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

universality of level correlation function of sparse random matrices the statistical properties of sparse random matrices ensembles are investigated by means of a supersymmetric approach with the use of a functional generalization of the hubbard stratonovich transformation when used to calculate the density of states the method is shown to be absolutely equivalent to the replica trick the model turns out to bear a close resemblance to the anderson model on the bethe lattice it possesses a delocalization transition that occurs with an increase in the mean connectivity parameter in the delocalized phase the level level correlation function proves to have a universal dyson form with the full density of states replaced by the contribution from the infinite cluster

dsc ritz method for the free vibration analysis of mindlin plates this paper introduces a novel method for the free vibration analysis of mindlin plates the proposed method takes the advantage of both the local bases of the discrete singular convolution dsc algorithm and the pb 2 ritz boundary functions to arrive at a new approach called dsc ritz method two basis functions are constructed by using dsc delta sequence kernels of the positive type the energy functional of the mindlin plate is represented by the newly constructed basis functions and is minimized under the ritz variational principle extensive numerical experiments are considered by different combinations of boundary conditions of mindlin plates of rectangular and triangular shapes the performance of the proposed method is carefully validated by convergence analysis the frequency parameters agree very well with those in the literature numerical experiments indicate that the proposed dsc ritz method is a very promising new method for vibration analysis of mindlin plates copyright 2004 john wiley sons ltd

plate vibration under irregular internal supports this paper studies the problem of plate vibration under complex and irregular internal support conditions such a problem has its widely spread industrial applications and has not been addressed in the literature yet partially due to the numerical difficulties a novel computational method discrete singular convolution dsc is introduced for solving this problem the dsc algorithm exhibits controllable accuracy for approximations and shows excellent flexibility in handling complex geometries boundary conditions and internal support conditions convergence and comparison studies are carried out to check the validity and accuracy of the dsc method case studies are considered to the combination of a few different boundary conditions and irregular internal supports the latter are generated by using an image processing algorithm completely independent verifications are conducted by using the established pb 2 ritz method which is available for two relatively simpler support patterns the morphology of the first few eigenmodes is found to be localized to largest support free spatial regions

wavelets generated by using discrete singular convolution kernels this paper explores the connection between wavelet methods and an efficient computational algorithm the discrete singular convolution dsc many new dsc kernels are constructed and they are identified as wavelet scaling functions two approaches are proposed to generate wavelets from dsc kernels two well known examples the canny filter and the mexican hat wavelet are found to be special cases of the present dsc kernel generated wavelets a family of wavelet generators proposed in this paper are found to form an infinite dimensional lie group which has an invariant subgroup of translation and dilation if dsc kernels form an orthogonal system they are found to span a wavelet subspace in a multiresolution analysis

dsc analysis of free edged beams by an iteratively matched boundary method this communication introduces a novel scheme for the treatment of free edge supports in the analysis of beams by using the discrete singular convolution dsc algorithm accommodating free edges has been a challenging issue in the dsc analysis of beams plates and shells an iteratively matched boundary imb method is proposed to overcome the difficulty numerical experiments are carried out to demonstrate that the proposed imb method works very well in dealing with arbitrary combinations of beam edge supports

free vibration analysis of beams and rectangular plates with free edges by the discrete singular convolution in this paper free vibration of beams annular plates and rectangular plates with free boundaries are analyzed by using the discrete singular convolution dsc a novel method to apply the free boundary conditions is proposed detailed derivations are given to validate the proposed method eight examples including the free vibrations of beams annular plates and rectangular plates with free boundaries are analyzed two kernels the regularized shannon s kernel and the non regularized lagrange s delta sequence kernel are tested dsc results are compared with either analytical solutions or and differential quadrature dq data it is demonstrated that the proposed method to incorporate the free boundary conditions is simple to use and can yield accurate frequency data for beams with a free end and plates with free edges thus the proposed method for applying the boundary conditions extends the application range of the dsc

