transverse vibrations of non homogeneous orthotropic rectangular plates of variable thickness a spline technique an analysis and numerical results are presented for free transverse vibrations of non homogeneous orthotropic rectangular plates of non uniform thickness and resting on an elastic foundation of winkler type on the basis of classical plate theory the non homogeneity of the plate material is assumed to arise due to the exponential variation in young s moduli and density along one direction following levy approach i e the two parallel edges are simply supported the fourth order differential equation governing the motion of such plates of exponentially varying thickness in one direction has been solved by using the quintic splines interpolation technique for three different combinations of clamped simply supported and free boundary conditions at the other two edges effect of the non homogeneity and elastic foundation together with other plate parameters such as orthotropy aspect ratio and thickness variation on the natural frequencies of vibration is illustrated for the first three modes of vibration normalized displacements are presented for specified plates for all the three boundary conditions

generic buckling curves for specially orthotropic rectangular plates using a double affine transformation the classical buckling equation for specially orthotropic plates and the corresponding virtual work theorem are presented in a particularly simple fashion these dual representations are characterized by a single material constant called the generalized rigidity ratio whose range is predicted to be the closed interval from 0 to 1 if this prediction is correct then the numerical results using a ratio greater than 1 in the specially orthotropic plate literature are incorrect when natural boundary conditions are considered a generalized poisson s ratio is introduced thus the buckling results are valid for any specially orthotropic material hence the curves presented in the text are generic rather than specific the solution trends are twofold the buckling coefficients decrease with decreasing generalized rigidity ratio and when applicable they decrease with increasing generalized poisson s ratio since the isotropic plate is one limiting case of the above analysis it is also true that isotropic buckling coefficients decrease with increasing poission s ratio

a generalized approach for implementing general boundary conditions in the gdq free vibration analysis of plates abstract a new approach for implementing general boundary conditions in the gdq free vibration analysis of rectangular plates is presented in this paper the proposed approach directly couples the boundary conditions with the governing equations and is referred to as the cbcge approach it can be applied to any combination of simply supported clamped and free boundary conditions the generality and accuracy of the cbcge approach are demonstrated through its application to the vibration analysis of a rectangular plate with various combinations of free edges and corners in particular the effect of grid point distribution on the numerical results for plates with free boundary conditions is discussed and a new grid point distribution is suggested

a differential quadrature analysis of vibration and buckling of an ss c ss c rectangular plate loaded by linearly varying in plane stresses abstract thin rectangular plates having two opposite edges simply supported with those edges subjected to linearly varying in plane stresses and the other two edges clamped are encountered in engineering practice recently leissa and kang used the classical power series method and obtained the first known exact vibration and some buckling solutions the classical plate theory based on the kirchhoff hypothesis is employed in the analysis the relatively wild character of the convergence is observed however and 20 or 30 more terms of the series are needed to obtain reasonably accurate results the differential quadrature dq method has proved an accurate and computationally efficient numerical method thus the dq method is used to study the vibration and buckling of an ss c ss c rectangular plate loaded by linearly varying in plane stresses convergence study shows that dq method with 15 15 or more non uniform grid points can yield very accurate results for cases considered exactly the same accurate results as of leissa and kang are easy to reproduce

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

a new method for free vibration and buckling analysis of rectangular orthotropic plates a new method for free vibration and buckling analysis of rectangular orthotropic plates is presented the proposed method differs significantly from previously published methods in that it allows obtaining practically exact results for free vibration and buckling of orthotropic plates by enhancing the method of superposition the boundary value problem is essentially reduced to an infinite system of linear algebraic equations of particular significance of this research is that the existence of bounded solution of the infinite system after elimination of the unknowns has been captured in an elegant but quantitative way to converge upon any natural frequency or critical buckling load of the orthotropic plate to any desired accuracy the theory is applied to the particular case of orthotropic plates with clamped edges but it can be extended to other boundary conditions buckling analysis is carried out as a degenerate case of free vibration at zero frequency comparisons of computed results from the present theory with those available in the literature are made wherever possible and some noteworthy conclusions are drawn

