an efficient wave based prediction technique for dynamic plate bending problems with corner stress singularities the finite element method is commonly used for simulations of dynamic plate bending problems a major disadvantage of this method is its practical frequency limitation in that the computational loads become prohibitively large at higher frequencies a newly developed wave based prediction technique aims to relax this frequency limitation through an enhanced computational efficiency this paper discusses the application of the wave based method for the particular case where stress singularities appear in one or more corners of a polygonal plate domain in this case the conventional set of field variable expansion functions is extended with some special purpose functions which incorporate the corner point singularities the beneficial convergence rate of the wave based method as compared with the finite element method is verified for various validation examples

stability and vibration of thick laminated composite sector plates this study presents a simple analytical formulation for the eigenvalue problem of buckling and free vibration analysis of shear deformable laminated sector plates made up of cylindrically orthotropic layers the non axisymmetric formulation in cylindrical coordinates is discretized in space domain in terms of two dimensional chebyshev polynomials several combinations of simply supported clamped and free edge conditions are considered convergence study has been carried out and the obtained results are compared with the results of laminated square plates and isotropic sector plates available in literature extensive results pertaining to critical buckling loads and natural frequencies are presented effects of boundary conditions number of layers moduli ratio rotary and in plane inertia plate thickness sector angle and annularity are studied

free vibration analysis of plates using least square based finite difference method in this paper we apply the two dimensional least square based finite difference lsfd method for solving free vibration problems of isotropic thin arbitrarily shaped plates with simply supported and clamped edges using the chain rule we show how the fourth order derivatives of the plate governing equation can be discretized in two or three steps as well as how the boundary conditions can be implemented directly into the governing equation by analyzing vibrating plates of various shapes and comparing the solutions obtained against existing results we clearly demonstrate the effectiveness of lsfd as a mesh free method for computing vibration frequencies of generally shaped plates accurately

vibration of thick annular sector plates using semi analytical methods abstract this paper deals with the vibration of thick annular sector plates with simply supported straight edges the finite strip method based on the mindlin plate theory and the finite prism method based on the three dimensional elastic theory which are known as semi analytical methods are used to demonstrate the accuracy of the semi analytical methods results are compared with those obtained by other analytical and numerical methods comparison of the results of the two methods is discussed in order to analyze the thick annular plates with different thickness ratios sector angles and boundary conditions it is seen that the results of the two methods show good agreement while some discrepancies between them are shown in the cases of larger thickness ratios of higher modes and of plates with free edges

nonlinear elliptic systems with general growth we prove local lipschitz continuity and as a consequence c k and c regularity of weak solutions u for a class of nonlinear elliptic differential systems of the formn 1 xi a i du 0 1 2 m the growth conditions on the dependence of functions a i on the gradient du are so mild to allow us to embrace growths between the linear and the exponential cases and they are more general than those known in the literature

free vibration analysis of a cylindrical shell circular plate system with general coupling and various boundary conditions abstract the free vibration of a structure consisting of a finite circular cylindrical shell closed at one end by a circular plate is analyzed in this paper emphasis is given to the characterization of structural coupling and boundary conditions these are incorporated into the model by means of continuous distributions of springs along the shell and the plate interface a general formulation based on a variational principle is used this formulation allows a wide spectrum of boundary conditions and coupling conditions between the shell and the plate an issue the importance of which is clearly shown by a literature review very good accuracy of the method is demonstrated by solving test problems for lower order modes of the plate and of the shell for which some results are available in the literature comparisons are also made using finite element analysis on a plate ended shell showing that the proposed approach is a convenient effecient and accurate one for determining the modal behavior of such a complex structural system other numerical results are then presented for a shell rigidly attached to a plate to illustrate the coupling phenomena between the shell and the plate it is shown that there exist three different types of modes for this combined structure they are termed plate controlled modes shell controlled modes and strongly coupled modes respectively it is also shown that each type is closely related to the modal character of each of uncoupled elements