deviations from the circular law consider ginibre s ensemble of n n non hermitian random matrices in which all entries are independent complex gaussians of mean zero and variance open image in new window as n the normalized counting measure of the eigenvalues converges to the uniform measure on the unit disk in the complex plane in this note we describe fluctuations about this circular law first we obtain finite n formulas for the covariance of certain linear statistics of the eigenvalues asymptotics of these objects coupled with a theorem of costin and lebowitz then result in central limit theorems for a variety of these statistics

gaussian fluctuation for the number of particles in airy bessel sine and other determinantal random point fields we prove the central limit theorem clt for the number of eigenvalues near the spectrum edge for certain hermitian ensembles of random matrices to derive our results we use a general theorem essentially due to costin and lebowitz concerning the gaussian fluctuation of the number of particles in random point fields with determinantal correlation functions as another corollary of the costin lebowitz theorem we prove the clt for the empirical distribution function of the eigenvalues of random matrices from classical compact groups

discrete singular convolution for the prediction of high frequency vibration of plates theoretical analysis of high frequency vibrations is indispensable in a variety of engineering designs much effort has been made on this subject in the past few decades however there is no single technique which can be applied with confidence to various engineering structures for high frequency predictions at present this paper introduces a novel computational approach the discrete singular convolution dsc algorithm for high frequency vibration analysis of plate structures square plates with six distinct boundary conditions are considered to validate the proposed method a completely independent approach the levy method is employed to provide exact solutions for a comparison the proposed method is also validated by convergence studies we demonstrate the ability of the dsc algorithm for high frequency vibration analysis by providing extremely accurate frequency parameters for plates vibrating in the first 5000 modes

discrete singular convolution element method for static buckling and free vibration analysis of beam structures a new version of discrete singular convolution dsc algorithm called the dsc element method is proposed the new method combines the high computational efficiency and accuracy of the original dsc algorithm with the convenience and generality of the finite element method in application to structural analysis the shortage existing in the original dsc algorithm has been overcome besides the proposed method provides a unique way to apply various boundary conditions in using dsc algorithm two types of dsc beam element are presented and a variety of problems such as static buckling and free vibrations with discontinuities in geometry or load have been successfully solved by the proposed method numerical results show that the proposed dsc element method is an accurate and efficient method for analyzing beam structures

dsc analysis of rectangular plates with non uniform boundary conditions this paper introduces the discrete singular convolution dsc for the vibration analysis of rectangular plates with non uniform and combined boundary conditions a systematic scheme is proposed for the treatment of boundary conditions required in the proposed approach the validity of the dsc approach for plate vibration is tested by using a large number of numerical examples that have a combination of simply supported clamped and transversely supported with non uniform elastic rotational restraint edges the present results are in excellent agreement with those in the literature

free vibration analysis of multiple stepped beams by the discrete singular convolution in this paper free vibration of beams with multiple step changes are successfully analyzed by using the modified discrete singular convolution dsc the jump conditions at the steps are used to overcome the difficulty in using ordinary dsc for dealing with ill posed problems an nth order interpolation polynomial is established on each side of the step then two or three jump conditions together with two continuous conditions at steps are used to relate the two polynomials five examples are analyzed results obtained by the modified dsc and existing solutions are compared it is seen that the dsc results agree well with existing analytical numerical and experimental data it is also found that the dsc results are even more accurate than the data obtained by the differential quadrature element method for much higher mode frequencies the present research extends the application range of the dsc algorithm

the interband light absorption coefficient in the weak disorder regime an asymptotically exactly solvable model we consider the interband light absorption coefficient ilac for a d dimensional discrete disordered system whose hamiltonian consist of a translation invariant part d dimensional discrete laplacian and an off diagonal random part assuming that the range r of the latter is large and that its magnitude is of the order r d 2 we find that r infinity limit of the ilac we discuss some properties of the ilac in this limit its boundedness edge singularities its singular form in the limits of vanishingly translationally invariant part or infinite random part we also show that the latter property is the same for the system with a diagonal smoothly distributed disorder i e for the discrete schrodinger operator whose random potential has a smooth probability distribution this should be contrasted with the integrated density of states which is always smoother than the distribution of the random potential