generalized spatio chromatic diffusion a framework for diffusion of color images is presented the method is based on the theory of thermodynamics of irreversible transformations which provides a suitable basis for designing correlations between the different color channels more precisely we derive an equation for color evolution which comprises a purely spatial diffusive term and a nonlinear term that depends on the interactions among color channels over space we apply the proposed equation to images represented in several color spaces such as rgb cielab opponent colors and ihs

transverse vibrations of rectangular plates with edges elastically restrained against translation and rotation abstract the fundamental frequency coefficient for a rectangular plate with edges elastically restrained against both translation and rotation is calculated by using polynomial coordinate functions and the rayleigh ritz method the approach is simple and straightforward and allows the solution of a rather difficult elastodynamics problem complicating factors orthotropic properties in plane forces concentrated masses etc can also be taken into account without formal difficulties

the strong relaxation limit of the multidimensional isothermal euler equations we construct global smooth solutions to the multidimensional isothermal euler equations with a strong relaxation when the relaxation time tends to zero we show that the density converges towards the solution to the heat equation

axisymmetric vibrations of an isotropic elastic non homogeneous circular plate of linearly varying thickness abstract free axisymmetric vibrations of an isotropic elastic non homogeneous circular plate of linearly varying thickness have been studied on the classical theory of plates the non homogeneity of the material of the plate is assumed to arise due to the variation of young s modulus and density with the radius vector whereas poisson s ratio is assumed to remain constant the governing differential equation of motion is solved by the method of frobenius the transverse displacement of the plate has been expressed as a power series in terms of the radial co ordinate the frequency parameters corresponding to the first two modes of vibration have been computed for different values of the non homogeneity parameter and taper constant and for clamped and simply supported edge conditions of the plate a comparison between the numerical results for homogeneous and non homogeneous material of the plate is also made

calculation of the natural frequencies of composite plates by the rayleigh ritz method with orthogonal polynominals orthogonal polynomials are used as admissible functions and the approach has been found to be numerically stable

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

theory and experiments for nonlinear vibrations of imperfect rectangular plates with free edges abstract large amplitude vibrations of completely free rectangular plates are investigated for the first time nonlinear higher order shear deformation theory is used and the nonlinear response to transverse harmonic excitation in the frequency neighborhood of the fundamental mode is studied geometric imperfections are taken into account the numerical analysis is carried out in two steps first the plate displacements and rotations are expanded in terms of chebyshev polynomials and a linear analysis is conducted to obtain the natural frequencies and modes of vibration then the energy functional is discretized by using the natural modes of vibration and a system of nonlinear ordinary differential equations with cubic and quadratic nonlinear terms is obtained a pseudo arc length continuation and collocation scheme is used for bifurcation analysis of periodic solutions moreover to validate the numerical results experimental tests have been conducted for the fundamental vibration mode at several harmonic excitation amplitudes by using a laser doppler vibrometer to characterize the nonlinear response of the plate with imperfections and closed loop control of the excitation the effects of geometric imperfections on the trend of nonlinearity and on natural frequencies are fully discussed and the convergence of the numerical solutions has been verified

information measures in scale spaces this article investigates renyi s 1976 generalized entropies under linear and nonlinear scale space evolutions of images scale spaces are useful computer vision concepts for both scale analysis and image restoration we regard images as densities and prove monotony and smoothness properties for the generalized entropies the scale space extended generalized entropies are applied to global scale selection and size estimations finally we introduce an entropy based fingerprint description for textures

global quasi neutral limit of euler maxwell systems with velocity dissipation abstract we consider smooth solutions to the cauchy problem for an isentropic euler maxwell system with velocity dissipation and small physical parameters for initial data uniformly close to constant equilibrium states we prove the global in time convergence of the system as the parameters go to zero the limit systems are the e mhd system and the incompressible euler equations both with velocity dissipation the proof of the results relies on a single uniform energy estimate with respect to the time and the parameters together with compactness arguments for this purpose the classical energy estimates for the symmetrizable hyperbolic system are not sufficient we construct a lyapunov type energy by controlling the divergence and the curl of the velocity the electric and magnetic fields

