axisymmetric solutions for the multi layered transversely isotropic piezoelectric medium by introducing the precise integration algorithm pia and the technique of the mixed variable formalism accounting for any number of layers variations of components of the axisymmetric piezoelectric field including elastic displacement vertical normal stress electric potential and electric displacement along the axis of symmetry in the cylindrical coordinate system are explored the piezoelectric field is induced by the vertical loadings of mechanical or electric types uniformly distributed over a circular region with the aid of the mixed variable formulations along with the hankel integral transform and the corresponding matrix algebraic operations the governing partial differential equations of equilibrium expressed in terms of displacements and electric potential are reduced to the first order ordinary differential matrix equations as a highly accurate algorithm the pia is provided to evaluate the obtained ordinary differential matrix equations in the transformed domain both mechanical and electrical quantities in the physical domain can be acquired by taking the inversion of the hankel integral transform an example as benchmark is illustrated to examine the applicability and performance of the proposed technique compared with results in the literature numerical examples are used to demonstrate the influence of the degree of the material anisotropy and stratified parameters

green s functions for transversely isotropic piezoelectric functionally graded multilayered half spaces by virtue of two systems of vector functions and the propagator matrix method greens functions for transversely isotropic piezoelectric functionally graded exponentially graded in the vertical direction and multilayered half spaces are derived it is observed that the homogeneous solution and propagator matrices for each functionally graded layer in the transformed domain are independent of the choice of the two systems of vector functions for a point force and point charge density applied at any location of the functionally graded half space greens functions are expressed in terms of one dimensional infinite integrals to carry out the numerical integral involving bessel functions an adaptive gauss quadrature approach is introduced and modified the piezoelectric functionally graded greens functions include those in the corresponding elastic functionally graded media as special results with the latter being also unavailable in the literature two piezoelectric functionally graded half space models are analyzed numerically one is a functionally graded pzt 4 half space and the other a coated functionally graded pzt 4 layer over a homogeneous batio3 half space the effects of different exponential factors on greens function components are clearly demonstrated which could be useful in the design and manufacturing of piezoelectric functionally graded structures 2004 elsevier ltd all rights reserved

finite time asynchronous h control for markov jump repeated scalar non linear systems with input constraints finite time control issue for a quite comprehensive class of system model that is markov jump repeated scalar nonlinear systems mjrsnss has been addressed an asynchronous controller is first proposed in mjrsnss which has less conservatism than mode dependent when the partly available mode information is encountered the input constraints associated with physical limitations in some practical applications have been fully considered which make our model more realistic this paper is concerned with the problem of finite time h control for markov jump repeated scalar nonlinear systems mjrsnss with input constraints the jumps between mjrsnss and desired mode dependent controllers are considered to be nonsynchronous the mode transition of the controllers is governed by a nonstationary markov chain which can model the different degrees of asynchronous jumps between mjrsnss and controllers with the aid of lyapunov krasovskii methodology some h performance criteria for the mjrsnss are proposed based on these criteria sufficient conditions on the existence of the desired controllers are established and then the gains of the controllers can be obtained by solving a convex optimization problem finally an example is presented to illustrate the effectiveness of our method

a two dimensional eshelby problem for two bonded piezoelectric half planes the present paper concerns a two dimensional eshelby problem for an inclusion of arbitrary shape embedded within one of two bonded dissimilar piezoelectric halfplanes the elastic and piezoelectric constants of the inclusion and its surrounding half plane are assumed to be the same a simple explicit solution is derived in terms of some auxiliary functions which can be determined using several related conformal mappings of the inclusion shape the obtained solution is exact provided that the expansions of all conformal mappings include only a finite number of terms on the other hand if an exact conformal mapping includes infinite terms a truncated polynomial mapping function should be used and then the method gives an approximate solution the existing solutions obtained in an earlier work for a homogeneous piezoelectric plane or half plane can be derived from the present solution as special cases in particular the closed form solutions are given for the eshelby problem of an arbitrarily shaped inclusion in a piezoelectric half plane with various mixed surface conditions such as rigid insulating surface or traction free conducting surface these solutions are used to study the effects of various surface electrical conditions on an electro elastic field in a piezoelectric half plane

