vibration of twisted and curved cylindrical panels with variable thickness abstract a numerical procedure with an exact strain displacement relationship of twisted and curved cylindrical panels having variable thickness derived by considering the green strain tensor on general shell theory is presented using the principle of virtual work and the rayleigh ritz method with algebraic polynomials as in plane and transverse displacement functions the accuracy and applicability of the procedure are verified by comparing the present results with previous experimental and theoretical results for several panels the effects of variation ratio of thickness in chordwise and lengthwise directions twist and curvature both in two directions aforementioned on vibrations of cylindrical panels are studied in detail and typical vibration mode shapes are plotted to demonstrate the effects

numerical analysis of free vibrations of laminated composite conical and cylindrical shells discrete singular convolution dsc approach a numerical study on the free vibration analysis for laminated conical and cylindrical shell is presented the analysis is carried out using love s first approximation thin shell theory and solved using discrete singular convolution dsc method numerical results in free vibrations of laminated conical and cylindrical shells are presented graphically for different geometric and material parameters free vibrations of isotropic cylindrical shells and annular plates are treated as special cases the effects of circumferential wave number number of layers on frequencies characteristics are also discussed the numerical results show that the present method is quite easy to implement accurate and efficient for the problems considered

free vibration of rotating ring stiffened cylindrical shells with non uniform stiffener distribution in this research the free vibration analysis of simply supported rotating cylindrical shells with circumferential stiffeners i e rings with non uniform stiffeners eccentricity and non uniform stiffeners spacing distribution is investigated ritz method is applied while stiffeners are treated as discrete elements in strain energy formulation by adopting sander s theorem stretching and bending characteristics of shells are considered also stretching bending and wrapping effects of stiffeners are investigated the translational inertia in three directions for shell and stiffeners and rotary inertia for stiffeners are considered the effects of initial hoop tension centrifugal and coriolis forces due to the rotation of shell are studied the polynomial functions are used for ritz functions natural frequency results for rings with uniform spacing and constant eccentricity have been compared with analytical and experimental results of other researchers which showed good agreement fortunately the agreements of the presented analytical results with the experimental values are better than the analytical values at constant total mass of stiffeners the effects of non uniform eccentricity distribution and non uniform rings spacing distribution separately and simultaneously on natural frequencies are investigated moreover the influence of rotating speed on natural frequencies for the so called non uniform stiffeners distribution is studied

a hybrid energy approach for vibrational modelling of laminated trapezoidal plates with point supports abstract an investigation on the free flexural vibration of symmetric angle ply thin trapezoidal plates continuous over arbitrarily distributed point supports is reported a hybrid energy approach which combines the pb 2 rayleigh ritz method with the lagrangian multiplier method is proposed for the modelling of the aforementioned plate problem the pb 2 rayleigh ritz method uses a set of ritz functions generated from the product of a two dimensional polynomial and the equations of boundaries each raised to the power of 0 1 or 2 corresponding to a free simply supported or clamped edge respectively the geometric boundary conditions associated with the point supports are satisfied through the use of lagrangian multipliers in this paper some new solutions for the natural frequencies of several laminated trapezoidal plates with different stacking sequences and location of point supports are presented the first known mode shapes by means of contour plots for such laminated plates are also included

buckling of a conical thin shell with variable thickness under a dynamic loading this study considers the buckling of an elastic truncated conical shell having a meridional thickness expressed by an arbitrary function subject to a uniform external pressure which is a power function of time at first the fundamental relations and donnell type dynamic buckling equation of an elastic conical shell with variable thickness have been obtained then employing galerkin s method those equations have been reduced to a time dependent differential equation with variable coefficients finally applying the ritz type variational method the critical static and dynamic loads the corresponding wave numbers dynamic factor and critical stress impulse have been found analytically using the results thus obtained the effects of the thickness variations with a power or an exponential function the variation of the semi vertex angle and the variation of the power of time in the external pressure expression are studied through pertinent computations it is observed that these factors have appreciable effects on the critical parameters of the problem in the heading

formulation of mindlin engesser model for stiffened plate vibration in this paper a mindlin engesser model is developed for the vibration analysis of moderately thick plates with arbitrarily oriented stiffeners the theoretical derivation incorporates the mindlin theory to account for the effects of transverse shear deformation and rotary inertia of plates and the engesser theory to account for the shear deformation of stiffeners with the inclusion of torsion effect in the method of solution the resulting energy functionals are minimized using the ritz procedure with a set of admissible two dimensional functions expressed in the form of simple polynomials the key kinematic feature of these shape functions is that they are boundary oriented and no boundary losses are introduced as in discretization methods with the aim of demonstrating the applicability and versatility of the method numerical examples including plates of various shapes with arbitrarily oriented stiffeners are presented several findings and conclusions regarding the method have been highlighted and discussed

modeling of biological population problems using the element free kp ritz method a degenerate parabolic equation arising in the spatial diffusion of biological population is analyzed using the mesh free kp ritz method the mesh free kernel particle estimate is employed to approximate the 2d displacement field a system of discrete equations is obtained through application of the ritz minimization procedure to the energy expressions to validate the accuracy of the results and stability of the present method convergence studies were carried out based on influences of support size and number of nodes effectiveness of the mesh free kp ritz method for biological population model is investigated by numerical examples in this paper the present results were compared with results reported in extant literature and were found to be in good agreement with the literature

vibration analysis of non circular curved panels by the differential quadrature method free vibration characteristics of cantilever non circular curved panels are analyzed by using the differential quadrature method dqm in this paper the equations of motion of a curved panel are based on the love s hypothesis and are expressed in an orthogonal curvilinear co ordinate system by applying the differential quadrature formulation and the proposed modified relationships for specified boundary conditions the free vibration equations of motion of the curved panel are transformed to a set of algebraic equations natural frequencies of a cantilever flat plate and a circular curved panel are obtained for verifying the applicability of the present approach good convergent trend and accuracy are observed effects of shallowness thickness and aspect ratios on the natural frequencies of a cantilever curved panel are also investigated furthermore natural frequencies of parabolic curved panels are obtained in all cases studied the efficiency and convenience of the dqm are illustrated