interior gradient regularity for bv minimizers of singular variational problems we consider a class of vectorial integrals with linear growth where as a key feature some degenerate singular behavior is allowed for generalized minimizers of these integrals in bv we establish interior gradient regularity and as a consequence uniqueness up to constants in particular these results apply for 1 p 2 to the singular model integrals z 1 jrw x j p 1 p dx

vibration of annular sector plates from three dimensional analysis accurate three dimensional elasticity solutions are presented for the free vibration analysis of annular sector plates with arbitrary but continuous boundary conditions the ritz procedure is used to minimize the integral energy functional which is formulated in a cylindrical polar coordinate system in the derivation of the governing eigenvalue equation the vibratory characteristics of annular sector plates with variations in boundary condition sector angle and thickness are examined the accuracy of the method is validated through appropriate convergence and comparison studies the first known results presented here provide a basis for understanding the physics of vibrations of annular sector plates and can be used to assess numerical results obtained from various refined two dimensional theories

une preuve simple des conjectures de langlands pour gl n sur un corps p adique let f be a finite extension of p for each integer n 1 we construct a bijection from the set f 0 n of isomorphism classes of irreducible degree n representations of the absolute weil group of f onto the set f 0 n of isomorphism classes of smooth irreducible supercuspidal representations of gl n f those bijections preserve epsilon factors for pairs and hence we obtain a proof of the langlands conjectures for gl n over f which is more direct than harris and taylor s our approach is global and analogous to the derivation of local class field theory from global class field theory we start with a result of kottwitz and clozel on the good reduction of some shimura varieties and we use a trick of harris who constructs non galois automorphic induction in certain cases

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

influence of boundary stress singularities on the vibration of clamped and simply supported sectorial plates with arbitrary radial edge conditions abstract this paper extends previous studies made for sectorial plates having re entrant i e interior corners causing stress singularities to provide accurate frequencies when the circular edge is either clamped or simply supported an extensive review of the literature is also given herein spanning nearly the past two decades explaining the free vibration characteristics of sectorial plates in this work the classical ritz method is employed with two sets of admissible functions assumed for the transverse vibratory displacements these sets include 1 mathematically complete algebraic trigonometric polynomials which guarantee convergence to exact frequencies as sufficient terms are retained and 2 corner functions which account for the bending moment singularities at the re entrant vertex corner of the radial edges having arbitrary edge conditions extensive convergence studies summarized herein confirm that the corner functions substantially enhance the convergence and accuracy of non dimensional frequencies for sectorial plates having either a clamped or hinged circumferential edge and various combinations of clamped hinged and free conditions on the radial edges accurate to at least four significant figure frequencies and normalized contours of the transverse vibratory displacement are presented for the spectra of sector angles 90 180 semi circular 270 300 330 350 355 360 complete circular causing a re entrant vertex corner of the radial edges for sector angles of 360 a clamped clamped clamped hinged clamped free hinged free or free free radial crack ensues one general observation is the substantial reduction in the first six frequencies as the sector angle increases for all plates except in the first two modes of plates having free free radial edges

vibration of tapered thickness annular sector plates by spline element method abstract this paper deals with the determination of the vibrations of thin annular sector plates of tapered thickness by using the spline element method to demonstrate the accuracy of the present method several examples are solved and results are compared with those obtained by analytical methods and other numerical methods good accuracy is obtained frequencies of tapered annular sector plates with several boundary conditions are analyzed for the different sector angles and thickness parameters

caracterisation de la correspondance de langlands locale par les facteurs e de paires soitf un corps local non archimedien a corps residuel fini la conjecture de langlands locale prouvee par laumon rapoport et stuhler quandf est de caracteristique non nulle associe a une classe d isomorphisme de representations irreductibles du groupe de weil def une classe d isomorphisme de representations admissibles irreductibles supercuspidales d un groupe lineaire surf le groupe gl n f si est de dimensionn nous prouvons dans cet appendice qu il existe au plus une telle correspondance qui preserve les facteurs e de paires et coincide en dimension 1 avec l application donnee par la theorie du corps de classes