estimating effective elasticity tensors from christoffel equations we consider the problem of obtaining the orientation and elasticity parameters of an effective tensor of particular symmetry that corresponds to measurable traveltime and polarization quantities these quantities the wavefront slowness and polarization vectors are used in the christoffel equation a characteristic equation of the elastodynamic equation that brings seismic concepts to our formulation and relates experimental data to the elasticity tensor to obtain an effective tensor of particular symmetry we do not assume its orientation thus the regression using the residuals of the christoffel equation results in a nonlinear optimization problem we find the absolute extremum and to avoid numerical instability of a global search obtain an accurate initial guess using the tensor of given symmetry closest to the generally anisotropic tensor obtained from data by linear regression the issue is twofold first finding the closest tensor of particular symmetry without assuming its orientation is challenging second the closest tensor is not the effective tensor in the sense of regression because the process of finding it carries neither seismic concepts nor statistical information rather it relies on an abstract norm in the space of elasticity tensors to include seismic concepts and statistical information we distinguish between the closest tensor of particular symmetry and the effective one the former is the initial guess to search for the latter

a domain decomposition approach for full field measurements based identification of local elastic parameters abstract we propose a domain decomposition formalism specifically designed for the identification of local elastic parameters based on full field measurements this technique is made possible by a multi scale implementation of the constitutive compatibility method contrary to classical approaches the constitutive compatibility method resolves first some eigenmodes of the stress field over the structure rather than directly trying to recover the material properties a two steps micro macro reconstruction of the stress field is performed a dirichlet identification problem is solved first over every subdomain the macroscopic equilibrium is then ensured between the subdomains in a second step we apply the method to large linear elastic 2d identification problems to efficiently produce estimates of the material properties at a much lower computational cost than classical approaches

a learning result for continuous time recurrent neural networks abstract the following learning problem is considered for continuous time recurrent neural networks having sigmoidal activation functions given a black box representing an unknown system measurements of output derivatives are collected for a set of randomly generated inputs and a network is used to approximate the observed behavior it is shown that the number of inputs needed for reliable generalization the sample complexity of the learning problem is upper bounded by an expression that grows polynomially with the dimension of the network and logarithmically with the number of output derivatives being matched

mindlin s problem for an anisotropic piezoelectric half space with general boundary conditions this paper considers mindlin s problem in an anisotropic and piezoelectric halfspace with general boundary conditions including 16 different sets of surface conditions the green s function due to

on realizability of neural networks based input output models in the classical state space form this paper proves that the typical neural network based input output model does not have a state space realization and suggests the additive nonlinear auto regressive with exogenous input anarx structure as an excellent choice for neural network based input output models the advantage of the anarx model is that the time steps in the argument are pair wise decomposed which allows the anarx model to be realized in state space and to be linearized via dynamic output feedback moreover accessibility of the state space realization has been proved

symmetry characterization and measurement errors of elasticity tensors it is often desirable to approximate a full anisotropic tensor given by 21 independent parameters by one with a higher symmetry if one considers measurement errors of an elasticity tensor the standard approaches of finding the best approximation by a higher symmetric tensor do not produce the most likely tensor to find such a tensor i replace the distance metric used in previous studies with one based on probability distribution functions of the errors of the measured quantities in the case of normally distributed errors the most likely tensor with higher symmetries coincides with the closest higher symmetric tensor using a deviation scaled euclidean metric