effect of elastic foundation on asymmetric vibration of polar orthotropic linearly tapered circular plates asymmetric vibrations of polar orthotropic circular plates of linearly varying thickness resting on an elastic foundation of winkler type are discussed on the basis of the classical plate theory ritz method has been employed to obtain the natural frequencies of vibration using the functions based upon the static deflection of polar orthotropic plates which has faster rate of convergence as compared to the polynomial co ordinate functions frequency parameter of the plate with elastically restrained edge conditions are presented for various values of taper parameter rigidity ratio and foundation parameter a comparison of the results with those available in the literature obtained by finite element method receptance method and polynomial co ordinate functions shows an excellent agreement

free vibration analysis of arbitrarily shaped plates with clamped edges using wave type functions the basic idea related to the non dimensional dynamic influence green s function defined in an infinite membrane has been applied to the free vibration analysis of arbitrarily shaped plates with clamped edges another non dimensional dynamic influence function newly defined in the paper exactly satisfies the governing homogeneous differential equations of plates and is regular in the entire domain the proposed method uses the boundary discretization scheme similar to that of the boundary element method but does not require any interpolation function between the nodes distributed along the boundary as a result the method has a significant advantage in its simplicity and accuracy although the method uses no interpolation function it gives very accurate eigenvalues and mode shapes compared with the exact solutions or fem results it should be also noted that particular attention is given to reduce the size of the system matrix whose determinant equation yields eigenvalues and to overcome the functional dependence problem of the non dimensional dynamic influence functions

on the average speed of lemke s algorithm for quadratic programming in this paper we show that the average number of steps of the lemke algorithm for the quadratic programming problems grows at most linearly in the number of variables while fixing the number of constraints the result and method were motivated by smale s result on linear programming problems cf 4 we also give the probability that a quadratic programming problem indeed possesses a finite optimal solution

bending and buckling analysis of antisymmetric laminates using the moving least square differential quadrature method in this paper the moving least square differential quadrature mlsdq method is employed to bending and buckling analysis of antisymmetric thick laminates based on the first order shear deformation theory the displacement and rotation components of the plate are independently assumed with the centered moving least square mls approximation within each domain of influence the weighting coefficients are associated with the nodal partial derivatives which are calculated through a fast computation procedure together with the mls nodal shape functions numerical examples are illustrated to study the accuracy stability and convergence of the mlsdq method effects of support size order of the complete basis functions and node irregularity on the numerical accuracy are investigated typical computational results of displacements stresses and critical buckling loads of various laminated plates are presented and compared with the available exact and finite element solutions

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

the number of outcomes in the pareto optimal set of discrete bargaining games a set of n players is to bargain over which one of m possible outcomes will be chosen the preference of outcome i to player j is assumed to be a random variable with all preference rankings equally likely and without ties this would arise in case the payoffs are chosen as independent samplings from a continuous distribution fj the mean and distribution of the number of outcomes in the pareto optimal set are calculated for finite m as m the mean is asymptotic to log m 0 577n 1 n 1 and for n 2 m the distribution approaches the normal distribution the results are also applied to a problem in multiattribute utility theory suppose we wish to select an individual with high values on two personal attributes that are independent and continuously measurable of a world population of four billion the efficient set would have an expectation of 22 7 individuals

trellis coded vector quantization a vector generalization of trellis coded quantization tcq called trellis coded vector quantization tcvq and experimental results showing its performance for an i i d gaussian source are presented for a given rate tcvq yields a lower distortion that tcq at the cost of an increase in implementation complexity in addition tcvq allows fractional rates which tcq does not

on the average number of steps of the simplex method of linear programming the goal is to give some theoretical explanation for the efficiency of the simplex method of george dantzig fixing the number of constraints and using dantzig s self dual parametric algorithm we show that the number of pivots required to solve a linear programming problem grows in proportion to the number of variables on the average

a ritz vibration analysis of doubly curved rectangular shallow shells using a refined first order theory integral expressions for strain and kinetic energies in vibration analysis of shear deformable doubly curved shallow shells are presented although the formulation follows the first order shear deformation theory the consideration of lame parameters for the transverse shear strain through shell thickness which have been hitherto neglected by other researchers shows linear distribution functions instead of constant values if the lame parameters were dropped finite higher order two dimensional orthogonal polynomials pb 2 functions previously used in thin shell analyses 3 6 have been generalized from three to five degrees to account for the additional rotation fields of a moderately thick shell these global shape functions satisfy the kinematic boundary conditions at the outset the excellent performance and versatility of the computational methodology of the pb 2 ritz method are illustrated in representative numerical simulations the resultant matrix size is far smaller than other discretization methods and yet accurate solutions can be obtained the validity of the results is verified through direct comparisons the discrepancy of various formulations with and without the lame parameters is presented and discussed

asymptotically dense spherical codes ii laminated spherical codes for pt i see ibid vol 43 no 6 p 1774 85 1997 new spherical codes called laminated spherical codes are constructed in dimensions 2 49 using a technique similar to the construction of laminated lattices each spherical code is recursively constructed from existing spherical codes in one lower dimension laminated spherical codes outperform the best known spherical codes in the minimum distance sense for many code sizes the density of a laminated spherical code approaches the density of the laminated lattice in one lower dimension as the minimum distance approaches zero in particular the three dimensional laminated spherical code is asymptotically optimal in the sense that its density approaches the fejes toth 1959 upper bound as the minimum distance approaches zero laminated spherical codes perform asymptotically as well as wrapped spherical codes in those dimensions where laminated lattices are optimal sphere packings

a refined asymptotic theory for dynamic analysis of doubly curved laminated shells the asymptotic theory developed recently for dynamic analysis of doubly curved laminated shells is refined by including the transverse rotations as auxiliary variables the theory embraces the first order shear deformation theory fsdt and the higher order shear deformation theory hsdt as the first order approximation higher order corrections to the approximation are determined by solving the fsdt or hsdt equations in a hierarchic way the secular terms in the asymptotic solution are eliminated systematically by means of multiple scales and solvability conditions for the higher order equations the performance of the refined theory is illustrated by applying it to benchmark problems numerical comparisons are made to examine the convergence of the solutions

