global weak solution to the inhomogeneous navier stokes vlasov equations abstract the inhomogeneous navier stokes vlasov equations for fluid particle flows are considered in the three dimensional space the coupling in the fluid particle system arises from the drag force in the fluid equations and the acceleration in the vlasov equation an initial boundary value problem is studied in a bounded domain with large initial data the existence of global weak solution is established through an approximation scheme a fixed point argument energy estimates and a weak convergence method

free vibrations of rectangular plates with interior point supports abstract a new approach for the representation of point supports in the vibration analysis of plates was presented in earlier work 1 3 the approach was based on simulating a point support on a free edge as a zero of a flexibility function representing a fictitious elastic restraint distribution over the free edge the application of this approach to a variety of problems concerning rectangular plates with point supports located on the free edges was demonstrated in subsequent studies 4 5 the present study provides an extension of the flexibility function approach to the problem of rectangular plates with interior point supports in the analysis a rectangular plate is considered with two opposite edges simply supported and classical boundary conditions on the other two edges with one or more interior point supports along the line perpendicular to the simply supported edges extensive numerical results for a range of problem parameters have been obtained the results show the versatility of the flexibility function approach in the vibration analysis of rectangular plates with arbitrarily located interior point supports

on the spurious solutions in the high order finite difference methods for eigenvalue problems in this paper the origins of spurious solutions occurring in the high order finite difference methods are studied based on a uniform mesh spurious modes are found in the high order one sided finite difference discretizations of many eigenvalue problems spurious modes are classified as spectral pollution and non spectral pollution the latter can be partially avoided by mesh refinement while the former persists when the mesh is refined through numerical studies of some prototype eigenvalue problems such as those of the helmholtz and beam equations we show that perfect central differentiation schemes do not produce any spurious modes nevertheless high order central difference schemes encounter difficulties in implementing complex boundary conditions we further show that the central difference schemes will produce spurious modes as well if asymmetric approximation is involved in boundary treatments in general central difference schemes are less likely to produce spurious modes than one sided difference schemes 2007 elsevier b v all rights reserved

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

discrete singular convolution and its application to the analysis of plates with internal supports part 2 applications part 2 of this series of two papers presents the applications of the discrete singular convolution dsc algorithm the main purpose of this paper is to explore the utility test the accuracy and examine the convergence of the proposed approach for the vibration analysis of rectangular plates with internal supports both partial internal line supports and complex internal supports are considered for 21 square plates of various combinations of edge support conditions the effects of different size shape and topology of the internal supports and different boundary conditions on the vibration response of plates are investigated the partial internal line supports may vary from a central point support to a full range of cross or diagonal line supports several closed loop supports such as ring square and rhombus and their combinations are studied for complex internal supports convergence and comparison studies are carried out to establish the correctness and accuracy of the dsc algorithm the dsc results are compared with those in the available literature obtained by using other methods numerical results indicate that the dsc algorithm exhibits controllable accuracy for plate analysis and shows excellent flexibility in handling complex geometries boundary conditions and support conditions copyright 2002 john wiley sons ltd

dsc time domain solution of maxwell s equations a new computational algorithm the discrete singular convolution dsc is introduced for solving scattering and guided wave problems described by time domain maxwell s equations the dsc algorithm is utilized for the spatial discretization and the fourth order runge kutta scheme is used for the time advancing staggered meshes are used for electromagnetic fields four standard test problems a hollow air filled waveguide a dielectric slab loaded rectangular waveguide a shield microstrip line and a dielectric square are employed to illustrate the usefulness to test the accuracy and to explore the limitation of the dsc algorithm results are compared with those of finite difference scaling function multi resolution time domain and finite element based high frequency structure simulator numerical experiments indicate that the present algorithm is a promising approach for achieving high accuracy in electromagnetic wave computations