three dimensional green s functions in anisotropic piezoelectric solids abstract explicit expressions for three dimensional extended green s displacements in general anisotropic piezoelectric solids are derived a very efficient procedure for the numerical evaluation of the derivatives of the extended green s displacements is also proposed numerical comparisons are carried out for a transversely isotropic piezoelectric solid for which exact closed form solutions are available it is found that the extended green s displacements and their derivatives obtained with the present explicit formulation are in perfect agreement with the exact closed form solutions these green s functions can be used in the boundary integral equations for piezoelectric solids of general anisotropy and for subsequent numerical solutions of these equations by means of the boundary element method

a classical perturbation technique which is valid for large parameters there are various perturbation techniques for constructing analytical approximations to the oscillatory solutions of second order non linear differential equations 1 2 but many of them apply to weakly non linear cases only to overcome the limitations many novel techniques have been proposed in recent years for example cheung et al 3 proposed a modified lindstedt poincare method and lim et al 4 presented a modified mickens procedure for certain non linear oscillators recently he 5 proposed a perturbation technique which is valid for large parameters but unfortunately o1 and b in ref 5 are the functions of z which is unknown the main purpose of this paper is to point out that there already exists a classical perturbation technique which is valid for large parameters in this paper the following well known duffing equation is considered

identification of symmetry type of linear elastic stiffness tensor in an arbitrarily orientated coordinate system abstract we develop a method through the mirror plane mp to identify the symmetry type of linear elastic stiffness tensor whose components are given with respect to an arbitrarily oriented coordinate system the method is based on the irreducible decomposition of high order tensor into a set of deviators and the multipole representation of a deviator into a scalar and a unit vector set since a unit vector depends on two euler angles we can illustrate the mp normals of the elastic tensor as zeros of a characteristic function on a unit disk and identify its symmetry immediately which is clearer and simpler than the methods proposed before furthermore by finding the common mps of three unit vector sets using fortran recipes we can also analytically recognize the symmetry type first and then recover the natural coordinate system associated with the linear elastic tensor the structures of linear elastic stiffness tensors of real materials with all possible anisotropies are investigated in detail

subdivision schemes for the fair discretization of the spherical motion group we present two subdivision schemes for the fair discretization of the spherical motion group the first one is based on the subdivision of the 600 cell according to the tetrahedral octahedral subdivision scheme in s schaefer j hakenberg j warren smooth subdivision of tetrahedral meshes in r scopigno d zorin eds eurographics symposium on geometry processing 2004 pp 151 158 the second presented subdivision scheme is based on the spherical kinematic mapping in the first step we discretize an elliptic linear congruence by the icosahedral discretization of the unit sphere then the resulting lines of the elliptic three space are discretized such that the difference in the maximal and minimal elliptic distance between neighboring grid points becomes minimal

distance of a stiffness tetrad to the symmetry classes of linear elasticity abstract in the scope of linear anisotropic elasticity the fourth order elasticity tensor or tetrad has to be identified this can be done either by measurements or by numerical simulations an important task is then to identify a given tetrad probably with some experimental or numerical scattering with one of the symmetry classes for this purpose one needs a distance function between a given tetrad and the class of all tetrads with a particular symmetry which is zero if the tetrad obeys this symmetry or non zero otherwise in this paper we present a fast method to solve these problems we firstly introduce the 8th order projectors that map any stiffness tetrad into the part that is invariant under the action of a specific fixed symmetry group for this purpose we consider the seven out of the eight symmetry classes that are distinguishable in linear elasticity secondly since the symmetry axes of the specific stiffness tensor under consideration is generally not aligned with the used tensorial basis of the projector we need to rotate the sample stiffness the optimal orientation is obtained when the distance between the rotated stiffness and the rotated and projected stiffness is minimal thus we need to apply only linear mappings and minimize over three euler angles the latter is quite simple as the domain of the euler angles is periodic and the number of local minima is limited this procedure has the advantage that it is applicable in an algorithmic manner and does not require an a priori identification of symmetry planes symmetry axes or component symmetries which are only apparent under special choices for the tensorial basis