analytical coding of gaussian sources several procedures for encoding a stationary gaussian source are investigated in contrast to vector quantization by the lbg algorithm coding and rate distortion performance can be described analytically due to the regular structure of the code vectors

vibration of pretwisted cantilever shallow conical shells abstract this paper presents a mathematical model to investigate the effects of initial twist on the vibratory characteristics of cantilever shallow conical shells the energy functional is minimized according to the ritz procedure to arrive at the governing eigenvalue equation a set of orthogonally generated two dimensional polynomials associated with a basic function which accounts for the boundary expressions and constraints is introduced to approximate the in plane and transverse displacement amplitude functions the complete procedure has been automated to compute the vibration frequencies and mode shapes for exemplary problems in the numerical experiments the convergence of eigenvalues is confirmed by increasing the degrees of polynomials employed in the admissible shape functions to enhance the existing literature a set of first known frequency parameters is presented the paper highlights the important effects of angle of twist on the vibration frequencies and mode shapes of conical shells the fundamental physical frequency decreases monotonically for a longer conical shell the result shows that an increase in the angle of twist does not ensure higher torsional stiffness for a conical shell which is in contradiction with previous observation for a pretwisted beam or plate the symmetry of modes is absent when the angle of twist is non zero

an element free imls ritz method for numerical solution of three dimensional wave equations abstract this paper presents an element free based numerical approach for solving three dimensional wave equations based on the ritz minimization procedure the method involves the use of a set of orthogonal shape functions to approximate its field variables in this study an improved moving least squares imls is used to generate sets of orthogonal shape functions that reduced the number of unknown coefficients in the trial functions the entire approximation procedure can be easily implemented numerically the accuracy of the approximation can be enhanced by increasing the number of nodes used in the computation as the result of the above procedures a final algebraic equation system is derived through discretizing the constructed functional the functional is established by enforcing the dirichlet boundary conditions via the penalty approach the simplicity and applicability of the element free method are demonstrated by solving several selected linear and nonlinear three dimensional wave equations besides the convergence study the present results are compared with the available published solutions from the literature where possible verifying the accuracy efficiency and reliability of the imls ritz method

simplified method for solving problems of vibrating plates of doubly connected arbitrary shape part ii applications and experiments abstract the eigenfrequencies of ring shaped polygonal plates ring shaped elliptical plates rectangular plates with elliptical inner boundaries and circular plates with elliptical inner boundaries are obtained the method developed by the author in the companion paper part i is applied for finding the eigenfrequencies to verify the present results experimental tests have also been carried out for some important cases

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

dynamic stability analysis of composite laminated cylindrical shells via the mesh free kp ritz method abstract in this paper a novel numerical technique is developed for the dynamic stability analysis of composite laminated cylindrical shells under static and periodic axial forces the mesh free kernel particle kp estimate is employed in hybridized form with harmonic functions to approximate the 2 d transverse displacement field a system of mathieu hill equations is obtained through the application of the ritz minimization procedure to the energy expressions the principal instability regions are then analyzed via bolotin s first approximation the mesh free kp ritz method is validated through comparison with existing available numerical data taken from open literature effects of boundary conditions and lamination schemes on the instability regions are also examined in detail

progressive coding of a gaussian source using matching pursuit in this paper the application of matching pursuit mp in progressive coding of memoryless gaussian sources is studied in addition a detailed analysis of the rate distortion performance of our proposed mp encoder is presented and the distortion of the mp encoder is derived in terms of dictionary size and number of quantization levels and the optimum parameters are calculated our analysis is based on a probabilistic model for matching pursuit residual vectors our simulation results verify the accuracy of our analysis and show that matching pursuit can produce an embedded bitstream with comparable quality to existing quantizers the mp encoder outperforms quantizers that are capable of producing embedded bitstreams

simplified method for solving problems of vibrating plates of doubly connected arbitrary shape part i derivation of the frequency equation abstract a simplified approximate method for solving problems of vibrating plates of doubly connected arbitrary shapes is presented in the analysis an arbitrarily shaped boundary is divided into small segments and general transformed expressions for the bending slope the bending moment and the shearing force of a segment are given under the assumption that the angle between the normal to the segment and the reference axis is constant the boundary conditions along the outer and the inner edges are satisfied by means of the fourier expansion collocation method the equation for finding the eigenfrequencies and mode shapes is obtained for arbitrarily shaped boundaries

vibrational response of symmetrically laminated trapezoidal composite plates with point constraints abstract this paper presents the first known results for free vibrations of thin points supported symctrically laminated trapezoidal composite plates the solution method developed is based on the rayleigh ritz method and the admissible 2 d orthogonal polynomials to derive the governing eigenvalue equation the natural frequencies and mode shapes for the laminated plates are obtained by solving this governing eigenvalue equation several test problems are solved to demonstrate the accuracy and flexibility of the proposed method the effects of fibre orientations points location and the number of layers in the stacking sequences on the vibrational response for the plate problems are investigated variation of spring constants for the clastic points on the effect of the frequency parameters is also considered

static analysis of mindlin plates the differential quadrature element method dqem abstract the differential quadrature method dqm is a new numerical method for fast solving linear and nonlinear differential equations based on global basis functions in the present study a discrete approximate method based on the dqm the differential quadrature element method dqem is developed for the axisymmetric static analysis of moderately thick circular and annular plates described by the mindlin shear deformable theory the basic idea of the dqem is 1 to divide the whole variable domain into several sub domains elements 2 to form discretized element governing equations by applying the dqm to each element and 3 to assemble all the discretized element governing equations into the overall characteristic equations with the consideration of displacement and stress compatibility conditions between adjacent elements the annular and circular mindlin plate elements of differential quadrature dq are established the convergence characteristics of the proposed method are carefully investigated from the view points of element refinement and element grid refinement and some general regulations and suggestions on element division and element grid selection are provided a number of numerical examples are calculated and the results are compared with the corresponding exact solutions which exhibits high accuracy simplicity and applicability of the present method