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

on the validity of a proof that the discrete singular convolution dsc lagrange distributed approximation function ldaf method is inferior to high order finite differences a few families of counterexamples are provided to a proof that the discrete singular convolution dsc lagrange distributed approximation function ldaf method is inferior to high order finite differences journal of computational physics 214 538 549 2006

dispersion of waves and characteristic wave surfaces in functionally graded piezoelectric plates an inhomogeneous layer element method is presented to analyze the dispersion of waves and characteristic wave surfaces in plates of functionally graded piezoelectric material fgpm in this method the fgpm plate is divided into a number of layered elements the elemental elastic and electric properties are assumed as linear functions of the thickness to adopt the variety of the material property of fgpm the hamilton principle is applied to determine the governing equations the phase velocity surface phase slowness surface phase wave surface group velocity surface group slowness surface and group wave surface for fgpm plate are formulated using rayleigh quotient and the orthogonality condition of the eigenvectors these six surfaces are then used to illustrate the characteristics of waves in fgpm plates numerical examples are presented using the present formulations to analyze dispersions and characteristics of waves in fgpm plates

high order fdtd methods via derivative matching for maxwell s equations with material interfaces this paper introduces a series of novel hierarchical implicit derivative matching methods to restore the accuracy of high order finite difference time domain fdtd schemes of computational electromagnetics cem with material interfaces in one 1d and two spatial dimensions 2d by making use of fictitious points systematic approaches are proposed to locally enforce the physical jump conditions at material interfaces in a preprocessing stage to arbitrarily high orders of accuracy in principle while often limited by numerical instability orders up to 16 and 12 are achieved respectively in 1d and 2d detailed stability analyses are presented for the present approach to examine the upper limit in constructing embedded fdtd methods as natural generalizations of the high order fdtd schemes the proposed derivative matching methods automatically reduce to the standard fdtd schemes when the material interfaces are absent an interesting feature of the present approach is that it encompasses a variety of schemes of different orders in a single code another feature of the present approach is that it can be robustly implemented with other high accuracy time domain approaches such as the multiresolution time domain method and the local spectral time domain method to cope with material interfaces numerical experiments on both 1d and 2d problems are carried out to test the convergence examine the stability access the efficiency and explore the limitation of the proposed methods it is found that operating at their best capacity the proposed high order schemes could be over 2000 times more efficient than their fourth order versions in 2d in conclusion the present work indicates that the proposed hierarchical derivative matching methods might lead to practical high order schemes for numerical solution of time domain maxwell s equations with material interfaces

dynamic theory of suspensions with brownian effects we consider a suspension of particles in a fluid settling under the influence of gravity and dispersing by brownian motion a mathematical description is provided by the stokes equations and a fokker planck equation for the one particle phase space density this is a nonlinear system that depends on a number of parametric functions of the spatial concentration of the particles these functions are known only empirically or for dilute suspensions we analyze the system its stability its asymptotic behavior under different scalings and its validity from more microscopic description we summarize our conclusions at the end

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

numerical solution of the helmholtz equation with high wavenumbers this paper investigates the pollution effect and explores the feasibility of a local spectral method the discrete singular convolution dsc algorithm for solving the helmholtz equation with high wavenumbers fourier analysis is employed to study the dispersive error of the dsc algorithm our analysis of dispersive errors indicates that the dsc algorithm yields a dispersion vanishing scheme the dispersion analysis is further confirmed by the numerical results for one and higher dimensional helmholtz equations the dsc algorithm is shown to be an essentially pollution free scheme furthermore for large scale computation the grid density of the dsc algorithm can be close to the optimal two grid points per wavelength the present study reveals that the dsc algorithm is accurate and efficient for solving the helmholtz equation with high wavenumbers copyright 2003 john wiley sons ltd

discrete singular convolution finite subdomain method for the solution of incompressible viscous flows this paper proposes a discrete singular convolution finite subdomain method dsc fsm for the analysis of incompressible viscous flows in multiply connected complex geometries the dsc algorithm has its foundation in the theory of distributions a block structured grid of fictitious overlapping interfaces is designed to decompose a complex computational geometry into a finite number of subdomains in each subdomain the governing navier stokes equations are discretized by using the dsc algorithm in space and a third order runge kutta scheme in time information exchange between fictitious overlapping zones is realized by using the dsc interpolating algorithm the taylor problem with decaying vortices could be solved to machine precision with an excellent comparison against the exact solution the reliability of the proposed method is tested by simulating the flow in a lid driven cavity the utility of the dsc fsm approach is further illustrated by two other benchmark problems viz the flow over a backward facing step and the laminar flow past a square prism the present results compare well with the numerical and experimental data available in the literature