the cowin mehrabadi theorem for an axis of symmetry abstract the well known cowin mehrabadi theorem deals with necessary and sufficient conditions for a normal n to a symmetry plane necessary conditions require that n be a common eigenvector of c ijkk c ikjk and c ijkl n j n l it is shown that a vector parallel to an axis of symmetry must also satisfy these conditions an axis of rotational symmetry is also a normal to a plane of symmetry except in the case of a trigonal material being a common eigenvector of c ijkk and c ikjk belonging to a nondegenerate eigenvalue guarantees it to be an axis of symmetry

complete controllability of continuous time recurrent neural networks this paper studies controllability for the class of control systems commonly called continuous time recurrent neural networks it is shown that under a generic condition on the input matrix the system is controllable for every possible state matrix the result holds when the activation function is the hyperbolic tangent

recurrent neural networks coupled with linear systems observability in continuous and discrete time we give necessary and sufficient conditions for observability of a class of recurrent neural networks having a subsystem where the activation function is the identity an algorithm for computing all pairs of indistinguishable states is also given

a stochastic model for elasticity tensors with uncertain material symmetries in this paper we consider the probabilistic modeling of media exhibiting uncertainties on material symmetries more specifically we address both the construction of a stochastic model and the definition of a methodology allowing the numerical simulation and consequently the inverse experimental identification of random elasticity tensors whose mean distance in a sense to be defined to a given class of material symmetry is specified following the eigensystem characterization of the material symmetries the proposed approach relies on the probabilistic model derived in mignolet and soize 2008 allowing the variance of selected eigenvalues of the elasticity tensor to be partially prescribed in this context a new methodology regarding in particular the parametrization of the model is defined and illustrated in the case of transversely isotropic materials the efficiency of the approach is demonstrated by computing the mean distance of the random elasticity tensor to a given material symmetry class the distance and projection onto the space of transversely isotropic tensors being defined by considering the riemmanian metric and the euclidean projection respectively it is shown that the methodology allows the above distance to be partially reduced as the overall level of statistical fluctuations increases no matter the initial distance of the mean model used in the simulations a comparison between this approach and the initial nonparametric approach introduced in soize 2008 is finally provided

bounds of the induced norm and model reduction errors for systems with repeated scalar nonlinearities the class of nonlinear systems described by a discrete time state equation containing a repeated scalar nonlinearity as in recurrent neural networks is considered sufficient conditions are derived for the stability and induced norm of such systems using positive definite diagonally dominant lyapunov functions or storage functions satisfying appropriate linear matrix inequalities results are also presented for model reduction errors for such systems

general solution for eshelby s problem of 2d arbitrarily shaped piezoelectric inclusions abstract eshelby s problem of piezoelectric inclusions arises sometimes in exploiting the electromechanical coupling effect in piezoelectric media for example it intervenes in the nanostructure design of strained semiconductor devices involving strain induced quantum dot qd and quantum wire qwr growth using the extended stroh formalism the present work gives a general analytical solution for eshelby s problem of two dimensional arbitrarily shaped piezoelectric inclusions the key step toward obtaining this general solution is the derivation of a simple and compact boundary integral expression for the eigenfunctions in the extended stroh formalism applied to eshelby s problem the simplicity and compactness of the boundary integral expression derived make it much less difficult to analytically tackle eshelby s piezoelectric problem for a large variety of non elliptical inclusions in the present work explicit analytical solutions are obtained and detailed for all polygonal inclusions and for the inclusions characterized by jordan s curves and laurent s polynomials by considering the piezoelectric material gaas 110 the analytical solutions provided are illustrated numerically to verify the coincidence between different expressions and to clarify the jump across the boundary of the inclusion and the singularity around the corner of the inclusion