a rayleigh ritz approach to transverse vibration of isotropic and anisotropic trapezoidal plates using orthogonal plate functions abstract to overcome the lack of a more general method for free vibration analysis of trapezoidal plates a computationally efficient and highly accurate rayleigh ritz approach with the newly developed orthogonal plate functions is proposed to solve these problems with any combination of clamped simply supported and free edge support conditions the deflection of the plate is approximated by a set of two dimensional orthogonal plate functions generated using the gram schmidt procedure which expresses the entire plate domain into two implicitly related variables in the present paper the effects of the fibre orientation on the vibrational behaviour of the plates are considered the numerical results for isotropic and anisotropic trapezoidal plates are presented where possible the numerical results are verified with other existing values in the literature

successive refinement of information the successive refinement of information consists of first approximating data using a few bits of information then iteratively improving the approximation as more and more information is supplied the goal is to achieve an optimal description at each stage in general an ongoing description which is rate distortion optimal whenever it is interrupted is sought it is shown that in order to achieve optimal successive refinement the necessary and sufficient conditions are that the solutions of the rate distortion problem can be written as a markov chain in particular all finite alphabet signals with hamming distortion satisfy these requirements it is also shown that the same is true for gaussian signals with squared error distortion and for laplacian signals with absolute error distortion a simple counterexample with absolute error distortion and a symmetric source distribution which shows that successive refinement is not always achievable is presented

orthotropic influence on frequency characteristics of a rotating composite laminated conical shell by the generalized differential quadrature method by using the generalized differential quadrature gdq method this paper presents the influence of orthotropic material on the frequency characteristics for a rotating thin truncated circular symmetrical cross ply laminated composite conical shell with simply supported boundary conditions at both edges the present analysis includes the effects of initial hoop tension and the centrifugal and coriolis accelerations due to rotation frequency characteristics is obtained for various orthotropic parameters the orthotropic influences of material on the frequency characteristics are also discussed for different cone angles to validate the accuracy and efficiency of present analysis by the gdq method comparisons are made with those available in open literature very good agreements are achieved

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

solution of vibration problems for shallow shells of arbitrary form by the r function method an effective method for the free vibration of arbitrary plan form shallow shells is proposed the algorithm is based on the r function theory and variational ritz method the effectiveness of the method offered is illustrated by examples of shallow shells of a complex plan form at different boundary conditions three types of curvatures are considered which are the spherical circularly cylindrical and of hyperbolic paraboloid shape a number of the test problems were solved to check the veracity of the proposed method the comparison between the obtained results and those available in the literature was carried out

statical and dynamical behaviour of thin fibre reinforced composite laminates with different shapes abstract based on the classical laminated plate theory a variational approach for the study of the statical and dynamical behaviour of arbitrary quadrilateral anisotropic plates with various boundary conditions is developed the analytical formulation uses the ritz method in conjunction with natural coordinates to express the geometry of general plates in a simple form the deflection of the plate is approximated by a set of beam characteristic orthogonal polynomials generated using the gram schmidt procedure the algorithm developed is quite general and can be used to study fibre reinforced composite laminates with symmetric lay ups which may have general anisotropy and any combinations of clamped simply supported and free edge support conditions various numerical applications are presented and some results are compared with existing values in the literature to demonstrate the accuracy and flexibility of the present method new results were also determined for plates with different geometrical shapes combinations of boundary conditions several stacking sequences and various angles of fibre orientation

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 frequency response of moderately thick simply supported rectangular plates with arbitrary lamination a here to fore unavailable analytical solution to the boundary value problem of free vibration response of arbitrarily laminated moderately thick rectangular plates subjected to an admissible boundary condition is presented a novel boundary continuous solution approach is employed to solve the highly coupled governing partial differential equations that arise from the implementation of the yang norris stavsky 1966 theory incorporating first order shear deformation and rotary and in plane inertias the numerical results presented for various parametric effects to study first lowest seven eigenvalues and corresponding eigenvectors can be capitalized as bench marks for a future comparison an eight node isoparametrics shear flexible element is considered to validate its performance with respect to the present solutions

differential quadrature element method a new approach for free vibration analysis of polar mindlin plates having discontinuities this paper presents the numerical development of the differential quadrature element method dqem for free vibration analysis of the shear deformable plates in polar coordinates this is an improvement on the global differential quadrature method dqm the formulations of the dqem for polar plate vibration element are derived in detail the convergence characteristics of the dqem for solving the free vibration of polar plates are carefully examined the reliability and flexibility of the dqem are illustrated by solving several selected example polar plates having discontinuities which are not solvable directly by the dqm the accuracy of the dqem is evaluated and verified by comparing the present numerical results with the existing exact or approximate solutions or the fem solutions computed using the software package ansys version 5 3

a new differential quadrature methodology for beam analysis and the associated differential quadrature element method this paper presents a computationally efficient and an accurate new methodology in differential quadrature analysis of beam elements the methodology would overcome the difficulties in boundary conditions implementations of fourth order differential equations encountered in such problems the methodology benefited from defining the second order derivatives along the boundaries as independent degrees of freedom would enable the differential quadrature method to exactly satisfy some types of boundary conditions where by most other conventional algorithms have to be satisfied approximately the weighting coefficients employed are not exclusive and any accurate and efficient method such as the generalized differential quadrature method may be used to produce the methods weighting coefficients by solving some typical stability deflection and frequency analysis beam problems and by comparing the results with those of exact solutions and or those of other methodologies accuracy convergency and efficiency of the methodology is asserted in order to generalize its application to large scale beam structures and to the cases with the discontinuity in loading conditions and geometry a new one dimensional differential quadrature element method formulation is presented and implemented