high accuracy mixed finite element ritz formulation for free vibration analysis of plates with general boundary conditions abstract a high order accurate mixed finite element ritz method is introduced and developed to study the vibration problem of plates with general boundary conditions the finite element method fem with higher order interpolation functions is first used to discretize the spatial partial derivatives with respect to a co ordinate direction of the plate the ritz method is then employed to analogize the resulting system of ordinary differential equations a novel technique is also presented to exactly satisfy the mixed natural boundary conditions the proposed method is applied here to solve some benchmark vibration problems of plates including isotropic and anisotropic rectangular plates variable thickness rectangular plates multi span rectangular plates and skew plates comparisons with existing numerical and analytical solutions show that the proposed mixed method can yield highly accurate results for vibration problem of plates involving free edges free corners and irregular boundaries using a small number of finite elements and ritz terms

comparison of discrete singular convolution and generalized differential quadrature for the vibration analysis of rectangular plates this paper presents a comprehensive comparison study between the discrete singular convolution dsc and the well known global method of generalized differential quadrature gdq for vibration analysis so as to enhance the understanding of the dsc algorithm the dsc method is implemented through lagrange s delta sequence kernel dsc lk which utilizes local lagrange polynomials to calculate weighting coefficients whereas the gdq requires global ones moreover it is shown that the treatments of boundary conditions and the use of grid systems are different in the two methods comparison study is carried out on 21 rectangular plates of different combinations of simply supported s clamped c and transversely supported with nonuniform elastic rotational restraint e edges and five rectangular plates of mixed supporting edges some of which with a range of aspect ratios and rotational spring coefficients all the results of the dsc lk agree very well with both those in the literature and newly computed gdq results furthermore it is observed that the dsc lk performs much better for plates vibrating at higher order eigenfrequencies unlike the gdq the dsc lk is numerically stable for problems which require a large number of grid points

spectral properties of random reactance networks and random matrix pencils our goal is to study the statistical properies of dielectric resonances which are poles of conductance of a large random lc network such poles are a particular example of eigenvalues n of matrix pencils h w with w being a positive definite matrix and h a random real symmetric one we first consider spectra of the matrix pencils with independent identically distributed entries of h then we concentrate on an infinite range full connectivity version of a random lc network in all cases we calculate the mean eigenvalue density and the two point correlation function in the framework of efetov s supersymmetry approach fluctuations in spectra turn out to be the same as those provided by the wigner dyson theory of usual random matrices

a generalization of the lindeberg principle we generalize lindeberg s proof of the central limit theorem to an invariance principle for arbitrary smooth functions of independent and weakly dependent random variables the result is applied to get a similar theorem for smooth functions of exchangeable random variables this theorem allows us to identify for the first time the limiting spectral distributions of wigner matrices with exchangeable entries

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

a novel approach for the analysis of high frequency vibrations abstract despite much effort in the past few decades the numerical prediction of high frequency vibrations remains a challenging task to the engineering and scientific communities due to the numerical instability of existing computational methods however such prediction is of crucial importance to certain problems of pressing practical concern as pointed out by langley and bardell 1998 the aeronautical journal102 287 297 this paper introduces the discrete singular convolution dsc algorithm for the prediction and analysis of high frequency vibration of structures both a beam and two span plates are employed as test examples to demonstrate the capability of the dsc algorithm for high frequency vibration analysis a completely independent approach the levy method is employed to provide exact solutions for a cross validation of the proposed method the reliability of the dsc results is also validated by convergence studies remarkably extremely accurate and stable results are obtained in this work e g the relative dsc errors for the first 7100 modes of the beam and the first 4500 modes of the two span plates are all

