influence of the constituent volume fractions and the effects of configurations of the constituent materials on the parametric instability regions in particular the positions and sizes of these regions the material properties are graded in the thickness direction according to a material volume fraction power law distribution the present problem is formulated based on hamilton s principle and the assumed mode method bolotin s method is used here to determine the instability regions

buckling and vibration of polar orthotropic circular plate resting on winkler foundation buckling and vibrational behavior of polar orthotropic circular plates of linearly varying thickness is presented on the basis of classical plate theory the plate is resting on winkler type foundation an approximate solution has been obtained by ritz method which employs basis functions based upon static deflection of polar orthotropic plates the effect of elastic foundation and that of orthotropy on the natural frequency of plate has been illustrated for different values of taper parameter flexibility parameter in plane force and nodal diameter the critical buckling load for clamped and simply supported plates have been obtained a comparison of results with those available in literature has been presented

corrections to aggregation using the linguistic weighted average and interval type 2 fuzzy sets in the previous paper we have proposed linguistic weighted average lwa algorithms that can be used in distributed and hierarchical decision making the original lwa algorithms were completely based on the representation theorem for interval type 2 fuzzy sets it2 fss in later usage we found that when the lower membership functions lmfs of the inputs and weights are of different heights the lmf of the output it2 fs may be nonconvex and discontinuous in this letter a correction to the original lwa algorithms is proposed the new lwa algorithms are simpler and easier to understand so it should facilitate the applications of the lwas

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

vibration of electro elastic versus magneto elastic circular annular plates using the chebyshev ritz method abstract the aim of this paper is to analyze three dimensional free vibration of magneto elastic electro elastic circular annular plates with different boundary conditions using the chebyshev ritz method in which a set of duplicate chebyshev polynomial series multiplied by the boundary function satisfying the boundary conditions are chosen as the trial functions of the displacement components the electric potential and the magnetic potential convergence of the method is checked using various chebyshev polynomial terms the effect of geometrical parameters and material properties of magneto elastic electro elastic circular annular plates on the eigenfrequencies of free vibration is considered

a singular perturbation analysis of the fundamental semiconductor device equations in this paper we present a singular perturbation analysis of the fundamental semiconductor device equations which form a system of three second order elliptic differential equations subject to mixed neumann dirichlet boundary conditions the system consists of poisson s equation and the continuity equations and describes potential and carrier distributions in an arbitrary emiconductor device the singular perturbation parameter is the minimal normed debye length of the device under consideration using matched asymptotic expansions we demonstrate the occurrence of internal layers at surfaces across which the impurity distribution appearing as an inhomogeneity of poisson s equation has a jump discontinuity these surfaces are called junctions and the occurrence of boundary layers at semiconductor oxide interfaces we derive the layer equations and the reduced problem charge neutral approximation and give existence proofs for these problems the layer solutions which characterize the solutions of the s

on the one dimensional current driven semiconductor equations the steady state semiconductor equations in one dimension are examined subject to a given current through the device supplemented by dirichlet boundary conditions on one end of the device solutions to this current driven model are identified as the fixed points of a mapping t and uniqueness of solutions for the unipolar model is shown for arbitrary currents by demonstrating that t is unconditionally a contraction for both the uni and the bipolar model existence of solutions close to thermodynamic equilibrium is shown this means that for the one dimensional unipolar current driven model the situation is complementary to that for the potential driven model where it is possible to show existence of solutions for arbitrary applied potentials and uniqueness close to thermodynamic equilibrium only for the unipolar case iteration with the mapping t defines an algorithm for the solution of this model which is unconditionally convergent to the unique solution if it exists