generalized cowin mehrabadi theorems and a direct proof that the number of linear elastic symmetries is eight abstract the cowin mehrabadi theorem is generalized to allow less restrictive and more flexible conditions for locating a symmetry plane in an anisotropic elastic material the generalized theorems are then employed to prove that the number of linear elastic symmetries is eight the proof starts by imposing a symmetry plane to a triclinic material and after new elastic symmetries are found another symmetry plane is imposed this process exhausts all possibility of elastic symmetries and shows that there are only eight elastic symmetries at each stage when a new symmetry plane is added explicit results are obtained for the locations of the new symmetry plane that lead to a new elastic symmetry it takes as few as three and at most five symmetry planes to reduce a triclinic material which has no symmetry plane to an isotropic material for which any plane is a symmetry plane

invariants and approximate solutions for certain non linear oscillators by means of the field method certain strongly non linear conservative oscillators are approached with the field method which is combined with the convolution integral method a complete set of their adiabatic invariants are derived on the basis of which approximate solutions for motion can be obtained

uniqueness of circuits and systems containing one nonlinearity we study systems containing one memoryless nonlinearity we show that two such systems have the same i o operator only when they are related by simple scaling delay and loop transformations the theory is applied to one port networks containing one nonlinear element

limit cycles of non smooth oscillators abstract an artificial parameter linstedt poincare method based on the introduction of a linear stiffness term a change of independent variable and the expansion of both the solution and the frequency of oscillation in power series of the artificial parameter and the theory of generalized functions are used to determine the frequency of limit cycles of non smooth oscillators the method is applied to three non smooth oscillators and it is shown that the first order approximation coincides with those obtained by means of harmonic balance and parameter expansion techniques whereas higher order ones are given in terms of convergent series

a convolution integral method for certain strongly nonlinear oscillators a modification of the convolution integral method for linear oscillators is presented for the analysis of certain strongly nonlinear oscillators the modification provides an iteration scheme two examples are given to illustrate the effectiveness of the proposed method

determination of the symmetries of an experimentally determined stiffness tensor application to acoustic measurements abstract for most materials the symmetry group is known a priori and deduced from the realization process this allows many simplifications for the measurements of the stiffness tensor we deal here with the case where the symmetry is a priori unknown as for biological or geological materials or when the process makes the material symmetry axis uncertain some composites monocrystals the measurements are then more complicated and the raw stiffness tensor obtained does not exhibit any symmetry in the voigt s matrical form as it is expressed in the arbitrarily chosen specimen s base a complete ultrasonic measurement of this stiffness tensor from redundant measurements is proposed in a second time we show how to make a plane symmetry pole figure able to give visual information about the quasi symmetries of a raw stiffness tensor determined by any measurement method finally we introduce the concept of distance from a raw stiffness tensor to one of the eight symmetry classes available for a stiffness tensor the method provides the nearest tensor to the raw stiffness tensor possessing a chosen symmetry class with its associated natural symmetry base

an artificial parameter decomposition method for nonlinear oscillators applications to oscillators with odd nonlinearities abstract a method for obtaining series solutions of nonlinear second order ordinary differential equations based on the introduction of an artificial parameter is presented and shown to be identical to the well known adomian s decomposition technique the method is formulated in both integral and differential forms for the determination of the limit cycle of oscillators with odd nonlinearities two differential forms and one integral form of the artificial parameter method are presented these versions are based on introducing a linear stiffness term with an unknown frequency and the use of either the original independent variable or a new independent variable that depends linearly on the unknown frequency of the oscillator the three formulations provide identical results and their application to eight oscillators with odd nonlinearities shows that the artificial parameter technique presented in this paper predicts the same frequency of oscillation as the harmonic balance and iterative techniques as well as modified linstedt poincare methods however the method presented here is based on the introduction of an artificial parameter and does not require the presence of small perturbation parameters in the ordinary differential equation it is also shown that two and three level iterative methods yield the same frequency of oscillation as the artificial parameter technique presented in this paper provided that the initial iterate of the former coincides with the leading order solution of the latter and only one iteration of iterative techniques and only the second approximation of the artificial parameter method are determined