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

3 d vibration analysis of annular sector plates using the chebyshev ritz method abstract the three dimensional free vibration of annular sector plates with various boundary conditions is studied by means of the chebyshev ritz method the analysis is based on the three dimensional small strain linear elasticity theory the product of chebyshev polynomials satisfying the necessary boundary conditions is selected as admissible functions in such a way that the governing eigenvalue equation can be conveniently derived through an optimization process by the ritz method the boundary functions guarantee the satisfaction of the geometric boundary conditions of the plates and the chebyshev polynomials provide the robustness for numerical calculation the present study provides a full vibration spectrum for the thick annular sector plates which cannot be given by the two dimensional 2 d theories such as the mindlin theory comprehensive numerical results with high accuracy are systematically produced which can be used as benchmark to evaluate other numerical methods the effect of radius ratio thickness ratio and sector angle on natural frequencies of the plates with a sector angle from 120 to 360 is discussed in detail the three dimensional vibration solutions for plates with a re entrant sector angle larger than 180 and shallow helicoidal shells sector angle larger than 360 with a small helix angle are presented for the first time

regularity results for vectorial minimizers of a class of degenerate convex integrals abstract we establish the higher differentiability and the higher integrability for the gradient of vectorial minimizers of integral functionals with p q growth conditions we assume that the non homogeneous densities are uniformly convex and have a radial structure with respect to the gradient variable only at infinity the results are obtained under a possibly discontinuous dependence on the spatial variable of the integrand

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

free vibration of annular sector plates with edges possessing different degrees of rotational restraint abstract results for the natural frequencies of annular sector plates possessing different degrees of elastic restraint along the edges are presented the analysis is based on a numerical method developed by the author the functions in the circumferential direction satisfying the boundary conditions along the radial edges which are required in the analysis are indicated to the best of the author s knowledge no previous results exist for such plates

sharp regularity for functionals with p q growth we prove regularity theorems for minimizers of integral functionals of the calculus of variations f x du x dx with non standard growth conditions of p q type z p f x z l z q 1 p q in particular we find that a sufficient condition for minimizers to be regular is qp n n where the function f x z is holder continuous with respect to the x variable and x rn this condition is also sharp we include results in the setting of orlicz spaces moreover we treat certain relaxed functionals too finally we address a problem posed by marcellini in 43 showing a minimizer with an isolated singularity

three dimensional vibrations of cylindrical elastic solids with v notches and sharp radial cracks abstract this paper provides free vibration data for cylindrical elastic solids specifically thick circular plates and cylinders with v notches and sharp radial cracks for which no extensive previously published database is known to exist bending moment and shear force singularities are known to exist at the sharp reentrant corner of a thick v notched plate under transverse vibratory motion and three dimensional 3 d normal and transverse shear stresses are known to exist at the sharp reentrant terminus edge of a v notched cylindrical elastic solid under 3 d free vibration a theoretical analysis is done in this work utilizing a variational ritz procedure including these essential singularity effects the procedure incorporates a complete set of admissible algebraic trigonometric polynomials in conjunction with an admissible set of edge functions that explicitly model the 3 d stress singularities which exist along a reentrant terminus edge i e 180 of the v notch the first set of polynomials guarantees convergence to exact frequencies as sufficient terms are retained the second set of edge functions in addition to representing the corner stress singularities substantially accelerates the convergence of frequency solutions this is demonstrated through extensive convergence studies that have been carried out by the investigators numerical analysis has been carried out and the results have been given for cylindrical elastic solids with various v notch angles and depths the relative depth of the v notch is defined as 1 c a and the notch angle is defined as 360 for a very small notch angle 1 or less the notch may be regarded as a sharp radial crack accurate four significant figure frequencies are presented for a wide spectrum of notch angles 360 depths 1 c a and thickness ratios a h for plates and h a for cylinders an extended database of frequencies for completely free thick sectorial semi circular and segmented plates and cylinders are also reported herein as interesting special cases a generalization of the elasticity based ritz analysis and findings applicable here is an arbitrarily shaped v notched cylindrical solid being a surface traced out by a family of generatrix which pass through the circumference of an arbitrarily shaped v notched directrix curve r several of which are described for future investigations and close extensions of this work