vibrations of clamped orthotropic rectangular plates abstract a solution in a double trigonometric series form is proposed for a forced vibration problem of a clamped orthotropic rectangular plate with the increasing number of terms of the series the solution satisfies more closely both the boundary condition and the governing equation the accuracy of the solution is discussed numerically as an example the solution is applied to the iteration method for the analysis of the free vibration problem of a clamped orthotropic rectangular plate very accurate natural frequencies are obtained for typical plates

analyzing the free vibrations of a plate using finite difference and differential transformation method this paper analyses the free vibrations of clamped and simply supported rectangular thin plates a hybrid method which combines the finite difference method and the differential transformation method is employed to reduce the partial differential equations of the plate to a set of algebraic equations the investigative parameters include the order of the differential transformation the number of sub domain spaces the variable conditions and the type of initial condition the numerical simulation results indicate that the solution of the natural frequency is more accurate when calculated using a higher number of sub domains the effect of the difference transformation order value k on the solution of the natural frequency is not significant when the combined t spectra method and differential transformation method is applied the initial mode shape of the plate has a significant influence on the solution of the natural frequency the current modeling results confirm the viability of using the hybrid method proposed in this paper to solve the free vibrations and natural frequency of clamped and simply supported plates

free vibration analysis of orthotropic rectangular plates with variable thickness and general boundary conditions a discrete method is developed for analyzing the free vibration problem of orthotropic rectangular plates with variable thickness the green function which is obtained by transforming the differential equations into integral equations and using numerical integration is used to establish the characteristic equation of the free vibration the effects of the aspect ratios boundary conditions the variation of the thickness on the frequencies are considered by comparing the numerical results obtained by the present method with the those previously published the efficiency and accuracy of the present method are investigated the frequency parameters are obtained for the orthotropic plates with general boundary conditions and variable thickness in one or two directions the model shapes are given for some of the square plates with three kinds of thickness variations

on the use of orthogonal polynomials in the rayleigh ritz method for the study of the flexural vibration and buckling of isotropic and orthotropic rectangular plates series composed of recently proposed orthogonal polynomial functions are used in the rayleigh ritz method to generate results for a number of flexural vibration and buckling problems for rectangular isotropic and orthotropic plates it is demonstrated that the approach yields excellent results not only for natural frequencies and buckling loads but also for the more sensitive mode shape bending moment and shear force distribution problem

the free vibrations of tapered rectangular plates using a new set of beam functions with the rayleigh ritz method abstract in19991999 academic pressacademic pressthis paper the free vibrations of a wide range of non uniform rectangular plates in one or two directions are considered the domain of the plate is bounded by copyright x 1a a and y 1b b in rectangular co ordinates the thickness of the plate is continuously varying and proportional to the power functionxsyt a variety of tapered rectangular plates can be described by giving the taper factors s and t different values s and t may be given arbitrary real numbers if both 1 0 and 1 0 or arbitrary non negative numbers if 1 0 or 1 0 the uniform rectangular plate is a special case by letting both s and t equal to zero a new set of admissible functions which are the static solutions of the tapered beam or a strip taken from the tapered rectangular plate under an arbitrary static load expanded into a taylor series is developed unlike conventional admissible functions the set of static beam functions will vary appropriately with the thickness variation of the plate the eigenfrequency equation is obtained by the use of the rayleigh ritz method a general computer program has been compiled and some numerical results are tabulated on the basis of comparison with available results in the literature it is shown that the first few eigenfrequencies can be obtained with good accuracy by using only a small number of terms of the static beam functions