elastic moduli approximation of higher symmetry for the acoustical properties of an anisotropic material the issue of how to define and determine an optimal acoustical fit to a set of anisotropic elastic constants is addressed the optimal moduli are defined as those which minimize the mean squared difference in the acoustical tensors between the given moduli and all possible moduli of a chosen higher material symmetry the solution is shown to be identical to minimizing a euclidean distance function or equivalently projecting the tensor of elastic stiffness onto the appropriate symmetry this has implications for how to best select anisotropic constants to acoustically model complex materials

maxwell s multipole representation of traceless symmetric tensors and its application to functions of high order tensors it is known from the theory of group representations that a general tensor can be expressed as a sum of traceless symmetric tensors in this paper based on sylvester9s theorem it is shown that a general traceless symmetric tensor of any finite order m in three dimensions can be expressed as the traceless symmetric part of tensor product of m unit vectors called the multipoles multiplied by a positive scalar the above two basic structures of tensors allow us to easily give complete and irreducible representations for tensor functions with high order tensor variables since those for tensor functions of vectors are well established in the literature examples are given for scalar valued functions of a single fourth order tensor of the elastic type and of a number of vectors and second order tensors in 1970 backus gave an alternative proof of sylvester9s theorem which shows how to compute the multipoles since backus9s result is not so well known to the community of researchers working on continuum mechanics in the present paper a direct without using sylvester9s theorem and constructive establishment of maxwell9s multipole representation is provided which is closer in spirit to a more modern approach to this topic

elasticity and symmetry of triangular lattice materials the elastic tensor of any triangular 2d lattice material is given with re spect to the geometry and the mechanical properties of the links between the nodes the links can bear central forces tensional material for example with hinged joints momentums flexural materials or a combination of the two the symmetry class of the stiffness tensor is detailed in any case by using the invariants of forte and vianello a distinction is made between the trivial cases where the elasticity symmetry group corresponds to the mi crostructure s symmetry group and the non trivial cases in the opposite case interesting examples of isotropic auxetic materials with negative poisson s ratio and non trivial materials with isotropic elasticity but anisotropic frac turation weak direction are shown the proposed set of equations can be used in a engineering process to create a 2d triangular lattice material of the desired elasticity

stabilization and performance synthesis for systems with repeated scalar nonlinearities the class of nonlinear systems described by a discrete time state equation containing a repeated scalar nonlinearity as in recurrent neural networks is considered given a plant of this form sufficient conditions are derived for 1 the parametrization of all controllers of the same form such that the closed loop is stable in the sense of a diagonally dominant lyapunov function and 2 the synthesis of a controller of the same form so that the induced norm of the closed loop is under a prescribed level several of these conditions can be written into linear matrix inequalities

on the variational iteration method and other iterative techniques for nonlinear differential equations abstract a variety of iterative methods for the solution of initial and or boundary value problems in ordinary and partial differential equations is presented these iterative procedures provide the solution or an approximation to it as a sequence of iterates for initial value problems it is shown that these iterative procedures can be written in either an integral or differential form the integral form is governed by a volterra integral equation whereas the differential one can be obtained from the volterra representation by simply differentiation it is also shown that integration by parts variation of parameters adjoint operators green s functions and the method of weighted residuals provide the same volterra integral equation and that this equation in turn can be written as that of the variational iteration method it is therefore shown that the variational iteration method is nothing else by the picard lindelof theory for initial value problems in ordinary differential equations and banach s fixed point theory for initial value problems in partial differential equations and the convergence of these iterative procedures is ensured provided that the resulting mapping is lipschitz continuous and contractive it is also shown that some of the iterative methods for initial value problems presented here are special cases of the bellman kalaba quasilinearization technique provided that the nonlinearities are differentiable with respect to the dependent variable and its derivatives but such a condition is not required by the techniques presented in this paper for boundary value problems it is shown that one may use the iterative procedures developed for initial value problems but the resulting iterates may not satisfy the boundary conditions and two new iterative methods governed by fredholm integral equations are proposed it is shown that the resulting iterates satisfy the boundary conditions if the first one does so the iterative integral formulation presented here is applied to ten nonlinear oscillators with odd nonlinearities and it is shown that its results coincide with those of differential two and three level iterative techniques harmonic balance procedures and standard and modified linstedt poincare techniques the method is also applied to two boundary value problems

