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

a refined quasi 3d isogeometric analysis for functionally graded microplates based on the modified couple stress theory the isogeometric analysis associated with a novel quasi 3d shear deformation theory is proposed to investigate size dependent behaviours of functionally graded microplates the modified couple stress theory with only one material length scale parameter is employed to effectively capture the size dependent effects within the microplates meanwhile the quasi 3d theory which is constructed from a novel seventh order shear deformation refined plate theory with four unknowns is able to consider both shear deformations and thickness stretching effect without requiring shear correction factors the nurbs based isogeometric analysis is integrated to exactly describe the geometry and approximately calculate the unknown fields with higher order derivative and continuity requirements the proposed approach is successfully applied to study the static bending free vibration and buckling responses of rectangular and circular functionally graded microplates with various types of boundary conditions in which some benchmark numerical examples are presented a number of investigations are also conducted to illustrate the effects of the material length scale material index and aspect ratios on the responses of the microplates

learning overcomplete representations in an overcomplete basis the number of basis vectors is greater than the dimensionality of the input and the representation of an input is not a unique combination of basis vectors overcomplete representations have been advocated because they have greater robustness in the presence of noise can be sparser and can have greater flexibility in matching structure in the data overcomplete codes have also been proposed as a model of some of the response properties of neurons in primary visual cortex previous work has focused on finding the best representation of a signal using a fixed overcomplete basis or dictionary we present an algorithm for learning an overcomplete basis by viewing it as probabilistic model of the observed data we show that overcomplete bases can yield a better approximation of the underlying statistical distribution of the data and can thus lead to greater coding efficiency this can be viewed as a generalization of the technique of independent component analysis and provides a method for bayesian reconstruction of signals in the presence of noise and for blind source separation when there are more sources than mixtures

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

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

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

temporal homogenization of linear odes with applications to parametric super resonance and energy harvest we consider the temporal homogenization of linear odes of the form dot x ax epsilon p t x f t where p t is periodic and epsilon is small using a 2 scale expansion approach we obtain the long time approximation x t approx rm exp at left omega t int 0 t rm exp a tau f tau rm d tau right where omega solves the cell problem dot omega epsilon b omega epsilon f t with an effective matrix b and an explicitly known f t we provide necessary and sufficient conditions for the accuracy of the approximation over a mathcal o epsilon 1 time scale and show how b can be computed at a cost independent of epsilon as a direct application we investigate the possibility of using rlc circuits to harvest the energy contained in small scale oscillations of ambient electromagnetic fields such as schumann resonances although a rlc circuit parametrically coupled to the field may achieve such energy extraction via parametric resonance its resistance r needs to be smaller than a threshold kappa proportional to the fluctuations of the field thereby limiting practical applications we show that if n rlc circuits are appropriately coupled via mutual capacitances or inductances then energy extraction can be achieved when the resistance of each circuit is smaller than n kappa hence if the resistance of each circuit has a non zero fixed value energy extraction can be made possible through the coupling of a sufficiently large number n of circuits n approx 1000 for the first mode of schumann resonances and contemporary values of capacitances inductances and resistances the theory is also applied to the control of the oscillation amplitude of a damped oscillator

hybrid uncertainty analysis of functionally graded plates via multiple imprecise random field modelling of uncertain material properties abstract this paper presents the mixed probabilistic non probabilistic uncertainty problem regarding the hybrid uncertainty propagation on physical model of functionally graded plates through dissimilarly uncertain characterisation of material properties in the presence of the multiple imprecise random field modelling the spectral stochastic finite element framework is extended to perform mixed uncertainty analysis of functionally graded material whereby the spatial variation of elastic modulus of the plate is uniquely characterised as the multiple imprecise random field modelling more than a purely homogeneous random field this characterisation has originated in heeding the construction of physical models and the significant influences of separately uncertain characteristics propagated on the physical model through different material ingredients are examined to make physical models more reliable and realistic mechanics and mathematics intrusive formulations are then established to explicitly produce the uncertain but bounded statistical characteristics of responses namely interval mean value interval standard deviation bounded surfaces of statistical moments and bounding distribution functions are vividly depicted for demonstration the feasibility and effectiveness of the presented work are illustrated via test cases of numerical examples