analysis of the m1 model well posedness and diffusion asymptotics abstract this paper is devoted to the analysis of the m 1 model which arises in radiative transfer theory the derivation of the model is based on the entropy minimization principle which leads to a hyperbolic system of balance laws with relaxation in the multi dimensional case we establish the existence uniqueness of a globally defined smooth solution under a suitable smallness condition on the initial data in the one dimensional case we show that the smallness condition does not depend on the particles mean free path so that we can also rigorously justify the consistency of the model with the diffusion asymptotics the result extends the analysis of coulombel et al j f coulombel f golse t goudon diffusion approximation and entropy based moment closure for kinetic equations asymptotic analysis 45 2005 1 39 to the case where the entropy functional accounts for relaxation towards the planckian state which is physically more relevant

numerical approximation of the euler maxwell model in the quasineutral limit we derive and analyze an asymptotic preserving scheme for the euler maxwell system in the quasi neutral limit we prove that the linear stability condition on the time step is independent of the scaled debye length l when l 0 numerical validation performed on riemann initial data and for a model plasma opening switch device show that the ap scheme is convergent to the euler maxwell solution when dx l 0 where dx is the spatial discretization but when l dx 0 the ap scheme is consistent with the quasi neutral euler maxwell system the scheme is also perfectly consistent with the gauss equation the possibility of using large time and space steps leads to several orders of magnitude reductions in computer time and storage

natural frequencies of rectangular plates using a set of static beam functions in rayleigh ritz method abstract a fast converging series consisting of a set of static beam functions which is a combination of sine series and polynomials is developed and these functions are used as the basis functions in the rayleigh ritz method to study the vibrational characteristics of thin isotropic rectangular plates in applications a relatively small number of functions are required and consequently a modest amount of computation is necessary the approach is very simple and straightforward some numerical results are given for rectangular plates with various aspects ratios and boundary conditions good accuracy and fast convergence of the method are demonstrated by comparison with available results complicating factors orthotropic properties in plane forces etc can also be taken into account without formal difficulties

behavioral analysis of anisotropic diffusion in image processing in this paper we analyze the behavior of the anisotropic diffusion model of perona and malik 1990 the main idea is to express the anisotropic diffusion equation as coming from a certain optimization problem so its behavior can be analyzed based on the shape of the corresponding energy surface we show that anisotropic diffusion is the steepest descent method for solving an energy minimization problem it is demonstrated that an anisotropic diffusion is well posed when there exists a unique global minimum for the energy functional and that the ill posedness of a certain anisotropic diffusion is caused by the fact that its energy functional has an infinite number of global minima that are dense in the image space we give a sufficient condition for an anisotropic diffusion to be well posed and a sufficient and necessary condition for it to be ill posed due to the dense global minima the mechanism of smoothing and edge enhancement of anisotropic diffusion is illustrated through a particular orthogonal decomposition of the diffusion operator into two parts one that diffuses tangentially to the edges and therefore acts as an anisotropic smoothing operator and the other that flows normally to the edges and thus acts as an enhancement operator

vibration analysis of non homogeneous circular plate of nonlinear thickness variation by differential quadrature method free axisymmetric vibrations of non homogeneous isotropic circular plates of nonlinear thickness variation have been analyzed on the basis of classical plate theory employing the differential quadrature dq method the non homogeneity is assumed to arise due to the variation in young s modulus and also the density of the plate material the first three natural frequencies have been obtained for clamped simply supported and free edge conditions taking grid points as zeros of chebyshev polynomials the effect of non homogeneity and thickness variation on natural frequencies of vibration has been investigated for the first three modes of vibration the results for linear as well as parabolic thickness variations have been obtained as special cases comparison studies have been carried out to establish the accuracy and versatility of the present dq method

approximate solution for free vibrations of thin orthotropic rectangular plates abstract in this paper the problem of approximate evaluation of the frequencies of orthotropic plates is investigated starting from a general approximate formula for the frequency proposed by hearmon it is shown how to calculate the fundamental mode of an orthotropic rectangular plate with different restraint conditions using the proper coefficient values already available in the scientific literature for the higher modal frequencies a particular form of the rayleigh method is proposed leading to a simple procedure to calculate the fundamental frequency in fact the frequency calculation is reduced to the evaluation of the fundamental frequency of a special plate associated to the real one in order to test the accuracy of the proposed method an extensive finite element investigation was carried out the numerical results obtained show that the average difference between the values computed with the approximate new method and the finite element values is less than 0 74