free vibration of a cantilever annular sector plate with curved radial edges and varying thickness abstract the free vibration of a cantilever annular sector plate with curved radial edges and varying thickness is analyzed by the ritz method for this purpose the plate is transformed into a regular sector plate with unit outer radius by a transformation of variables the transverse deflection of the transformed plate is expressed in a power series the dynamical energies of the plate are evaluated and the frequency equation of the plate is derived by the conditions for a stationary value of the lagrangian functional this method is applied to annular sector plates with symmetrically or unsymmetrically curved radial edges and also with varying thickness the natural frequencies and the mode shapes are calculated numerically and the effects of varying thickness on the vibration are studied

partial regularity of strong local minimizers of quasiconvex integrals with p q growth defined on vector valued maps u r n 1 here denotes a bounded open set in r n 2 and f r r is a c function satisfying suitable assumptions described below the existence and the partial regularity of minimizers of f are classical issues in the modern calculus of variations and they have been extensively studied especially over the last twenty years specifically in the present paper we will focus on gradient regularity under the basic assumption that f is quasiconvex that is

an efficient wave based prediction technique for plate bending vibrations the finite element method is a commonly used prediction method for dynamic simulations of plate bending problems a major disadvantage of this method is its practical frequency limitation as its application involves prohibitively large computational efforts at higher frequencies a newly developed wave based prediction technique pushes up the frequency limit through an enhanced computational efficiency this paper discusses the principles of the wave based method for convex plate problems the beneficial convergence rate of the wave based method as compared with the finite element method is verified for various validation examples which include the most commonly encountered boundary conditions

three dimensional hierarchical finite element free vibration analysis of annular sector plates an annular sector solid hierarchical finite element is presented and applied to three dimensional free vibration analysis of annular sector plates the element s displacements are expressed in terms of a fixed number of linear polynomial shape functions plus a variable number of shape functions which are forms of the shifted legendre orthogonal polynomial the linear polynomial shape functions are used to describe the element s nodal displacements and the higher order shape functions are used to provide additional freedom to the edges faces and interior of the element results of frequency calculations are found for annular sector plates with two straight edges simply supported like a diaphragm condition and comparisons are made with those obtained by the finite prism method the manner of convergence of the solution as a function of the numbers of hierarchical modes is also investigated furthermore contributions to original three dimensional frequencies are made for annular sector plates with other boundary conditions along the two straight edges

vibration of rectangular plates with edge restraints and intermediate stiffeners vibrations of stiffened plates with elastically restrained edges are analyzed by the rayleigh ritz method the first lower four frequencies for restrained plates with up to six intermediate stiffeners are calculated the results of this study are compared with existing data and the agreement is excellent

on the analysis of laterally vibrating slender beams subject to various complicating effects the rayleigh ritz method with orthogonally generated polynomials as admissible functions is used to obtain a simple analysis of the free vibration problem of slender beams subject to various complicating effects these effects are the presence of concentrated masses and or concentrated moments of inertia intermediate supports axial loading and non uniformity of cross section such may exist separately or in any combination numerical results are presented for several example beams illustrating the accuracy and versatility of the approach