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

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

geometrically nonlinear analysis of functionally graded plates using the element free kp ritz method abstract the nonlinear response of functionally graded ceramic metal plates fgps under mechanical and thermal loads is investigated using the mesh free kp ritz method the nonlinear formulation is based on the first order shear deformation plate theory and the von karman strains which deal with small strains and moderate rotations the material properties of fgps are assumed to be graded through the thickness direction according to a power law distribution of the volume fraction of the constituents the approximation of the displacement field is expressed in terms of a set of mesh free kernel particle functions the bending stiffness of the plates is evaluated using a stabilized conforming nodal integration method and the membrane and shear stiffnesses are computed using direct nodal integration to eliminate shear locking the nonlinear behavior of the deflection and axial stress is studied for fgps under thermal and mechanical loading and the influences of the volume fraction exponent boundary condition and material properties on the nonlinear response of fgps are examined

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

on the use of computational intelligence in the optimal shape control of functionally graded smart plates functionally graded material fgm plates are an essential component for most advanced integrated systems in terms of vibration and acoustic controls or condition monitoring in general these fgm plates are designed with embedded piezoelectric sensors and actuators to achieve their shape control this optimal control problem is normally required to find appropriate actuator voltage and displacement control gains that will generate the desired shape such an optimal control problem is known to be highly non linear and often posses slope and functional discontinuity that will limit the efficiency of the gradient based methods stochastic zero order population based optimization methods are ideal for solving this class of problems in this paper we introduce a stochastic zero order optimization algorithm based on the principles of learning this algorithm is embedded with three key learning strategies that control who to learn from i e leader identification and leader selection and what to learn i e information acquisition to reach a common goal the leader identification mechanism partitions the individuals into a set of leaders and a set of followers the followers interact with the leaders and move toward the better performing leaders in searching for better solutions the parameter free algorithm provides the designer with the true flexibility that is necessary to handle various forms of design problem effectively and at a computational cost that is comparable to existing stochastic optimization methods in this study numerical results are presented for the shape control of the fgm plates under a temperature gradient by optimizing i the voltage distribution for the open loop control and ii the displacement control gain values for the closed loop feedback control we also examine the effect of the constituent volume fractions of zirconia through the varying of volume fraction exponent n on the optimal voltages and gain values

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

finite elements for functionally graded reissner mindlin plates abstract equations governing the behavior of rectangular plates made of functionally graded materials fgms are determined in this paper using the variational approach derivation of such equations is based on reissner mindlin plate theory that is extended to handle two constituent material distribution through the thickness material properties are assumed to vary with the power law in terms of the volume fractions of the constituent within a static analysis framework the main focus of the paper is the proposal of a locking free hierarchic family of finite elements that is numerically tested on plates of different material grading convergence and stability properties of our approach are assessed and comparisons with available solutions presented

dynamic stability of cylindrical panels with transverse shear effects abstract the dynamic stability of simply supported isotropic cylindrical panels under combined static and periodic axial forces are investigated an extension of donnells shell theory to a first order shear deformation theory is used and a system of mathieu hill equations are obtained via a normal mode expansion and the parametric resonance response was analyzed using bolotins method results are compared with those obtained using the classical shell theory the effects of the thickness to radius ratio on the instability regions are examined in detail

analytical solutions for single and multi span functionally graded plates in cylindrical bending abstract a recently developed plate theory using the concept of shape function of the transverse coordinate parameter is extended to determine the stress distribution in an orthotropic functionally graded plate subjected to cylindrical bending the transfer matrix method is presented to derive the shape function the equations governing the plate deformation are then solved analytically using the transfer matrix method for arbitrary boundary conditions for a simply supported functionally graded plate a comparison of the present solution with the exact elasticity solution the first and third order shear deformation plate theories is presented and discussed it is demonstrated that the present method yields more accurate stresses than the first and third order shear deformation theories the effect of boundary conditions and inhomogeneity of material on the displacements and stresses in functionally graded plates are investigated a multi span functionally graded plate with arbitrary boundary conditions is further considered to demonstrate the efficiency of the present method