global solutions of the euler maxwell two fluid system in 3d the fundamental two uid model for describing plasma dynamics is given by the euler maxwell system in which compressible ion and electron uids interact with their own self consistent electromagnetic eld we prove global stability of a constant neutral background in the sense that irrotational smooth and localized perturbations of a constant background with small amplitude lead to global smooth solutions in three space dimensions for the euler maxwell system our construction is robust in dimension 3 and applies equally well to other plasma models such as the euler poisson system for two uids and a relativistic euler maxwell system for two uids our solutions appear to be the rst nontrivial global smooth solutions in all of these models

an efficient mixed methodology for free vibration and buckling analysis of orthotropic rectangular plates abstract in this paper a simple and efficient mixed ritz differential quadrature dq method is presented for free vibration and buckling analysis of orthotropic rectangular plates the mixed scheme combines the simplicity of the ritz method and high accuracy and efficiency of the dq method the accuracy of the proposed method is demonstrated by comparing the calculated results with those available in the literature it is shown that highly accurate results can be obtained using a small number of ritz terms and dq sample points the proposed method is suitable for the problem considered due to its simplicity and potential for further development

accurate and elegant free vibration and buckling studies of orthotropic rectangular plates using untruncated infinite series this paper presents the extension of a novel superposition method put forth for static analysis earlier for carrying out free vibration and bifurcation buckling studies of orthotropic rectangular plates with any combination of classical boundary conditions viz clamped simply supported and free edges it is shown that use of infinite series counterparts of conventional levy type closed form expressions result in a tremendous simplification of the problem without any compromise on accuracy the complicating effects of an elastic foundation and initial stresses are also shown to be easily accounted for results useful as benchmarks in future are presented for a chosen set of cases

determination of the steady state response of viscoelastically corner point supported rectangular specially orthotropic plates under the effect of sinusoidally varying moment abstract vibration of orthotropic rectangular plates having viscoelastic point supports at the corners under the effect of sinusoidally varying concentrated moment is analyzed the lagrange equation is used to examine the free vibration characteristics and the steady state response to a sinusoidally varying concentrated moment acting at the centre of a viscoelastically point supported orthotropic elastic plate of rectangular shape in the study for applying the lagrange equation the trial function denoting the deflection of the plate is expressed in the polynomial form by using the lagrange equation the problem is reduced to the solution of a system of algebraic equations the influence of the mechanical properties and of the damping of the supports on the mode shapes and the steady state response of the viscoelastically point supported rectangular plates is investigated numerically for a concentrated moment at the centre for various values of the mechanical properties which characterize the anisotropy of the plate material and for various damping ratios the results of the natural frequencies are given for the first three antisymmetrical symmetrical modes and the steady state responses to a sinusoidally varying concentrated moment are determined for the frequency ranges of the first two antisymmetrical symmetrical mode types convergence studies are made the validity of the obtained results is demonstrated by comparing them with other solutions for free vibration analysis of point supported or completely free rectangular plates for the first three antisymmetrical symmetrical vibration modes based on the kirchhoff love plate theory

global existence of smooth solutions for partially dissipative hyperbolic systems with a convex entropy we consider the cauchy problem for a general one dimensional n n hyperbolic symmetrizable system of balance laws it is well known that in many physical examples for instance for the isentropic euler system with damping the dissipation due to the source term may prevent the shock formation at least for smooth and small initial data our main goal is to find a set of general and realistic sufficient conditions to guarantee the global existence of smooth solutions and possibly to investigate their asymptotic behavior for systems which are entropy dissipative a quite natural generalization of the kawashima condition for hyperbolic parabolic systems can be given in this paper we first propose a general framework for this kind of problem by using the so called entropy variables then we go on to prove some general statements about the global existence of smooth solutions under different sets of conditions in particular the present approach is suitable for dealing with most of the physical examples of systems with a relaxation extension our main tools will be some refined energy estimates and the use of a suitable version of the kawashima condition