on the use of computational intelligence in the optimal shape control of functionally graded smart plates functionally graded material fgm plates are an essential component for most advanced integrated systems in terms of vibration and acoustic controls or condition monitoring in general these fgm plates are designed with embedded piezoelectric sensors and actuators to achieve their shape control this optimal control problem is normally required to find appropriate actuator voltage and displacement control gains that will generate the desired shape such an optimal control problem is known to be highly non linear and often posses slope and functional discontinuity that will limit the efficiency of the gradient based methods stochastic zero order population based optimization methods are ideal for solving this class of problems in this paper we introduce a stochastic zero order optimization algorithm based on the principles of learning this algorithm is embedded with three key learning strategies that control who to learn from i e leader identification and leader selection and what to learn i e information acquisition to reach a common goal the leader identification mechanism partitions the individuals into a set of leaders and a set of followers the followers interact with the leaders and move toward the better performing leaders in searching for better solutions the parameter free algorithm provides the designer with the true flexibility that is necessary to handle various forms of design problem effectively and at a computational cost that is comparable to existing stochastic optimization methods in this study numerical results are presented for the shape control of the fgm plates under a temperature gradient by optimizing i the voltage distribution for the open loop control and ii the displacement control gain values for the closed loop feedback control we also examine the effect of the constituent volume fractions of zirconia through the varying of volume fraction exponent n on the optimal voltages and gain values

free vibration of line supported rectangular plates using a set of static beam functions the free vibration of thin orthotropic rectangular plates which may be continuous over a number of intermediate line supports in one or two directions is analyzed by the rayleigh ritz method a new set of admissible functions which are the static solutions of a point supported beam under a series of sine loads is developed the eigenfrequency equation for the plate is derived by minimizing the potential energy a very simple and general computer programme has been compiled the basic concept to form the set of static beam functions is very clear and requires no complicated mathematical knowledge some numerical results presented are compared with those obtained by other numerical methods in the literature it is shown that this set of static beam functions has some advantages in terms of computational cost application versatility and numerical accuracy especially for the plate problem with a large number of intermediate line supports and or when higher vibrating modes need to be calculated

a unified approach for the solution of the fokker planck equation this paper explores the use of a discrete singular convolution algorithm as a unified approach for numerical integration of the fokker planck equation the unified features of the discrete singular convolution algorithm are discussed it is demonstrated that different implementations of the present algorithm such as global local galerkin collocation and finite difference can be deduced from a single starting point three benchmark stochastic systems the repulsive wong process the black scholes equation and a genuine nonlinear model are employed to illustrate the robustness and to test the accuracy of the present approach for the solution of the fokker planck equation via a time dependent method an additional example the incompressible euler equation is used to further validate the present approach for more difficult problems numerical results indicate that the present unified approach is robust and accurate for solving the fokker planck equation

hydrodynamic limit for the inhomogeneous incompressible navier stokes vlasov fokker planck equations abstract in this paper we study the hydrodynamic limit for the inhomogeneous incompressible navier stokes vlasov fokker planck equations in a two or three dimensional bounded domain when the initial density is bounded away from zero the proof relies on the relative entropy argument to obtain the strong convergence of macroscopic density of the particles n in l 0 t l 1 which extends the works of goudon jabin vasseur 15 and mellt vasseur 26 to inhomogeneous incompressible navier stokes vlasov fokker planck equations precisely the relative entropy estimates in 15 and 26 give the strong convergence of u and n and n respectively however we only obtain the strong convergence of n and u from the relative entropy estimate and we use another way to obtain the strong convergence of via the convergence of u furthermore when the initial density may vanish taking advantage of compactness result l m h 1 of orlicz spaces in 2d we obtain the convergence of n in l 0 t h 1 which is used to obtain the relative entropy estimate thus we also show the hydrodynamic limit for 2d inhomogeneous incompressible navier stokes vlasov fokker planck equations when there is initial vacuum