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

nonlinear vibrations of functionally graded doubly curved shallow shells nonlinear forced vibrations of fgm doubly curved shallow shells with a rectangular base are investigated donnell s nonlinear shallow shell theory is used and the shell is assumed to be simply supported with movable edges the equations of motion are reduced using the galerkin method to a system of infinite nonlinear ordinary differential equations with quadratic and cubic nonlinearities using the multiple scales method primary and subharmonic resonance responses of fgm shells are fully discussed and the effect of volume fraction exponent on the internal resonance conditions softening hardening behavior and bifurcations of the shallow shell when the excitation frequency is i near the fundamental frequency and ii near two times the fundamental frequency is shown moreover using a code based on arclength continuation method a bifurcation analysis is carried out for a special case with two to one internal resonance between the first and second doubly symmetric modes with respect to the panel s center 13 2 11 bifurcation diagrams and poincare maps are obtained through direct time integration of the equations of motion and chaotic regions are shown by calculating lyapunov exponents and lyapunov dimension

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

higher order piezoelectric plate theory derived from a three dimensional variational principle a three dimensional mixed variational principle is used toderive a kth order two dimensional lineartheory for an anisotropichomogeneouspiezoelectric pzt plate themechanicaldisplacements theelectricpotential theinplane components of the stress tensor and the in plane components of the electric displacement are expressed as a e niteseries of orderk inthethickness coordinate bytakinglegendrepolynomialsas thebasisfunctions however the transverse shear stress the transverse normal stress and the transverse electric displacement are expressed as a e nite series of order k 2 in the thickness coordinate the formulation accounts for the double forces without moments that may change the thickness of the plate results obtained by using the plate theory are given for the bending of a cantilever thick plate loaded on the top and the bottom surfaces by uniformly distributed 1 normal tractions and 2 tangential tractions results are also computed for the bending of a cantilever thick pzt beam loaded by 1 a uniformly distributed charge density on the top and the bottom surfaces and 2 equal and opposite normal tractions distributed uniformly only on a part of the beam the seventh order plate theory captures well the boundary layer effects near the clamped and the free edges and adjacent to the top and the bottom surfaces of a thick orthotropic cantilever beam with the span to the thickness ratio of two also through the thickness variation of the transverse shear and the transverse normal stresses agree well with those computed from the analytical solution of the three dimensional elasticity equations the governing partial differential equations are second order so that lagrange basis functions can be used to solve the problem by the e nite element 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

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

an analytical method for free vibration analysis of functionally graded beams with edge cracks abstract in this paper an analytical method is proposed for solving the free vibration of cracked functionally graded material fgm beams with axial loading rotary inertia and shear deformation the governing differential equations of motion for an fgm beam are established and the corresponding solutions are found first the discontinuity of rotation caused by the cracks is simulated by means of the rotational spring model based on the transfer matrix method then the recurrence formula is developed to get the eigenvalue equations of free vibration of fgm beams the main advantage of the proposed method is that the eigenvalue equation for vibrating beams with an arbitrary number of cracks can be conveniently determined from a third order determinant due to the decrease in the determinant order as compared with previous methods the developed method is simpler and more convenient to analytically solve the free vibration problem of cracked fgm beams moreover free vibration analyses of the euler bernoulli and timoshenko beams with any number of cracks can be conducted using the unified procedure based on the developed method these advantages of the proposed procedure would be more remarkable as the increase of the number of cracks a comprehensive analysis is conducted to investigate the influences of the location and total number of cracks material properties axial load inertia and end supports on the natural frequencies and vibration mode shapes of fgm beams the present work may be useful for the design and control of damaged structures

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

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

nonlinear dynamic response and active vibration control for piezoelectric functionally graded plate the nonlinear dynamic response and active vibration control of the piezoelectric functionally graded plate are analyzed in this paper based on higher order shear plate theory and elastic piezoelectric theory the nonlinear geometric and constitutive relations of the piezoelectric functionally graded plate are established and then the nonlinear motion equations of the piezoelectric functionally graded plate are obtained through hamilton s variational principle the nonlinear active vibration control of the structure is carried out with adoption of the negative velocity feedback control algorithm by applying finite difference method the whole problem is solved by using iterative method synthetically in numerical examples the effects of mechanical load electric load the volume fraction and the geometric parameters on the dynamic response and vibration control of the piezoelectric fgm plate are investigated