free vibration analysis of circular and annular sectorial thin plates using curve strip fourier p element abstract a curve strip fourier p element for free vibration analysis of circular and annular sectorial thin plates is presented the element transverse displacement is described by a fixed number of polynomial shape functions plus a variable number of trigonometric shape functions the polynomial shape functions are used to describe the element s nodal displacements and the trigonometric shape functions are used to provide additional freedom to the edges and the interior of the element with the additional fourier degrees of freedom dof and reduce dimensions the accuracy of the computed natural frequencies is greatly increased results are obtained for a number of circular and annular sectorial thin plates and comparisons are made with exact the curve strip fourier p element the proposed fourier p element and the finite strip element the results clearly show that the curve strip fourier p element produces a much higher accuracy than the proposed fourier p element the finite strip element

regularity and existence of solutions of elliptic equations with p q growth conditions for some positive constants m a4 and for exponents q 2 p 2 2 under 1 2 1 3 and some other assumptions by assuming also that the quotient q p is sufficiently close to one in dependence on n precisely if q p c n n 2 then we prove that every weak solution to 1 1 of class 4 4 0 is locally lipschitz continuous in q moreover there are positive constants 8 c and 0 2 1 such that

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

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

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

a semi analytical dqem for free vibration analysis of thick plates with two opposite edges simply supported this paper is introducing a semi analytical differential quadrature element method dqem based on first order shear deformation theory for free vibration analysis of thick plates by decomposing the plate into a series of sub domains or elements any discontinuity in geometry material properties and elastic foundations in one direction can be handled conveniently classical as well as non classical boundary conditions can be imposed one benefits of this semi analytical dqem is reducing the storage requirements and the computational efforts needed to assemble the global equations the method would also increase the computational efficiency in comparison with the finite element method fem or differential quadrature method dqm analysis of such problems the accuracy versatility stability and convergence of the algorithm are certified

on the free transverse vibration of annular and circular thin sectorial plates subject to certain complicating effects abstract the rayleigh ritz method with orthogonally generated polynomials as admissible functions is used to obtain an eigenvalue equation for the free transverse vibration of thin annular sectorial plates circular sectorial plates are treated with this equation by permitting the inner radius to become negligibly small the plates may be of isotropic or polar orthotropic material of uniform or radially and or circumferentially varying thickness and may include interior circumferential or radial line supports numerical values for the natural frequency parameters of several different plates are presented and compared with previously published values where available

non uniform rational lagrange functions and its applications to isogeometric analysis of in plane and flexural vibration of thin plates abstract new basis functions were developed for isogeometric analysis iga to overcome the difficulties of iga using nurbs non uniform rational b splines on coping with dirichlet boundary conditions the new basis functions were constructed through nesting rational local lagrange interpolations like the t spline and were evaluated in similar procedure as the finite difference method explicit expressions for the new basis functions were presented due to their equivalence to the nurbs the new basis functions were named as non uniform rational lagrange nurl basis iga using nurl includes the finite element method as a special case but the geometry in iga using nurl is exact iga using nurl can carry out p refinement that has the nesting feature of the k refinement of nurbs dirichlet boundary conditions can be directly imposed in iga using nurl because the nurl are interpolation basis functions a method of directly transforming the tensor product basis of triangular patches to area coordinates was presented and the singularity problem at the edge degenerated to a single point was solved the methods developed in this work were applied to in plane and flexural vibration of thin plates comparisons with available results in literatures showed the fast convergence and high accuracy of iga using nurl and the transformation method for triangular patches introduction of a matlab toolbox of the nurl was appended

differential quadrature method for vibration analysis of shear deformable annular sector plates this paper presents differential quadrature solutions for free vibration analysis of moderately thick annular sector plates based on the mindlin first order shear deformation theory numerical characteristics of the differential quadrature method are illustrated through solving selected annular sector plates with different boundary conditions relative thickness ratios inner to outer radius ratios and various sector angles parametric studies in terms of the vibration frequency parameters are thoroughly investigated