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

a pb 2 ritz formulation for flexural vibration of shallow cylindrical shells of rectangular planform abstract this paper presents a free flexural vibration analysis of shallow cylindrical shells of rectangular planform with arbitrary combinations of free simply supported and clamped boundaries the pb 2 ritz method previously used in the plate analysis by one of the authors is now extended to shallow shell studies the ritz approach along with the in plane and transverse displacements assumed in the form of orthogonal polynomials is used to formulate the problems numerical results for the vibration frequencies for wide ranges of aspect ratio shallowness ratio and thickness ratio are presented several selected contour plots of the mode shapes for six different combinations of boundary conditions are presented as usual the accuracy of the present method is illustrated by convergence tests and comparison with the well established results from the literature

analytical and numerical results for vibration analysis of multi stepped and multi damaged circular arches this paper investigates the in plane linear dynamic behaviour of multi stepped and multi damaged circular arches under different boundary conditions cracked cross sections are modelled as massless elastic rotational hinges in damaged configuration cracks can be located both at the interface between two adjacent portions as well as inside the portion itself for each arch portion bounded by two cracks the differential equations of motion have been established considering axial extension transverse shear effects and rotatory inertia the equilibrium equations of arch portions are combined in the coupled fundamental system in terms of radial displacement tangential displacement and rotation analytical and numerical solutions for multi stepped arches in undamaged as well as in damaged configurations are proposed the analytical solution is based on the euler characteristic exponent procedure involving the roots of characteristic polynomials while the numerical method is focused on the generalized differential quadrature gdq method and the generalized differential quadrature element gdqe technique numerical results are shown in terms of the first 10 analytical and numerical frequencies of multi stepped and multi damaged arches with different boundary conditions finally convergence and stability characteristics of the gdqe procedure are investigated the convergence rate of the natural frequencies is shown to be very fast and the stability of the numerical procedure is very good

analytical investigation of structurally stable configurations in shape memory alloy actuated plates strains produced by active materials embedded in plates have been extensively used to manipulate the shape of surface like engineering structures shape memory alloys smas are active materials that provide a significant amount of strain under large stresses a characteristic of great utility in such morphing structures in this work an analytical approach to approximate the deformation of plates with sma constituents is developed via the rayleigh ritz method an additive set of kinematically admissible displacement fields with unknown coefficients is used to describe the plate displacement field the total potential energy is then calculated using the displacement field loading conditions and constitutive relations for the plate layer s composed of sma wire meshes dense sma films and or elastic material the unknown coefficients are then found via minimization of the total potential energy this approach provides closed form expressions for the approximate deformation of the plates including multistable configurations the response of circular sma based plates is studied herein the results show that temperature fields with a linear variation in the radial direction induce multistable configurations in which the plate gaussian curvature is determined by the direction of the temperature gradient an alternative inversion of the proposed approach is used to directly compute the temperature field required to morph a plate towards a prescribed goal shape the obtained closed form expressions show good agreement with detailed non linear finite element analysis simulations the proposed approach provides analysts with a low computational cost and relatively simple implementation to assess the potentially stable configurations of sma based plates under given loading conditions knowledge of such stable configurations is very valuable in the design of sma based morphing structures c 2015 elsevier ltd all rights reserved

an efficient differential quadrature methodology for free vibration analysis of arbitrary straight sided quadrilateral thin plates in this paper a new differential quadrature dq methodology is employed to study free vibration of irregular quadrilateral straight sided thin plates a four nodded super element is used to map the irregular physical domain into a square domain in the computational domain second order transformation schemes with relative ease and less computation are employed to transform the fourth order governing equation of thin plates between the two domains the only degree of freedom within the domain is the displacement whereas along the boundaries the displacement as well as the second order derivative of the displacement with respect to associated normal co ordinate variable in computational domain are the two degrees of freedom implementing the method the formulation for the dq method for the free vibration analysis of plates of straight sided shapes was presented together with the implementation procedure for the different boundary conditions to demonstrate the accuracy convergency and stability of the new methodology detail studies are made on isotropic plates at acute angles with different geometries boundary and loading conditions including dq free edge boundary condition implementations accurate results even with fewer degrees of freedom than for those of comparable numerical algorithms were achieved

nonconservative stability problems via generalized differential quadrature method abstract in this paper the generalized differential quadrature gdq method is applied to solve classical and nonclassical nonconservative stability problems various cantilever beams subjected to slope dependent forces are considered first the governing differential equation for a nonuniform column subjected to an arbitrary distribution of compressive subtangential follower forces is obtained the effect of the variability of the mechanical properties along the beam length is also considered then the application of the gdq procedure leads to a discrete system of algebraic equations from which the system critical loads can be obtained by solving an associated eigenvalue problem a parametrical study for different levels of nonconservativeness of the applied load is carried out for some classical benchmark cases such as beck s leipholz s and hauger s column problems finally applications to geometrically and mechanically tapered beams subjected to nonpotential subtangential follower forces are investigated as nonclassical cases it has been proved that the method can efficiently solve structural nonconservative elastic problems and more in general problems governed by a nonsymmetric system of algebraic equations

an improved moving least squares ritz method for two dimensional elasticity problems we propose an improved moving least squares ritz imls ritz method with its element free framework developed for studying two dimensional elasticity problems using the imls approximation for the field variables the discretized governing equations of the problem are derived via the ritz procedure in the imls an orthogonal function system with a weight function is employed as the basis for construction of its displacement field by using the element free imls ritz method solutions of the two dimensional elasticity problems are obtained the applicability of the element free imls ritz method is illustrated through three selected example problems the convergence characteristics of the method are examined by varying the number of nodes and geometric parameters of these examples the accuracy of the method is validated by comparing the computed results with the efg and exact solutions

use of two dimensional orthogonal polynomials for vibration analysis of circular and elliptical plates abstract a general numerical method is developed to estimate the natural frequencies and the mode shapes for transverse vibration of circular and elliptical plates a set of orthogonal plate functions is used as the admissible functions in the rayleigh ritz approach to approximate the eigenvalues and eigenvectors new starting functions are proposed which are used in a recurrence formula to generate the higher terms in the set of orthogonal plate functions to approximate the mode shapes for circular and elliptical plates these functions are general and easily formed for circular and elliptical plates having classical boundary conditions several numerical examples are solved to demonstrate the applicability and the accuracy of the new proposed plate functions