natural frequencies of a functionally graded anisotropic rectangular plate we use the first order shear deformation theory fsdt coupled with the finite element method fem to study free vibrations of a functionally graded fg anisotropic rectangular plate with the objective of maximizing one of its first five natural frequencies the following edge conditions are considered i all edges clamped ii all edges simply supported iii two opposite edges clamped and the other two free and iv two opposite edges simply supported and the other two free an advantage of a functionally graded plate over a laminated plate is that material properties vary continuously through the plate thickness thus no sudden discontinuities in stresses occur across an interface between any two adjoining laminae thereby eliminating the delamination mode of failure whereas there have been numerous works on studying the response of fg plates made of isotropic elastic constituents with the homogenized material also modeled as isotropic elastic e g see refs 1 2 and references cited therein the only other study on fg anisotropic plate 3 has assumed that all elastic constants vary exponentially through the plate thickness at the same rate it is highly unlikely that elastic moduli of a fg anisotropic plate will exhibit this property here we consider a fg anisotropic plate in which the fiber orientation varies smoothly through the plate thickness

vibration of an incompressible isotropic linear elastic rectangular plate with a higher order shear and normal deformable theory abstract we use a mixed higher order shear and normal deformable plate theory hosndpt of batra and vidoli with poisson s ratio equal to 0 49 and the finite element method to analyze vibrations of a homogeneous isotropic rectangular plate made of an incompressible linear elastic material through the thickness integrals are evaluated exactly and those over an element in the midplane of the plate are evaluated by using the 2 2 gauss quadrature rule the plate theory equations are used to ascertain frequencies of a clamped clamped and a clamped free square rectangular plate of different aspect ratios through the thickness modes of vibration valid for compressible and incompressible materials and missed by previous investigators are also identified computed frequencies are found to match well with those deduced from the analytical solution

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

natural frequencies of thick plates made of orthotropic monoclinic and hexagonal materials by a meshless method abstract we use the first order shear deformation theory and a meshless method based on radial basis functions in a pseudospectral framework for predicting the free vibration behavior of thick orthotropic monoclinic and hexagonal plates the shape parameter is obtained by an optimization procedure the three translational and two rotational degrees of freedom of a point of the laminate are independently approximated through numerical experiments the capability and efficiency of the radial basis functions pseudospectral method for eigenvalue problems are demonstrated and the numerical accuracy and convergence are examined

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

pattern generation and the control of nonlinear systems many important engineering systems accomplish their purpose using cyclic processes whose characteristics are under feedback control examples involving thermodynamic cycles and electromechanical energy conversion processes are particularly noteworthy likewise cyclic processes are prevalent in nature and the idea of a pattern generator is widely used to rationalize mechanisms used for orchestrating movements such as those involved in locomotion and respiration in this paper we develop a linkage between the use of cyclic processes and the control of nonholonomic systems emphasizing the problem of achieving stable regulation the discussion brings to the fore characteristic phenomena that distinguish the regulation problem for such strongly nonlinear systems from the more commonly studied linear feedback regulators finally we compare this approach to controlling nonholonomic systems to another approach based on the idea of an open loop approximate inverse as discussed in the literature

homotopy continuation for spatial interference alignment in arbitrary mimo x networks in this paper we propose an algorithm to design interference alignment ia precoding and decoding matrices for arbitrary mimo x networks the proposed algorithm is rooted in the homotopy continuation techniques commonly used to solve systems of nonlinear equations homotopy methods find the solution of a target system by smoothly deforming the solution of a start system which can be trivially solved unlike previously proposed ia algorithms the homotopy continuation technique allows us to solve the ia problem for both unstructured i e generic and structured channels such as those that arise when time or frequency symbol extensions are jointly employed with the spatial dimension to this end we consider an extended system of bilinear equations that include the standard alignment equations to cancel the interference and a new set of bilinear equations that preserve the desired dimensionality of the signal spaces at the intended receivers we propose a simple method to obtain the start system by randomly choosing a set of precoders and decoders and then finding a set of channels satisfying the system equations which is a linear problem once the start system is available standard prediction and correction techniques are applied to track the solution all the way to the target system we analyze the convergence of the proposed algorithm and prove that for many feasible systems and a sufficiently small continuation parameter the algorithm converges with probability one to a perfect ia solution the simulation results show that the proposed algorithm is able to consistently find solutions achieving the maximum number of degrees of freedom in a variety of mimo x networks with or without symbol extensions further the algorithm provides insights into the feasibility of ia in mimo x networks for which theoretical results are scarce