transverse vibrations of a rotating uniform cantilever beam with tip mass as predicted by using beam characteristic orthogonal polynomials in the rayleigh ritz method abstract natural frequencies and mode shapes of a rotating uniform cantilever beam with a tip mass are studied by using beam characteristic orthogonal polynomials in the rayleigh ritz method the set of orthogonal polynomials which satisfy the geometrical boundary conditions are generated by using the gram schmidt process the results are compared with those obtained by the myklestad method the extended galerkin method and finite element methods the variation of natural frequencies with the speed of rotation is plotted for several parameter combinations such as setting angle tip mass moment of inertia of tip mass etc mode shapes at different rotational speeds are also plotted use of orthogonal polynomials for the deflection shapes enables the computation of higher natural frequencies of any order to be accomplished without facing any numerical difficulties which is not the case when arbitrary polynomial expressions are used

free vibration analysis of mindlin sector plates numerical solutions by differential quadrature method abstract in this paper the free vibration analysis of moderately thick sector plates based on mindlin s first order shear deformation theory is examined the solutions to this problem are determined using the differential quadrature dq method for numerical evaluation the dq formulations for free vibration of the mindlin sector plates in two dimensional polar co ordinate system are derived to demonstrate the accuracy of the dq method convergence and comparison studies are carried out in parametric study the first eight frequency parameters are computed for sector plates with different boundary conditions relative thickness ratios and sector angles 30 360 the effects of sector angle and relative thickness ratio on the frequency parameters are discussed

on the lateral vibration of thin annular and circular composite plates subject to certain complicating effects abstract series comprising orthogonally generated polynomial functions are used in the rayleigh ritz method to obtain an eigenvalue equation for the flexural vibration of thin flat annular and circular plates the plates may be of isotropic or polar orthotropic material of uniform or radially varying thickness and may pass over intermediate concentric ring supports numerical results are presented for a number of plates illustrating the versatility and accuracy of the approach

stability and vibration of mindlin sector plates an analytical approach this study presents a simple analytical formulation for the eigenvalue problem of buckling and free vibration analysis of mindlin sector plates the nonaxisymmetric formulation in cylindrical coordinates is discretized in the space domain in terms of two dimensional chebyshev polynomials the formulation facilitates application of several combinations of simply supported clamped and free edge conditions convergence study has been carried out and the obtained results are compared with those available in the literature extensive results pertaining to critical buckling loads and natural frequencies are presented effects of boundary conditions plate thickness and annularity are studied

exact analytical solutions for free vibrations of thick sectorial plates with simply supported radial edges abstract the first known exact analytical solutions are derived for the free vibrations of thick mindlin sectorial plates having simply supported radial edges and arbitrary conditions along the circular edge the general solutions to the mindlin differential equations of motion contain noninteger order ordinary and modified bessel functions of the first and second kinds and six arbitrary constants of integration by exercising a careful limiting process three regularity conditions at the vertex of the radial edges are invoked to yield three equations of constraint among the six constants for sector angles exceeding 180 re entrant corners three additional linearly independent equations among the six constants are obtained by satisfying the three boundary conditions along the circular edge frequency determinant equations are derived for mindlin sectorial plates with circular boundaries which are clamped simply supported or free nondimensional frequency parameters are presented for over a wide range of salient and re entrant sector angles 30 360 and thickness to radius ratios of 0 1 0 2 and 0 4 frequency results obtained for mindlin sectorial plates are compared to those determined for classically thin sectorial plates and the results are found to be considerably different than those derived from thin plate theory particularly for the fundamental frequencies of plates having sector angles slightly greater than 180 when the circular boundary is free the frequencies for 360 sectorial plates i e circular plates having a hinged crack are compared with those for complete circular ones

differential quadrature for multi dimensional problems the technique of differential quadrature for the solution of partial differential equations introduced by bellman et al is extended and generalized to encompass partial differential equations involving multiple space variables approximation formulae for a variety of first and second order partial derivatives and typical weighting coefficients are presented application of these formulae is demonstrated on the solution of the convection diffusion equation for the two and three dimensional space dependent cases and for both the transient and steady state dispersion of inert neutrally buoyant pollutants from continuous sources into an unbounded atmosphere