elastic and piezoelectric fields due to polyhedral inclusions abstract we derive explicit closed form expressions describing elastic and piezoelectric deformations due to polyhedral inclusions in uniform half space and bi materials our analysis is based on the linear elasticity theory and green s function method the method involves evaluation of volume and surface integrals of harmonic and bi harmonic potentials in case of polyhedra such integrals are expressed through algebraic functions our results generalize numerous studies on this subject and they allow to obtain fully analytical solutions for a number of physical and engineering problems in the limiting case of an infinite space our relations have an essentially more compact form than relations obtained by other authors we present solutions to classical mindlin and cherruti problems we describe the elastic relaxation of a misfitting polygonal quantum dot in bi materials assuming isotropic and vertically isotropic properties it is explained how to analyze non hydrostatic and non uniform inclusions we also study piezoelectric fields induced by inclusions in materials with cubic and hexagonal lattices among other results we have found that a cubic inclusion in an isotropic material reproduces fields of quantum dots in gaas 0 0 1 and gaas 1 1 1 depending on the orientation of the cube this suggests that one can qualitatively model crystals with different lattices by choosing an appropriate inclusion shape

further results on controllability of recurrent neural networks this paper studies controllability properties of recurrent neural networks the new contributions are 1 an extension of a previous result to a slightly different model 2 a formulation and proof of a necessary and sufficient condition and 3 an analysis of a low dimensional case for which the hypotheses made in previous work do not apply

symmetry types of the piezoelectric tensor and their identification the third order linear piezoelectricity tensor seems to be simpler than the fourth order linear elasticity one yet its total number of symmetry types is larger than the latter and the exact number

fourier integral representation of the green function for an anisotropic elastic half space this paper describes the development of a fourier integral representation of the green function for an anisotropic elastic half space the representation for an isotropic material is integrated in closed form and shown to reduce to mindlin s solution an application of the anisotropic representation is made to deduce the exact displacement caused by a two dimensional periodic vertical force distribu tion applied to the interior of a half space with cubic material symmetry

solutions of nonlinear oscillators with fractional powers by an iteration procedure a modified iteration procedure is applied to nonlinear oscillations with fractional powers with the procedure the excellent approximate frequencies and the corresponding periodic solutions can be easily obtained

a classical iteration procedure valid for certain strongly nonlinear oscillators a classical iteration procedure is applied to nonlinear oscillations of conservative single degree of freedom systems with odd nonlinearity with the procedure the analytical approximate frequency and the corresponding periodic solution valid for small as well as large amplitudes of oscillation can be obtained two examples are given to illustrate the accuracy and effectiveness of the method another advantage of this classical iteration approach is that it also works if the linear part of restoring force is zero

solutions for transversely isotropic piezoelectric infinite body semi infinite body and bimaterial infinite body subjected to uniform ring loading and charge abstract based on the fundamental solutions for transversely isotropic piezoelectric materials the fundamental solutions of axisymmetric problems are derived by integration and explicit expressions for three possible cases of different characteristic roots and multiple roots are all presented in the case of s 1 s 2 s 3 s 1 based on the greens functions for semi infinite piezoelectric body and bimaterial infinite piezoelectric body the greens functions for axisymmetric problems of semi infinite body and bimaterial infinite body are obtained taking pzt 4 as an example numerical computations are conducted by use of the fundamental solutions to axisymmetric problems comparison of the calculated results with those of fem shows good agreement between them

green s function of anisotropic piezoelectricity in this paper we give an algebraic formula for the green s function of piezoelectricity that is we write the green s function of piezoelectricity using the eigenvectors and or the generalized eigenvectors of the piezoelectric version of stroh s eigenvalue problem moreover applying this formula to piezoelectricity of hexagonal symmetry 622 we obtain an explicit expression of the green s function