dynamic buckling of functionally graded spherical caps the dynamic behavior of functionally graded spherical caps under suddenly applied loads is studied by using a three noded axisymmetric curved shell element based on field consistency approach the formulation is based on first order shear deformation theory and it includes the in plane and rotary inertia effects geometric nonlin earity is introduced in the formulation using von karman s strain displacement relations the material properties are graded in the thickness direction according to the power law distribution in terms of volume fractions of the constituents of the material the effective material properties are evaluated using homogenization method the governing equations obtained are solved employing the newmark s integration technique coupled with a modified newton raphson iteration scheme the load corresponding to a sudden jump in the maximum average displace ment in the time history of the shell structure is taken as the dynamic buckling pressure the present model is validated against the available isotropic cases a detailed numerical study is carried out to bring out the effects of shell geometries power law index of functional graded material boundary conditions and finite pressure pulse with different duration on the axisymmetric dynamic buckling load of shallow spherical shells

nonlinear and chaotic vibration and stability analysis of an aero elastic piezoelectric fg plate under parametric and primary excitations abstract in this study in the presence of supersonic aerodynamic loading the nonlinear and chaotic vibrations and stability of a simply supported functionally graded piezoelectric fgp rectangular plate with bonded piezoelectric layer have been investigated it is assumed that the plate is simultaneously exposed to the effects of harmonic uniaxial in plane force and transverse piezoelectric excitations and aerodynamic loading it is considered that the potential distribution varies linearly through the piezoelectric layer thickness and the aerodynamic load is modeled by the first order piston theory the von karman nonlinear strain displacement relations are used to consider the geometrical nonlinearity based on the classical plate theory cpt and applying the hamilton s principle the nonlinear coupled partial differential equations of motion are derived the galerkin s procedure is used to reduce the equations of motion to nonlinear ordinary differential mathieu equations the validity of the formulation for analyzing the limit cycle oscillation lco aero elastic stability boundaries is accomplished by comparing the results with those of the literature and the convergence study of the fgp plate is performed by applying the multiple scales method the case of 1 2 internal resonance and primary parametric resonance are taken into account and the corresponding averaged equations are derived and analyzed numerically the results are provided to investigate the effects of the forcing piezoelectric detuning parameter amplitude of forcing piezoelectric excitation and dynamic pressure on the nonlinear dynamics and chaotic behavior of the fgp plate it is revealed that under the certain conditions due to the existence of bi stable region of non trivial solutions system shows the hysteretic behavior moreover in absence of airflow it is observed that variation of control parameters leads to the multi periodic and chaotic motions

a blind source separation technique using second order statistics separation of sources consists of recovering a set of signals of which only instantaneous linear mixtures are observed in many situations no a priori information on the mixing matrix is available the linear mixture should be blindly processed this typically occurs in narrowband array processing applications when the array manifold is unknown or distorted this paper introduces a new source separation technique exploiting the time coherence of the source signals in contrast with other previously reported techniques the proposed approach relies only on stationary second order statistics that are based on a joint diagonalization of a set of covariance matrices asymptotic performance analysis of this method is carried out some numerical simulations are provided to illustrate the effectiveness of the proposed method

exact three dimensional elasticity solutions for bending of moderately thick inhomogeneous and laminated strips under normal pressure abstract an exact three dimensional solution is presented for the deformation and stress distribution in a semi infinite strip clamped along its two edges and subjected to uniform normal loading of the lateral surfaces the strip is of constant moderate thickness and composed of anisotropic elastic material which is arbitrarily inhomogeneous in the through thickness direction the only material symmetry assumed is that of reflectional elastic symmetry in planes parallel to the mid plane the important special case of an anisotropic laminated plate is given by assuming piecewise constant properties through the thickness the general method of solution is to reformulate the full three dimensional elasticity equations in a way that reduces the problem to solving a system of partial differential equations in the two in plane independent variables only and then obtaining asymptotic solutions in terms of an aspect ratio of the thickness divided by a typical in plane length in general successive terms are expressed in terms of the approximate classical laminate solution in the present problem this solution is very simple and the expansion terminates after no more than three terms this gives a closed form analytical solution that is valid for any aspect ratio