the local rankin selberg convolution for gl n divisibility of the conductor let f be a non archimedean local field and n geq 2 an integer let pi pi be irreducible supercuspidal representations of gl n f with pi not cong pi one knows that there exists an irreducible supercuspidal representation rho of gl m f with m n such that the local constants in the sense of jacquet piatetskii shapiro and shalika varepsilon pi times rho s psi varepsilon pi times rho s psi are distinct in this paper we show that when pi is an unramified twist chi pi of pi one may here takem dividingn and leq n ell for a prime divisor ell ofn depending on pi and the order of chi in particular m leq n ell 0 where ell 0 is the least prime divisor of n this follows from a result giving control of certain divisibility properties of the conductor of a pair of supercuspidal representations

regularity of minimizers of vectorial integrals with p q growth local lipschitz continuity of local minimizers of vectorial integrals f x du x dx is proved when f satisfies p q growth condition and f x is convex the uniform convexity and the radial structure condition with respect to the last variable are assumed only at infinity

general anisotropic doubly curved shell theory a differential quadrature solution for free vibrations of shells and panels of revolution with a free form meridian abstract the generalized differential quadrature gdq method is applied to study the dynamic behavior of anisotropic doubly curved shells and panels of revolution with a free form meridian the first order shear deformation theory fsdt is used to analyze the above mentioned moderately thick structural elements in order to include the effect of the initial curvature in the evaluation of the stress resultants three different approaches specifically qatu approach toorani lakis approach and reissner mindlin approach are considered and compared an improvement of the classical reissner mindlin theory crmt using a different kinematical model is considered by so doing a generalization of the theory of anisotropic doubly curved shells and panels of revolution is proposed four different anisotropic shell theories namely general first order shear deformation theory by qatu gfsdtq general first order shear deformation theory by toorani lakis gfsdttl general first order shear deformation theory by reissner mindlin gfsdtrm and classical reissner mindlin theory crmt are compared in order to show the differences and the accuracy of these theories the solution is given in terms of generalized displacement components of points lying on the middle surface of the shell simple rational bezier curves are used to define the meridian curve of the revolution structures results are obtained taking the meridian and circumferential coordinates into account without using the fourier modal expansion methodology furthermore gdq results are compared with those obtained by using commercial programs such as abaqus ansys nastran straus and pro mechanica very good agreement is observed

global lipschitz continuity for minima of degenerate problems we consider the problem of minimizing the lagrangian int f nabla u f u among functions on omega subset mathbb r n with given boundary datum varphi we prove lipschitz regularity up to the boundary for solutions of this problem provided omega is convex and varphi satisfies the bounded slope condition the convex function f is required to satisfy a qualified form of uniform convexity only outside a ball and no growth assumptions are made

high accuracy differential quadrature finite element method and its application to free vibrations of thin plate with curvilinear domain summary based on the differential quadrature dq rule the gauss lobatto quadrature rule and the variational principle a dq finite element method dqfem is proposed for the free vibration analysis of thin plates the dqfem is a highly accurate and rapidly converging approach and is distinct from the differential quadrature element method dqem and the quadrature element method qem by employing the function values themselves in the trial function for the title problem the dqfem without using shape functions essentially combines the high accuracy of the differential quadrature method dqm with the generality of the standard finite element formulation and has superior accuracy to the standard fem and fdm and superior efficiency to the p version fem and qem in calculating the stiffness and mass matrices by incorporating the reformulated dq rules for general curvilinear quadrilaterals domains into the dqfem a curvilinear quadrilateral dq finite plate element is also proposed the inter element compatibility conditions as well as multiple boundary conditions can be implemented simply and conveniently as in fem through modifying the nodal parameters when required at boundary grid points using the dq rules thus the dqfem is capable of constructing curvilinear quadrilateral elements with any degree of freedom and any order of inter element compatibilities a series of frequency comparisons of thin isotropic plates with irregular and regular planforms validate the performance of the dqfem copyright q 2009 john wiley sons ltd