a posteriori quantization of progressive matching pursuit streams this paper proposes a rate distortion optimal a posteriori quantization scheme for matching pursuit mp coefficients the a posteriori quantization applies to an mp expansion that has been generated offline and cannot benefit of any feedback loop to the encoder in order to compensate for the quantization noise the redundancy of the mp dictionary provides an indicator of the relative importance of coefficients and atom indices and subsequently on the quantization error it is used to define a universal upper bound on the decay of the coefficients sorted in decreasing order of magnitude a new quantization scheme is then derived where this bound is used as an oracle for the design of an optimal a posteriori quantizer the latter turns the exponentially distributed coefficient entropy constrained quantization problem into a simple uniform quantization problem using simulations with random dictionaries we show that the proposed exponentially upper bounded quantization euq clearly outperforms classical schemes stepping on the ideal oracle based approach a suboptimal adaptive scheme is then designed that approximates the euq but still outperforms competing quantization methods in terms of rate distortion characteristics finally the proposed quantization method is studied in the context of image coding it performs similarly to state of the art coding methods and even better at low rates while interestingly providing a progressive stream that is very easy to transcode and adapt to changing rate constraints

treatments of over restrained boundaries for doubly connected plates of arbitrary shape in vibration analysis abstract the problem of the free flexural vibrations of plates of doubly connected arbitrary shape is investigated a hybrid energy approach which combines both the advantages of the rayleigh ritz method and the lagrange multiplier method is developed for analysing the aforementioned plate problems the rayleigh ritz method with a set of pb 2 shape functions is used to formulate the plates with classical boundary conditions as a single continuum element while the lagrange multipliers are imposed at discrete points in the inner plate boundaries for instance when the overrestrained boundary has occurred the admissible pb 2 shape function consists of the product of a two dimensional polynomial and a basic function the basic function is defined by the product of the equations of the prescribed piecewise continuous boundary shape each raised to the power of 0 1 or 2 corresponding respectively to a free simply supported or clamped edge this set of functions automatically satisfies all the kinematic boundary conditions of the plate at the outset numerical results for several examples of doubly connected plates of arbitrary shape are presented to demonstrate the applicability and accuracy of the present method

random linear programs with many variables and few constraints we extend and simplify smale s work on the expected number of pivots for a linear program with many variables and few constraints our analysis applies to new versions of the simplex algorithm and to new random distributions

dsc ritz method for high mode frequency analysis of thick shallow shells this paper addresses a challenging problem in computational mechanics the analysis of thick shallow shells vibrating at high modes existing methods encounter significant difficulties for such a problem due to numerical instability a new numerical approach dsc ritz method is developed by taking the advantages of both the discrete singular convolution dsc wavelet kernels of the dirichlet type and the ritz method for the numerical solution of thick shells with all possible combinations of commonly occurred boundary conditions as wavelets are localized in both frequency and co ordinate domains they give rise to numerical schemes with optimal accurate stability and flexibility numerical examples are considered for mindlin plates and shells with various edge supports benchmark solutions are obtained and analyzed in detail experimental results validate the convergence stability accuracy and reliability of the proposed approach in particular with a reasonable number of grid points the new dsc ritz method is capable of producing highly accurate numerical results for high mode vibration frequencies which are hitherto unavailable to engineers moreover the capability of predicting high modes endows us the privilege to reveal a discrepancy between natural higher order vibration modes of a mindlin plate and those calculated via an analytical relationship linking kirchhoff and mindlin plates copyright 2004 john wiley sons ltd

2 d differential quadrature solution for vibration analysis of functionally graded conical cylindrical shell and annular plate structures this paper focuses on the dynamic behavior of functionally graded conical cylindrical shells and annular plates the last two structures are obtained as special cases of the conical shell formulation the first order shear deformation theory fsdt is used to analyze the above moderately thick structural elements the treatment is developed within the theory of linear elasticity when materials are assumed to be isotropic and inhomogeneous through the thickness direction the two constituent functionally graded shell consists of ceramic and metal that are graded through the thickness from one surface of the shell to the other two different power law distributions are considered for the ceramic volume fraction the homogeneous isotropic material is inferred as a special case of functionally graded materials fgm the governing equations of motion expressed as functions of five kinematic parameters are discretized by means of the generalized differential quadrature gdq method the discretization of the system leads to a standard linear eigenvalue problem where two independent variables are involved without using the fourier modal expansion methodology for the homogeneous isotropic special case numerical solutions are compared with the ones obtained using commercial programs such as abaqus ansys nastran straus pro mechanica very good agreement is observed furthermore the convergence rate of natural frequencies is shown to be very fast and the stability of the numerical methodology is very good different typologies of non uniform grid point distributions are considered finally for the functionally graded material case numerical results illustrate the influence of the power law exponent and of the power law distribution choice on the mechanical behavior of shell structures

the element free kp ritz method for free vibration analysis of conical shell panels in this paper the free vibration of conical panels is analyzed by the mesh free kp ritz method both 1 d and 2 d versions of the kp ritz approach are formulated for conical panels for conical panels with two simply supported straight edges the 1 d kp ritz version is used where the kernel particle estimation is employed in hybridized form with harmonic functions to approximate the 2 d displacement field for conical panels having arbitrary boundary conditions the displacement field is approximated by the 2 d kp ritz version with 2 d form of kernel particle functions employed the classical thin shell theory based on love s hypothesis is employed in the present analyses and based on the kernel particle concept and ritz technique the eigenequations of the frequencies of the conical panels are obtained to validate the accuracy of stability of the present method convergence studies were carried out based on the influences of the support size and the number of nodes comparisons were also made with existing results available in the open literature this study also examines in detail the effects of variation in the semi vertex angle and boundary conditions on the frequency characteristics of conical panels