exact correspondence between eigenvalues of membranes and functionally graded simply supported polygonal plates we use reddy s third order plate theory to study buckling and steady state vibrations of a simply supported functionally gradient isotropic polygonal plate resting on a winkler pasternak elastic foundation and subjected to uniform in plane hydrostatic loads young s modulus and the poisson ratio for the material of the plate are assumed to vary only in the thickness direction effects of rotary inertia are considered the problem of determining the critical buckling load or the vibration frequency of the plate is found to be analogous to that of ascertaining the frequency of a membrane clamped at the edges and whose shape coincides with that of the plate the critical buckling load and the vibration frequency are shown to be positive some available results for plates symmetric about the mid plane can be retrieved from the present analysis

a hierarchy of dynamic equations for micropolar plates this work considers homogeneous isotropic micropolar plates adopting a power series expansion method in the thickness coordinate variationally consistent equations of motion and end boundary conditions are derived in a systematic fashion up to arbitrary order for extensional and flexural displacement cases the plate equations are asymptotically correct to all studied orders numerical results are presented for various orders of the present method other approximate theories as well as the exact three dimensional theory the results illustrate that the present approach may render benchmark solutions provided higher order truncations are used and act as engineering plate equations using low order truncation

a hierarchy of dynamic equations for solid isotropic micropolar circular cylinders this work considers the derivation procedure and evaluation of dynamic equations for isotropic micropolar circular cylinders by adopting a power series expansion method in the radial coordinate variationally consistent equations of motion together with pertinent sets of boundary conditions are expressed in a systematic fashion up to arbitrary order the numerical results cover eigenfrequencies mode shapes and field distributions over cross sections for axisymmetric and flexural motion adopting different sets of end boundary conditions for equations of different truncation orders of the present method the results illustrate that the present approach may render benchmark solutions provided that higher order equations are used and act as accurate approximate engineering solution for lower order equations

approximation of functionally graded plates with non conforming finite elements in this paper rectangular plates made of functionally graded materials fgms are studied a two constituent material distribution through the thickness is considered varying with a simple power rule of mixture the equations governing the fgm plates are determined using a variational formulation arising from the reissner mindlin theory to approximate the problem a simple locking free discontinuous galerkin finite element of non conforming type is used choosing a piecewise linear non conforming approximation for both rotations and transversal displacement several numerical simulations are carried out in order to show the capability of the proposed element to capture the properties of plates of various gradings subjected to thermo mechanical loads

three dimensional solution of the free vibration problem of homogeneous isotropic cylindrical shells and panels abstract the free vibration problem of a homogeneous isotropic thick cylindrical shell or panel subjected to a certain type of simply supported edge boundary conditions is considered for this problem the governing equations of three dimensional linear elasticity are employed and solved by using a new iterative approach which in practice leads to the prediction of the exact frequencies of vibration in the particular case of a flat plate or a complete shell excellent agreement is achieved between results based on the present approach and corresponding results based on other exact analyses available in the literature for certain cylindrical panel geometries comparisons are also made between corresponding numerical results based on the present analysis and certain two dimensional shell theories

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

a contribution to the control of the non holonomic integrator including drift in this paper a three dimensional non holonomic integrator ni with drift terms is considered for this type of plant the question how to obtain desired piecewise constant output functions with minimum norm control inputs is explored it is shown that this can be achieved by a nonlinear controller that provides simultaneous modulation of both the amplitude and the frequency of the harmonic input vector the internal states are implicitly forced to follow natural periodic orbits satisfying the non holonomic constraints of the plant global asymptotic stability and high dynamics in the output response are achieved the problem of singularity at zero initial state is solved by a time optimal control scheme for the internal states by combining the nonlinear controller and the time optimal controller using an appropriate switching strategy a powerful control concept can be established the torque control of an induction machine is considered as an illustrative example for the application of the control scheme experimental results of the closed loop feedback control system are presented