solutions of the duffing harmonic oscillator by an iteration procedure a modified iteration procedure is applied to the duffing harmonic oscillator with the procedure the excellent approximate frequencies and the corresponding periodic solutions can be easily obtained

eshelby s problem for two dimensional piezoelectric inclusions of arbitrary shape eshelby s problem for piezoelectric inclusions of arbitrarily shaped crosssection remains a challenging topic in this paper a simple method is presented to obtain an analytic solution for eshelby

observability of automata networks fixed and switching cases automata networks are a class of fully discrete dynamical systems which have received considerable interest in various different areas this brief addresses the observability of automata networks and switched automata networks in a unified framework and proposes simple necessary and sufficient conditions for observability the results are achieved by employing methods from symbolic computation and are suited for implementation using computer algebra systems several examples are presented to demonstrate the application of the results

the relationship between damage variables and their evolution laws and microstructural and physical properties the major objective of this paper is to give a rational approach to identify the damage parameters in tensorial form based on the microstructure of the defects voids cavities microcracks and the overall physical properties of a solid material first the general representations for the effective linear and nonlinear reversible physical properties e g elastic and piezoelectric moduli of a material representative volume element rve containing a single defect of any shape are investigated second it is emphasized that the orientation distribution functions odfs of shapes separations etc of defects constitute the dominant and physically measurable signatures of the changing microstructure of a damaged material by assuming that the matrix behaves reversibly during damage nucleation and growth third it is shown that the odfs can be expanded as absolutely convergent fourier series with irreducible tensorial coefficients and that these infinitely many irreducible tensorial coefficients constitute the full list of generic damage variables furthermore to specify any given physical property only certain leading tensorial coefficients in these series are needed and therefore these leading coefficients act as the real damage tensors for such a physical property these physically based damage tensors vary significantly from one physical property to another for example it is shown that only the second and fourth tensorial coefficients effect the linear elastic moduli while only the first and third tensorial coefficients are needed in linear piezoelectricity theory finally it is observed from a simple example that the evolution equations for these physically based damage tensors normally involved tensorial terms of a higher order than those needed to define the considered physically based damage tensors consequently the evolution equations are not self closed

on linstedt poincare techniques for the quintic duffing equation abstract an artificial parameter method for the quintic duffing equation is presented the method is based on the introduction of a linear stiffness term and a new dependent variable both of which are proportional to the unknown frequency of oscillation the introduction of an artificial parameter and the expansion of both the solution and the unknown frequency of oscillation in series of the artificial parameter and results in linear ordinary differential equations at each order in the parameter by imposing the nonsecularity condition at each order in the expansion the method provides different approximations to both the solution and the frequency of oscillation the method does not require that a small parameter be present in the governing equation and its results are compared with those of linstedt poincare modified linstedt poincare harmonic balance and galerkin techniques it is shown that these four techniques predict the same first order approximation to the frequency of oscillation as the artificial parameter method presented in this paper and the latter introduces higher order corrections at second order whereas similar corrections are introduced by the linstedt poincare and modified linstedt poincare methods at orders equal to and higher than three

a non simultaneous variational approach for the oscillators with fractional order power nonlinearities abstract this paper is concerned with a class of conservative oscillators the restitution force of which is of a power form which includes positive non integer exponents it is shown how an approximate lagrangian and hamilton s variational principle can be used to obtain a second order approximate solution for their free vibrations due to the fact that in a general case when the restoring force is multi term the period cannot be obtained from the energy conservation law in a closed form the problem is formulated as a one point boundary value problem and a non simultaneous variation is introduced the explicit expressions for the amplitudes and frequency of oscillations are derived in which there are no restrictions on the values of the non integer powers the analytically obtained results are compared with numerical results as well as with some approximate analytical results from the literature