higher integrability for minimizers of asymptotically convex integrals with discontinuous coefficients abstract we study the local regularity of vectorial minimizers of integral functionals with standard p growth we assume that the non homogeneous densities are uniformly convex and have a radial structure with respect to the gradient variable only at infinity under a w 1 n sobolev dependence on the spatial variable of the integrand n being the space dimension we show that the minimizers have the gradient locally in l q for every q p as a consequence they are locally holder continuous for every 1

the flexural vibration of rectangular plates with point supports abstract orthogonally generated polynomial functions are used in the lagrangian multiplier method to study the free flexural vibration problem of point supported thin flat rectangular plates the analysis applies to isotropic and specially orthotropic plates having any combination of clamped simply supported or free edges with arbitrarily located point supports and to plates which are continuous over line supports parallel to the plate edges numerical results are presented for a number of specific problems illustrating the accuracy and versatility of the approach and which include natural frequencies and nodal patterns for a point supported plate which is continuous over two perpendicular line supports

free vibration of annular sector plates by an integral equation technique abstract a numerical method is presented for the free vibration analysis of polar orthotropic clamped annular sector plates the results are compared with analytical and experimental values of other investigators a parametric study has been done by varying the sector angle and radii ratio the frequencies for isotropic and orthotropic cases are presented in the form of graphs

an analytical solution for vibrations of a polarly orthotropic mindlin sectorial plate with simply supported radial edges abstract this paper presents the first known analytical solution for vibrations of a polarly orthotropic mindlin sectorial plate with simply supported radial edges the solution is a series solution constructed using the frobenius method and exactly satisfies not only the boundary conditions along the radial and circular edges but also the regularity conditions at the vertex of the radial edges the moment and shear force singularities at the vertex are exactly considered in the solution the correctness of the proposed solution is confirmed by comparing non dimensional frequencies of isotropic plates obtained from the present solution with published data obtained from a closed form solution this paper also investigates the effects of elastic and shear moduli on the vibration frequencies of the sectorial plates with free or fix boundary conditions along the circumferential edge a study is also carried out about the influence of elastic and shear moduli on the moment and shear force singularities at the plate origin r 0 for different vertex angles

in plane free vibration analysis of circular arches with varying cross sections using differential quadrature method abstract a differential quadrature dq methodology recently developed by the authors is used to obtain a general and a computationally efficient and accurate dq solution for free vibration of variable cross section circular thin arches as an improvement to the classical theory and in order to evaluate the higher order natural frequencies more accurately the commonly used hypothesis of the inextensibility of the central axis is removed this enables one to study the effects of slenderness ratio on the natural frequencies especially at higher order modes rotary inertia is included in the formulation and its influence on natural frequencies is studied arches with different types of boundary conditions including those with elastic constraint against rotation at their ends are considered for the cases where a change in the cross sectional or material properties of the arch occurs a numerical domain decomposition technique in conjunction with dq methodology is developed and incorporated to verify the accuracy of the methodology the results are compared with those of exact solutions and or other approaches such as finite elements rayleigh ritz galerkin cell discretization methods and other dq methodologies in particular excellent solution agreements are achieved with those of exact solutions the generalized differential quadrature rule and the optimized rayleigh ritz method solutions

application of the spline element method to analyze vibration of annular sector plates abstract this paper deals with the vibrations of isotropic annular sector plates with arbitrary boundary conditions using the spline element method to demonstrate the accuracy of the methods several examples are solved and results are compared with those obtained by analytical methods and by other numerical methods good accuracy is obtained frequencies of annular sector plates with free edges and with point supports are presented

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