on the free vibration of moderately thick spherical shell panel a new exact closed form procedure abstract a new exact closed form procedure for free vibration analysis of moderately thick spherical shell panel is presented based on the first order shear deformation theory the strain displacement relations of donnell and sanders theories are used to illustrate the procedure the shell has two opposite edges simply supported i e levy type based on the present solution the governing equations of the vibrated spherical shell panel were exactly solved by introducing the new auxiliary and potential functions as well as using the separation method of variables the accuracy and superiority of the formulations are validated by comparing the results with those available in the literature and the 3d finite element analysis the effects of various stretching bending couplings on the frequency parameters are discussed finally the validity and the range of applicability of the sanders and donnell shell theories are investigated

stabilization of nonholonomic integrators via logic based switching this paper explains how to stabilize a nonholonomic integrator using a hybrid control law employing switching and logic results concerning asymptotic stability and exponential convergence to the origin are derived the notion of a positively invariant set is extended to hybrid systems and sufficient conditions for invariance are presented the verification of these conditions does not require the computation of the state trajectories and their use goes beyond the analysis of the system presented in this paper

geometrically nonlinear analysis of functionally graded plates using a cell based smoothed three node plate element cs min3 based on the c0 hsdt abstract a cell based smoothed three node mindlin plate element cs min3 based on the first order shear deformation theory fsdt was recently proposed for static and dynamics analyses of mindlin plates in this paper the cs min3 is extended to geometrically nonlinear analysis of functionally graded plates fgps subjected to thermo mechanical loadings in the fgps the material properties are assumed to vary through the thickness by a simple power rule of the volume fractions of the constituents the nonlinear formulation is based on the c0 type high order shear deformation plate theory c0 hsdt and the von karman strains which deal with small strains and moderate rotations in the analysis process both thermal and mechanical loadings are considered and a two step procedure is performed including a step of analyzing the temperature field along the thickness of the plate and a step of analyzing the geometrically nonlinear behavior of the fgps subjected to both thermal and mechanical loadings the accuracy and reliability of the proposed method is verified by comparing its numerical solutions with those of available other numerical results

natural frequencies of orthotropic monoclinic and hexagonal plates by a meshless method the collocation method with multiquadrics basis functions and a first order shear deformation theory are used to find natural flexural frequencies of a square plate with various material symmetries and subjected to different boundary conditions computed results are found to agree well with the literature values obtained by the solution of the three dimensional elasticity equations using the finite element method

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

plane wave solutions and modal analysis in higher order shear and normal deformable plate theories abstract we use the three dimensional hellinger reissner mixed variational principle to derive a k th order k 0 1 2 shear and normal deformable plate theory the balance laws the constitutive relations and the boundary conditions for the plate theory are deduced the constitutive relations incorporate the shear and the normal tractions applied on the top and the bottom surfaces of the plate for a k th order plate theory with displacements expressed as a power series in the thickness co ordinate z with terms up to z k the transverse shear and the transverse normal stresses involve terms upto z k 2 while in plane stress components have terms up to z k the equations for the plate theory are expressed in a compact form by taking legendre polynomials as the basis functions the plate theory is used to study plane travelling waves and in particular the lengths of decay of the displacement components this allows for a rigorous ordering of the importance of the displacement descriptors in terms of decaying properties finally we study the free vibrations of a simply supported rectangular orthotropic thick plate results from the present theory are compared with an exact three dimensional solution and with other plate theories to this end a k th order compatible plate theory is also deduced the term compatible alludes to the fact that the reduction map for the stress fields is induced by the kinematical reduction map whilst in the mixed models it is postulated independently it is found that the frequencies up to the fifth mode of vibration computed with the fifth order theory and without introducing any shear correction factors match very well with the corresponding analytical solution also through the thickness distribution of all of the stress components is found to agree well with the three dimensional elasticitysolution while the stress distribution obtained from the compatible plate theories deviatesconsiderably especially for the higher modes