vibration analysis of rectangular plates with general elastic boundary supports abstract in this investigation the rayleigh ritz method is used to determine the modal characteristics of a rectangular plate with general elastic supports alone its edges each of the admissible functions here is composed of a trigonometric function and an arbitrary continuous function that is introduced to ensure the sufficient smoothness of the so called residual displacement function at the edges as a result a drastic improvement of the convergence can be expected of the solution expressed as a series expansion in terms of the admissible functions perhaps more importantly this study has developed a general approach for deriving a complete set of admissible functions that can be universally applied to various boundary conditions several numerical examples are given to demonstrate the accuracy and convergence of the current solution

transverse vibrations of an orthotropic rectangular plate of linearly varying thickness and with a free edge fil bambill diana virginia consejo nacional de investigaciones cientificas y tecnicas centro cientifico tecnologico conicet bahia blanca argentina universidad nacional del sur departamento de ingenieria argentina

a hierarchical functions set for predicting very high order plate bending modes with any boundary conditions in this paper a new hierarchical functions set is proposed to predict flexural motion of plate like structures in the medium frequency range this functions set is built from trigonometric functions instead of polynomials as classically encountered in the literature it is shown that such a trigonometric set presents all the advantages of a classical hierarchical polynomials set and additional ones which are of interest if very high order functions are intended to be used it is stated that this new trigonometric set can be used at very high orders up to 2048 without taking care of computer round off errors while the polynomials set fail at order 46 because of the limited numerical dynamics of computers this trigonometric set can be easily implemented on a computer it does not require quadruple precision pre computed arrays only a very low number which does not depend on the function order of basic operations is needed when calling such functions moreover it is shown that this trigonometric set presents a better convergence rate than polynomials when predicting high order natural flexural modes of rectangular plates with any boundary conditions

quintic splines in the study of transverse vibrations of non uniform orthotropic rectangular plates an analysis and numerical results are presented for free transverse vibrations of orthotropic rectangular plates of linearly varying thickness along one direction and resting on an elastic foundation of the winkler type on the basis of classical plate theory following the levy approach i e two parallel edges being simply supported the fourth order differential equation governing the motion of such plates has been solved by using the quintic splines interpolation technique for three different combinations of clamped simply supported and free boundary conditions at the other two edges the effect of the elastic foundation together with the orthotropy aspect ratio and thickness variation on the natural frequencies of vibration is illustrated for the first three modes of vibration normalized displacements are presented for two different values of the taper constant keeping other plate parameters fixed for all the three boundary conditions a comparison of the results with those available in literature is presented

free vibrations of rectangular plates of exponentially varying thickness and with a free edge abstract transverse vibrations of the structural system described in the title are analyzed by using classical plate theory and employing two different methodologies the recently developed optimized kantorovich approach and a finite element algorithmic procedure it is shown that the fundamental frequency coefficients obtained by using both techniques for a rather wide variation of the governing geometric parameters are in very good agreement lower frequency coefficients of the plate system determined by means of the finite element method are also presented

encoding visual information using anisotropic transformations the evolution of information in images undergoing fine to coarse anisotropic transformations is analyzed by using an approach based on the theory of irreversible transformations in particular we show that when an anisotropic diffusion model is used local variation of entropy production over space and scale provides the basis for a general method to extract relevant image features

block marching in time with dq discretization an efficient method for time dependent problems abstract in this paper an efficient method is presented to solve time dependent problems the proposed method marches in the time direction block by block in each block there are several time levels and the numerical results at these time levels are obtained simultaneously the global method of differential quadrature is applied in each block to discretize both the spatial and temporal derivatives the proposed method is validated by a sample problem which has an exact solution for easy comparison it was found that as compared to the conventional 4 stage runge kutta method the present method could give much higher order of accuracy for numerical results and require much less computational effort

singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids many interesting problems in classical physics involve the limiting behavior of quasilinear hyperbolic systems as certain coefficients become infinite using classical methods the authors develop a general theory of such problems this theory is broad enough to study a wide variety of interesting singular limits in compressible fluid flow and magneto fluid dynamics including new constructive local existence theorems for the time singular limit equations in particular the authors give an entirely self contained classical proof of the convergence of solutions of the compressible fluid equations to their incompressible limits as the mach number becomes small the theory depends upon a balance between certain inherently nonlinear structural conditions on the matrix coefficients of the system together with appropriate initialization procedures similar results are developed also for the compressible and incompressible navier stokes equations with periodic initial data independent of the viscosity coefficients as they tend to zero

axisymmetric vibrations of non homogeneous polar orthotropic annular plates of variable thickness in this study of the free axisymmetric vibrations of non homogeneous polar orthotropic annular plates of exponentially varying thickness on the basis of the classical theory of plates the chebyshev collocation technique has been employed to solve the differential equation governing the transverse motion of such plates the non homogeneity of the plate material is assumed to arise due to the variation of young s moduli and density which are assumed to vary exponentially with the radius vector the effect of various plate parameters such as radii ratio rigidity ratio non homogeneity and thickness variation on the vibrational characteristics of the plate have been studied for three different boundary conditions normalized displacements are presented for a specified plate for the first three modes of vibration a comparison of results with those available in the literature has been presented

vibration of non homogeneous circular mindlin plates with variable thickness free vibration analysis of non homogeneous circular plates of variable thickness has been presented using the first order shear deformation plate theory of mindlin chebyshev collocation technique has been employed to obtain the first three natural frequencies and mode shapes for clamped simply supported and free plate with four digit exactitude the effect of structural parameters such as taper non homogeneity and density and that of edge conditions on the natural frequencies has been investigated comparison of results for some special cases with published results obtained from other approximate methods has been presented which shows an excellent agreement

vibrations of rectangular plates with elastically restrained edges abstract the rayleigh ritz method is used to determined natural frequencies in transverse vibration of rectangular plates with elastically restrained edges by treating an elastically restrained edge as intermediate between an appropriate pair of classical boundary conditions and using the corresponding vibration mode shapes of beams with classical boundary conditions as assumed functions a relatively small number of functions is required consequently only a modest quantity of computation is necessary the good accuracy of the method is demonstrated by solving test problems the method can be applied to a wide range of elastic restraint conditions any aspect ratio and for higher modes in addition to the fundamental the usefulness and accuracy of existing simplified approaches to the problem are assessed the effect of in plane forces on the natural frequencies and the determination of critical loads for plates with these restraint conditions are considered also

natural frequencies of orthotropic rectangular plates obtained by iterative reduction of the partial differential equation natural frequencies of orthotropic rectangular plates are obtained by successive reduction of the plate partial differential equation and by solving the resulting ordinary differential equation exactly the reduction of the partial differential equation is carried out by assuming an approximate solution satisfying the boundary conditions along one direction and employing a galerkin averaging technique known as the kantorovich method the resulting ordinary differential equation along the other direction is solved exactly which provides the natural frequencies of the plate natural frequencies of the orthotropic rectangular plates with various boundary conditions are obtained by using this approach and presented along with the discussion of the convergence and accuracy of the results

accurate free vibration analysis of the completely free orthotropic rectangular plate by the method of superposition abstract the method of superposition is exploited to obtain highly accurate analytical type solutions for the free vibration of completely free orthotropic rectangular plates eigenvalues for 12 modes are provided for a particular set of problems representative of reinforced concrete and similar materials for a wide range of plate aspect ratios while it is recognized that data covering the entire range of possible problems cannot be tabulated it is hoped that the data provided will prove useful to some designers and provide a reference for other researchers to compare their results this appears to be the first study devoted to this problem to appear in the literature