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

uniform asymptotic error estimates for semiconductor device and electrochemistry equations abstract the paper is organized as follows section 1 sets up the problem our purpose and results and the existing results in the literature section 2 gives the notations used in the paper sections 3 and 4 set up the problem in the case of a symmetric piecewise constant junction and recall the associated asymptotic expansion in section 5 our method is introduced and uniform asymptotic error estimates for a symmetric piecewise constant junction are derived section 6 is an application of our technique for the case of a biological membrane with a constant concentration of fixed charges uniform asymptotic error estimates are also proved to hold in that case a brief summary and conclusion are given in the appendix we give the proofs of the lemmas which are used in sections 5 and 6

a variational formulation for vibro acoustic analysis of a panel backed by an irregularly bounded cavity abstract a weak form variational based method is developed to study the vibro acoustic responses of coupled structural acoustic system consisting of an irregular acoustic cavity with general wall impedance and a flexible panel subjected to arbitrary edge supporting conditions the structural and acoustical models of the coupled system are formulated on the basis of a modified variational method combined with multi segment partitioning strategy meanwhile the continuity constraints on the sub segment interfaces are further incorporated into the system stiffness matrix by means of least squares weighted residual method orthogonal polynomials such as chebyshev polynomials of the first kind are employed as the wholly admissible unknown displacement and sound pressure field variables functions for separate components without meshing and hence mapping the irregular physical domain into a square spectral domain is necessary the effects of weighted parameter together with the number of truncated polynomial terms and divided partitions on the accuracy of present theoretical solutions are investigated it is observed that applying this methodology accurate and efficient predictions can be obtained for various types of coupled panel cavity problems and in weak or strong coupling cases for a panel surrounded by a light or heavy fluid the inherent principle of velocity continuity on the panel cavity contacting interface can all be handled satisfactorily key parametric studies concerning the influences of the geometrical properties as well as impedance boundary are performed finally by performing the vibro acoustic analyses of 3d car like coupled miniature we demonstrate that the present method seems to be an excellent way to obtain accurate mid frequency solution with an acceptable cpu time

effect of built in edges on 3 d vibrational characteristics of thick circular plates the vibrational characteristics of thick circular plates built into a rigid medium in the vicinity of the circumference are studied the analysis procedure is based on the exact small strain three dimensional linear elasticity theory in the analysis the plate is considered as comprising an inner circular disc with free upper and lower surfaces connected to an outer annulus that is built into the rigid medium the chebyshev polynomials multiplied by suitable boundary characteristic functions are selected as the admissible functions of the displacement functions and the three dimensional displacement fields in each part can be expressed accordingly through the ritz method the eigenvalue equations can be established for the inner disc and the outer annulus respectively utilizing the displacement continuity conditions at the interface between the two parts the eigenvalue equation for the whole plate is derived convergence and comparison studies demonstrate the correctness and accuracy of the present method the effect of structural parameters such as plate thickness built in length and the end condition on eigenfrequencies of circular plate is investigated in detail it is shown that with the increase of plate thickness the effect of the built in annulus on eigenfrequencies significantly increases therefore for a thick plate the flexibility of the built in part should be considered in the dynamic analysis

a differential quadrature hierarchical finite element method using fekete points for triangles and tetrahedrons and its applications to structural vibration abstract a differential quadrature hierarchical finite element method dqhfem using fekete points was formulated for triangles and tetrahedrons and applied to structural vibration analyses first orthogonal polynomials on triangles and tetrahedrons that can be used as bases of the hierarchical finite element method hfem were derived and simple formulas of transforming one dimensional non uniform nodes to simplexes were presented then the non uniform nodes were used as initial guesses to solve the fekete points on simplexes through newton raphson s method together with the orthogonal polynomials new differential quadrature dq rules on simplexes were formulated using the hfem bases and the fekete points the numbers of nodes or bases on different edges and faces and inside the body of the new dq elements do not relate with each other like the hfem that can freely assign different numbers of bases on different edges and faces and inside the body so the new dq method was named as a differential quadrature hierarchical dqh method that uses either interpolation functions or orthogonal polynomials as bases inside the element its weak form was named as the dqhfem besides the dqh method and its weak form a simple method of generating high quality linear and high order triangular and tetrahedral meshes from a single nurbs patch was presented numerical tests of the dqhfem through structural vibration analyses showed that high accuracy results can be obtained using only a few nodes even on curvilinear domains using the dqh bases on both physical and geometric fields it was concluded that wide applications of the dqh method and the dqhfem to science and engineering are possible and commercial codes based on them are deserved to be developed