a new algorithm for solving some mechanical problems this paper explores the utility of a discrete singular convolution algorithm for solving certain mechanical problems benchmark mechanical systems including plate vibrations and incompressible flows are employed to illustrate the robustness and to test accuracy of the present algorithm numerical results indicate that the present approach is very accurate efficient and reliable for solving the aforementioned problems

limits of infinite interaction radius dimensionality and the number of components for random operators with off diagonal randomness we consider random one body operators that are analogs of the statistical mechanics hamiltonians with a varying interaction radiusr the dimensionality of spaced and the number of the field components orbitals n we prove that all the moments of the green functions for nonreal energies of these operators converge asr d n to the products of the average green functions just as in the mean field approximation of statistical mechanics we find in particular the selfconsistent equation for the limiting integrated density of states and the limiting form of the conductivity which is nonzero on the whole support of the integrated density of states

on the 1 n corrections to the green functions of random matrices with independent entries we propose a general approach to the construction of 1 n corrections to the green function gn z of the ensembles of random real symmetric and hermitian n n matrices with independent entries hk l by this approach we study the correlation function cn z1 z2 of the normalized trace n 1trgn assuming that the average of mod hk l5 is bounded we found that to leading order cn z1 z2 n 2f z1 z2 where f z1 2 only depends on the second and the fourth moments of hk l for the correlation function of the density of energy levels we obtain an expression which in the scaling limit only depends on the second moment of hk l this can be viewed as supporting the universality conjecture of random matrix theory

asymptotic properties of large random matrices with independent entries we study the normalized trace gn z n 1 tr h zi 1 of the resolvent of n n real symmetric matrices h 1 jk wjk n j k 1n assuming that their entries are independent but not necessarily identically distributed random variables we develop a rigorous method of asymptotic analysis of moments of gn z for iz 0 where 0 is determined by the second moment of wjk by using this method we find the asymptotic form of the expectation e gn z and of the connected correlator e gn z1 gn z2 e gn z1 e gn z2 we also prove that the centralized trace ngn z e ngn z has the gaussian distribution in the limit n based on these results we present heuristic arguments supporting the universality property of the local eigenvalue statistics for this class of random matrix ensembles

nonlinear morgan s problem case of p 1 inputs and p outputs noninvertible static state feedback solutions of the row by row decoupling problem are investigated for the class of nonlinear systems having one more input component than output components the analysis involves a combination of geometric and algebraic tools but notably avoids the use of regular or degenerate controllability distribution subspaces the main tools used to date for the class of linear systems the main idea is finding within the system a chain of integrators that may be attached to one of the inputs in order to appropriately modify the system s structure at infinity

a novel scheme for the discrete prediction of high frequency vibration response discrete singular convolution mode superposition approach abstract this study introduces a novel scheme for the discrete high frequency forced vibration analysis based on discrete singular convolution dsc and mode superposition ms approaches the accuracy of the dsc ms is validated for thin beams and plates by comparing with available analytical solutions the performance of the dsc ms is evaluated by predicting spatial distribution and discrete frequency spectra of the vibration response of thin plates with two different boundary conditions the frequency spectra of the time harmonic excitation forces are in the form of ideal and band limited white noise so that the natural modes in the frequency band are provoked the solution exposes high frequency response behaviour definitely therefore it is hoped with this paper to contribute the studies on the treatment of uncertainties in the high frequency design applications

static and free vibration analyses of rectangular plates by the new version of the differential quadrature element method a new version of the differential quadrature method is presented in this paper to overcome the difficulty existing in the ordinary differential quadrature method for applying multi boundary conditions in two dimensional problems since the weighting coefficients of the first derivative are the same as for the ordinary differential quadrature method even with the introduction of multi degree of freedom at the boundary points the method is easier to extend to two or three dimensional problems a new version of the differential quadrature plate element has been established for demonstration the essential difference from the existing old version of the differential quadrature plate element is the way the weighting coefficients are determined the methodology is worked out in detail and some numerical examples are given to show the efficiency of the present method