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

trellis based scalar vector quantizer for memoryless sources the paper describes a structured vector quantization approach for stationary memoryless sources that combines the scalar vector quantizer svq ideas laroia and farvardin 1993 with trellis coded quantization marcellin and fischer 1990 the resulting quantizer is called the trellis based scalar vector quantizer tb svq the svq structure allows the tb svq to realize a large boundary gain while the underlying trellis code enables it to achieve a significant portion of the total granular gain for large block lengths and powerful possibly complex trellis codes the tb svq can in principle achieve the rate distortion bound as indicated by the results obtained even for reasonable block lengths and relatively simple trellis codes the tb svq outperforms all other fixed rate quantizers at reasonable complexity

trellis coded quantization of memoryless and gauss markov sources trellis coded quantization tcq is developed and applied to the encoding of memoryless and gauss markov sources the theoretical justification for the approach is alphabet constrained rate distortion theory which is a dual to the channel capacity argument that motivates trellis coded modulation tcm the authors adopt the notions of signal set expansion set partitioning and branch labeling of tcm but modify the techniques to account for the source distribution to design tcq coders of low complexity with excellent mean squared error mse performance for a memoryless uniform source tcq provides an mse within 0 21 db of the distortion rate bound at all positive integral rates the performance is superior to that promised by the coefficient of quantization for all of the best lattices known in dimensions 24 or less for a memoryless gaussian source the tcq performance at rates of 0 5 1 and 2 b sample is superior to all previous results the authors found in the literature the encoding complexity of tcq is very modest tcq is incorporated into a predictive coding structure for the encoding of gauss markov sources simulation results for first second and third order gauss markov sources are presented

vibratory characteristics of cantilevered rectangular shallow shells of variable thickness in this paper a comprehensive study on the modeling of vibratory response of variable thickness cantilevered shallow cylindrical shells of rectangular planform is carried out through the principle of minimum total energy the equations of stretching and bending strain energies kinetic energy and the associated boundary conditions of the shells are derived the present model is developed based on the ritz formulation with the assumption of sets of mathematicall y complete admissible two dimensional polynomials to approximate the in plane and transverse displacement amplitude functions a basic function is introduced in the approximate method to enforce automatic satisfaction of the kinematic boundary conditions sets of comprehensive reasonably accurate vibration frequencies of the shallow shells are presented for wide ranges of aspect ratio thickness variation ratios and shallowness ratio these results where possible are verified by comparing with other established experimental and theoretical solutions few selected contour plots for the first known mode shapes of these cylindrical shells of variable thickness are included

on the vibration of shells with timoshenko mindlin type shear deflections and rotatory inertia equations of motion of shells are formulated in curvilinear co ordinates that are consistent with assumptions made in the timoshenko beam and also the mindlin plate equations this consistency is proven by obtaining the timoshenko and mindlin equations from the derived shell equations by geometrical reduction the implication of the timoshenko type shear is illustrated by constrasting the free vibration behavior of the special case of a cylindrical shell with the behavior of the timoshenko beam and the mindlin plate

analyzing two dimensional sine gordon equation with the mesh free reproducing kernel particle ritz method abstract we consider an analysis of the non linear two dimensional sine gordon sg equation the analysis is performed using the mesh free reproducing kernel particle ritz method kp ritz method the mesh free kernel particle estimate is employed to approximate the 2d displacement field a system of discrete equations is obtained through application of the ritz minimization procedure to the energy expressions to validate the accuracy of the results and stability of the present method convergence studies were carried out based on influences of support size and number of nodes the present results were compared with results reported in extant literature and were found to be in good agreement with the literature

free vibration analysis of circular plates using generalized differential quadrature rule the free vibration of solid circular plates has been studied using the generalized differential quadrature rule gdqr the effects such as stepped thickness intermediate concentric ring supports and elastic restraints have been considered discrete system equations for natural frequency analysis were derived based on the gdqr issues related to the implementation of the boundary and compatibility conditions were addressed two regularity conditions at the solid circular plate center were formularized since they were not quite clear in the present literature some wrong applications in the implementation of both differential quadrature methods and regularity conditions at the solid circular plate center have been pointed out excellent results have been obtained with the presented examples

design performance and complexity analysis of residual trellis coded vector quantizers multistage trellis coded vector quantization ms tcvq is developed as a constrained trellis source coding technique the performance of the two stage tcvq is studied for gaussian sources issues of stage by stage design output alphabet selection and complexity are addressed with emphasis on selecting and partitioning the stage codebooks for a given rate ms tcvq achieves low encoding and storage complexity compared to tcvq and comparisons with same dimensional multistage vector quantization indicate a 0 5 3 db improvement in signal to quantization noise ratio

uniform and piecewise uniform lattice vector quantization for memoryless gaussian and laplacian sources lattice vector quantizer design procedures for nonuniform sources are presented the procedures yield lattice vector quantizers with excellent performance and retaining the structure required for fast quantization analytical methods for truncating and scaling lattices to be used in vector quantizations are given and their utility is demonstrated for independent and identically distributed i i d gaussian and laplacian sources an analytical technique for piecewise linear multidimensional compandor designs is evaluated for i i d gaussian and laplacian sources by comparing its performance to that of the other vector quantizers

a highly accurate analytical solution for free vibration analysis of simply supported right triangular plates abstract a new analytical technique is described for the free vibration analysis of simply supported right triangular plates while it is seen that the basic mathematical approach is applicable to right triangular plates with various types of boundary conditions the problem of the simply supported right triangular plate is resolved for illustrative purposes and eigenvalues are presented for the first four modes the method employed is basically that of superposition the governing differential equation is completely satisfied and by means of a judicious choise of building blocks the boundary conditions are satisfied to any desired degree of accuracy

in loop atom modulus quantization for matching pursuit and its application to video coding this paper provides a precise analytical study of the selection and modulus quantization of matching pursuit mp coefficients we demonstrate that an optimal rate distortion trade off is achieved by selecting the atoms up to a quality dependent threshold and by defining the modulus quantizer in terms of that threshold in doing so we take into account quantization error re injection resulting from inserting the modulus quantizer inside the mp atom computation loop in loop quantization not only improves coding performance but also affects the optimal quantizer design for both uniform and nonuniform quantization we measure the impact of our work in the context of video coding for both uniform and nonuniform quantization the precise understanding of the relation between atom selection and quantization results in significant improvements in terms of coding efficiency at high bitrates the proposed nonuniform quantization scheme results in 0 5 to 2 db improvement over the previous method