free vibration solution for clamped orthotropic plates using lagrangian multiplier technique using the lagrangian multiplier technique an analysis was developed to compute the natural frequencies and mode shapes of clamped orthotropic laminated plates transverse shear deformation effects were included using a higher order plate theory predictions made with the developed analysis demonstrated excellent agreement with the available experimental test results and other analytical solutions the validated free vibration analysis has also been used to develop an analysis to predict the dynamic response of clamped orthotropic plates subjected to low velocity impact by a hard object

nonlinear image filtering with edge and corner enhancement the authors describe a model of nonlinear image filtering for noise reduction and edge enhancement using anisotropic diffusion the method is designed to enhance not only edges but corners and t junctions as well the method roughly corresponds to a nonlinear diffusion process with backward heat flow across the strong edges such a process is ill posed making the results depend strongly on how the algorithm differs from the diffusion process two ways of modifying the equations using simulations on a variable grid are studied

generic free vibration of orthotropic rectangular plates with clamped and simply supported edges abstract the generic free vibration of specially orthotropic rectangular plates with combinations of clamped and simply supported edges is investigated by the superposition technique the introduction of affine transformation reduces the two rigidity parameters required for the free vibration analysis to one making complete tabulation of computed eigenvalues much easier numerical calculations are performed on clamped plates plates with one edge simply supported and plates with two adjacent edges simply supported along with a number of representative values of the generalized rigidity parameter and the affine aspect ratio

entropy and global existence for hyperbolic balance laws this paper presents a general result on the existence of global smooth solutions to hyperbolic systems of balance laws in several space variables we propose an entropy dissipation condition and prove the existence of global smooth solutions under initial data close to a constant equilibrium state in addition we show that a system of balance laws satisfies a kawashima condition if and only if its first order approximation namely the hyperbolic parabolic system derived through the chapman enskog expansion satisfies the corresponding kawashima condition the result is then applied to bouchut s discrete velocity bgk models approximating hyperbolic systems of conservation laws

derivation of the zakharov equations this article continues the study initiated in 27 7 of the validity of the zakharov model which describes langmuir turbulence we give an existence theorem for a class of singular quasilinear equations this theorem is valid for prepared initial data we apply this result to the euler maxwell equations which describes laser plasma interactions to obtain in a high frequency limit an asymptotic estimate that describes solutions of the euler maxwell equations in terms of wkb approximate solutions the leading terms of which are solutions of the zakharov equations due to the transparency properties of the euler maxwell equations evidenced in 27 this study is carried out in a supercritical highly nonlinear regime in such a regime resonances between plasma waves electromagnetric waves and acoustic waves could create instabilities in small time the key of this work is the control of these resonances the proof involves the techniques of geometric optics of joly metivier and rauch 12 13 recent results by lannes on norms of pseudodifferential operators 14 and a semiclassical paradifferential calculus

on the representation of image structures via scale space entropy conditions this paper deals with a novel way for representing and computing image features encapsulated within different regions of scale space employing a thermodynamical model for scale space generation the method derives features as those corresponding to entropy rich image regions where within a given range of spatial scales the entropy gradient remains constant different types of image features defining regions of different information content are accordingly encoded by such regions within different bands of spatial scale

energy transport and drift diffusion limits of nonisentropic euler poisson equations abstract two relaxation limits in critical spaces for the scaled nonisentropic euler poisson equations with the momentum relaxation time and energy relaxation time are considered as the first step of this justification the uniform global classical solutions to the cauchy problem in chemin lerner s spaces with critical regularity are constructed furthermore by the compactness argument it is rigorously justified that the scaled classical solutions converge to the solutions of energy transport equations and drift diffusion equations respectively with respect to different time scales

an exact series solution for calculating the eigenfrequencies of orthotropic plates with completely free boundary abstract an analysis for solving boundary value problems in structural mechanics which was proposed by wang and lin 1996 journal of sound and vibration 196 285 293 1999 journal of applied mechanics 66 380 387 1 2 has been extended to the calculation of the eigenfrequencies of an orthotropic plate under all free boundary conditions the convergence of the series solution is assured and the procedure leads to pointwise exact solutions the calculated eigenfrequencies have been verified by a different approach and indicate that the present method is simple and effective