generalization of variationally consistent plate theories on the basis of a vectorial formulation abstract this paper deals with the vectorial formulation of variationally consistent sets of differential equations that with either transverse shear or transverse normal deformation effects taken into consideration govern the static and or dynamic behaviour of homogeneous or inhomogeneous elastic plates the present formulation is based on a general form of the displacement representation and yields the kinematic relations constitutive equations and equations of motion of a variationally consistent shear and normal deformable general plate theory the number of degrees of freedom as well as the performance of which can be controlled a posteriori it is shown to be equivalent with a variational approach and can further be considered as a generalization of several variationally consistent transverse shear and normal deformable plate theories in the sense that in particular cases it quotes their governing equations derived elsewhere variationally moreover just as happens with the application of a variational approach an a priori knowledge of the elastic law governing the material behaviour of the plate considered is not required under the general assumption that there exists a strain energy density function the present vectorial approach can be applied successfully

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

exact solution for thermoelastic deformations of functionally graded thick rectangular plates an exact solution is obtained for three dimensional deformations of a simply supported functionally graded rectangular plate subjected to mechanical and thermal loads on its top and or bottom surfaces suitable temperature and displacement functions that identically satisfy boundary conditions at the edges are used to reduce the partial differential equations governing the thermomechanical deformations to a set of coupled ordinary differential equations in the thickness coordinate which are then solved by employing the power series method the exact solution is applicable to both thick and thin plates 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 consistentschemes exact displacementsand stressesatseveral locations for mechanical and thermal loads are used toassess theaccuracyof the classical plate theory thee rst ordershear deformation theory and athird order shear deformation theory for functionally graded plates results are alsocomputed for a functionally graded plate with material properties derived by the mori tanaka method the self consistent scheme and a combination of these two methods

optimal design of functionally graded incompressible linear elastic cylinders and spheres we find closed form solutions for axisymmetric plane strain radial deformations of a functionally graded circular hollow cylinder and radial expansion contraction of a hollow sphere loaded on inner and outer surfaces by uniform hydrostatic pressures the cylinder and the sphere are presumed to be made of isotropic and incompressible linear elastic materials with the shear modulus a general function of the radius it is found that the optimal value of the hoop or the circumferential stress in a cylinder and a sphere is a constant and occurs for the linear variation in the radial direction of the shear modulus the analytical results presented here should serve as benchmarks for verifying numerical solutions of problems

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

wave propagation of functionally graded layers treated by recursion relations and effective boundary conditions wave propagation through a layer of a material that is inhomogeneous in the thickness direction typically a functionally graded material fgm is investigated the material parameters and the displacement components are expanded in power series in the thickness coordinate leading to recursion relations among the displacement expansion functions these can be used directly in a numerical scheme as a means to get good field representations when applying boundary conditions and this can be done even if the layer is not thin this gives a schema that is much more efficient than the approach of subdividing the layer into many sublayers with constant material properties for thin layers for which the material parameters do not depend on the layer thickness the recursion relations can be used to eliminate all but the lowest order expansion functions employing the boundary conditions this leads to a set of effective boundary conditions relating the displacements and stresses on the two sides of the layer thus completely replacing the layer by these effective boundary conditions numerical examples illustrate the convergence properties of the scheme for fg layers and the influence of different variations of the material parameters in the fg layer

mimo instantaneous blind identification based on second order temporal structure blind identification is a crucial subtask in signal processing problems such as blind signal separation bss and direction of arrival doa estimation this paper presents a procedure for multiple input multiple output instantaneous blind identification based on second order temporal properties of the signals such as coloredness and nonstationarity the procedure consists of two stages first based on assumptions on the second order temporal structure sots of the source and noise signals and using subspace techniques the problem is reformulated in a particular way such that each column of the unknown mixing matrix satisfies a system of multivariate homogeneous polynomial equations then this nonlinear system of equations is solved by means of a so called homotopy method which provides a general tool for solving possibly nonexact systems of nonlinear equations by smoothly deforming the known solutions of a simple start system into the desired solutions of the target system our blind identification procedure allows to estimate the mixing matrix for scenarios with more sources than sensors without resorting to sparsity assumptions something that is often believed to be impossible when using only second order statistics in addition since our algorithm does not require any assumption on the mixing matrix also mixing matrices that are rank deficient or even have identical columns can be identified finally we give examples and performance results for speech source signals