gaussian source coding with spherical codes a fixed rate shape gain quantizer for the memoryless gaussian source is proposed the shape quantizer is constructed from wrapped spherical codes that map a sphere packing in spl ropf sup k 1 onto a sphere in spl ropf sup k and the gain codebook is a globally optimal scalar quantizer a wrapped leech lattice shape quantizer is used to demonstrate a signal to quantization noise ratio within 1 db of the distortion rate function for rates above 1 bit per sample and an improvement over existing techniques of similar complexity an asymptotic analysis of the tradeoff between gain quantization and shape quantization is also given

upper and lower bounds for frequencies of trapezoidal and triangular plates upper and lower bounds are given for the two lowest frequencies of vibration of clamped trapezoidal and triangular plates it is believed that this is the first time that rigorous bounds have been calculated for the vibrational frequencies of plates of these shapes

a global continuum ritz formulation for flexural vibration of pretwisted trapezoidal plates with one edge built in abstract the development of a continuum ritz model for twisted plate vibration on the basis of minimization of the energy functional is presented this method involves the use of a set of orthogonally generated pb 2 shape functions to approximate the transverse and in plane deflections in this paper a two dimensional recurrence formula is proposed to generate this set of functions during the orthogonalization process a basic function is introduced to each transverse and in plane displacement to ensure the automatic satisfaction of the essential boundary conditions the whole process can be easily implemented numerically and the accuracy of the method can be achieved by increasing the number of terms used in the polynomial functions following the above procedures a governing eigenvalue equation is derived this equation is solved to determine the vibration response of trapezoidal plates with initial twist in order to verify the validity and reliability of this method in addition to the convergence study the present results are compared with the available values from the literature where possible

a generalized differential quadrature rule for bending analysis of cylindrical barrel shells the generalized differential quadrature rule gdqr proposed recently by the present authors is applied here to solve an eighth order boundary value differential equation with four boundary conditions at each boundary which governs the bending analysis of circular cylindrical barrel shells thus multiple boundary conditions are implemented exactly at boundaries without applying the approximate point non boundary point technique both hermite interpolation functions and gdqr s explicit weighting coefficients are obtained while the latter are the most important for an accurate implementation of the gdqr the analytical results for various cylindrical barrel shells are derived and calculated here in order to verify the accuracy of the calculated gdqr results in implementation of multiple conditions at one point the gdqr gains a clear advantage over the existing point technique in the differential quadrature applications and manifests a great potential for applications in many fields of applied mathematics

differential quadrature method for thick symmetric cross ply laminates with first order shear flexibility a global numerical technique the differential quadrature dq method is examined here for its suitability to solve the boundary value problem of symmetric cross ply laminates using the first order shear deformation plate theory by whitney and pagano j appl mech 37 1031 1036 1970 the bending behaviours of symmetric cross ply laminates subject to different boundary constraints are investigated in this study the method is used to transform the sets of governing differential equations and boundary conditions of the laminated plates into sets of linear algebraic equations boundary conditions along the edges are implemented through the discrete grid points by constraining the displacements bending moments and rotations the theoretical formulations and solution procedures of the method are illustrated through solving several numerical examples the accuracy and validity of the present formulation if available are examined by direct comparison with the known values

free vibrations of doubly curved in plane non homogeneous shells a method for investigating free vibrations rectangular non homogeneous shells is proposed by non homogeneity we define a chage of stiffness of shell bending caused by an introduction of another material or change of a shell thickness is defined it is assumed that a shell possesses an arbitrary value of rectangular parts with different bending stiffness

vibration of eccentric ring and line supported circular plates carrying concentrated masses abstract the vibration of circular plates supported by combinations of ring and line supports and which are carrying concentrated masses is investigated for the first time to the author s knowledge by using the newly developed pb 2 rayleigh ritz method a set of ritz functions consisting of the product of the boundary expressions is used as the admissible displacement function this set of pb 2 ritz functions can accurately approximate the mode shapes of these circular plates with any prescribed boundary conditions and interior supports such as eccentric annular and or line supports to validate the present method numerical calculations have been carried out for several simplified plate problems and these are compared with those results available in the literature excellent agreement is achieved in all cases

asymptotically dense spherical codes i wrapped spherical codes a new class of spherical codes called wrapped spherical codes is constructed by wrapping any sphere packing spl lambda in euclidean space onto a finite subset of the unit sphere in one higher dimension the mapping preserves much of the structure of spl lambda and unlike previously proposed maps the density of the wrapped spherical codes approaches the density of spl lambda as the minimum distance approaches zero we show that this implies that the asymptotically maximum spherical coding density is achieved by wrapped spherical codes whenever spl lambda is the densest possible sphere packing

random inequality constraint systems with few variables we show that a system of many linear inequality constraints will have a high proportion of redundant constraints with high probability implications for expected time of algorithms are indicated

free vibration of symmetrically laminated thick perforated plates abstract this paper investigates the free vibration of symmetrically laminated thick doubly connected plates of arbitray plate perimeter for the outer boundary and a hole defined by a super elliptical equation which is able to describe a rectangle ellipse or quasi rectangle the laminated perforated plates can be subject to free simply supported or clamped edge conditions convergence and comparisons with established work have been studied to ensure accuracy of results efforts are made to interpret the frequency results to provide physical insight to the problem

free vibration of cantilever quadrilateral plates in this paper a numerical method for the free vibration analysis of cantilever quadrilateral plates of general shape is presented using quadrilateral coordinates and integral equation of beams the expressions for the strain energy and kinetic energy have been developed the formulation and derivation of equations are in the matrix form ab initio then the eigenvalue problem is solved for frequencies and mode shapes numerical work has been done for particular cases and the results compared with those of other investigators the effect of sweep back angle has also been studied