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

semi analytical solutions for free vibration of anisotropic laminated plates in cylindrical bending elasticity solutions for free vibration of angle ply laminates subjected to cylindrical bending are obtained using a newly developed semi analytical approach the thickness domain is solved analytically using the transfer matrix method based on the state space concept while the in plane domain is solved approximately via the technique of differential quadrature the present method is applicable to arbitrarily thick laminates and for treating arbitrary edge conditions the method is verified by comparisons with the exact solutions of pagano s problem effects of variation of ply angle on the vibration properties of laminates are investigated mode shape switching is observed when ply angle varies numerical results for fully clamped thick laminates are presented for future references

global existence of solutions to the incompressible navier stokes vlasov equations in a time dependent domain in this article we prove the existence of global weak solutions for the in compressible navier stokes vlasov system in a three dimensional time dependent domain with absorption boundary conditions for the kinetic part this model arises from the study of respiratory aerosol in the human airways the proof is based on a regularization and approximation strategy designed for our time dependent framework

mib method for elliptic equations with multi material interfaces elliptic partial differential equations pdes are widely used to model real world problems due to the heterogeneous characteristics of many naturally occurring materials and man made structures devices and equipments one frequently needs to solve elliptic pdes with discontinuous coefficients and singular sources the development of high order elliptic interface schemes has been an active research field for decades however challenges remain in the construction of high order schemes and particularly for nonsmooth interfaces i e interfaces with geometric singularities the challenge of geometric singularities is amplified when they are originated from two or more material interfaces joining together or crossing each other high order methods for elliptic equations with multi material interfaces have not been reported in the literature to our knowledge the present work develops matched interface and boundary mib method based schemes for solving two dimensional 2d elliptic pdes with geometric singularities of multi material interfaces a number of new mib schemes are constructed to account for all possible topological variations due to two material interfaces the geometric singularities of three material interfaces are significantly more difficult to handle three new mib schemes are designed to handle a variety of geometric situations and topological variations although not all of them the performance of the proposed new mib schemes is validated by numerical experiments with a wide range of coefficient contrasts geometric singularities and solution types extensive numerical studies confirm the designed second order accuracy of the mib method for multi material interfaces including a case where the derivative of the solution diverges

finite elements for functionally graded reissner mindlin plates abstract equations governing the behavior of rectangular plates made of functionally graded materials fgms are determined in this paper using the variational approach derivation of such equations is based on reissner mindlin plate theory that is extended to handle two constituent material distribution through the thickness material properties are assumed to vary with the power law in terms of the volume fractions of the constituent within a static analysis framework the main focus of the paper is the proposal of a locking free hierarchic family of finite elements that is numerically tested on plates of different material grading convergence and stability properties of our approach are assessed and comparisons with available solutions presented

analytical solutions for single and multi span functionally graded plates in cylindrical bending abstract a recently developed plate theory using the concept of shape function of the transverse coordinate parameter is extended to determine the stress distribution in an orthotropic functionally graded plate subjected to cylindrical bending the transfer matrix method is presented to derive the shape function the equations governing the plate deformation are then solved analytically using the transfer matrix method for arbitrary boundary conditions for a simply supported functionally graded plate a comparison of the present solution with the exact elasticity solution the first and third order shear deformation plate theories is presented and discussed it is demonstrated that the present method yields more accurate stresses than the first and third order shear deformation theories the effect of boundary conditions and inhomogeneity of material on the displacements and stresses in functionally graded plates are investigated a multi span functionally graded plate with arbitrary boundary conditions is further considered to demonstrate the efficiency of the present method

moving least square ritz method for vibration analysis of plates this paper presents a novel numerical method the moving least square ritz method mls ritz for free vibration analysis of classical thin plates the proposed method utilizes the strength of the moving least square approach to define the ritz trial function for the transverse displacement of the plates a set of points is pre selected on the calculation domain of a plate that forms the basis for the mls ritz trial function the edge support conditions of the plate are satisfied by forcing the boundary points to meet the geometric boundary conditions of the plate via a point substitution technique virtual points points outside the plate domain are introduced for clamped edges to improve the convergence and accuracy of the calculations square and right angled isosceles triangular plates of various combinations of edge support conditions are selected to examine the validity and accuracy of the mls ritz method extensive convergence studies are carried out to investigate the influence of the mls mesh size the mls support radius the number of gaussian integration points and the shape of the mls weight function on the proposed method comparing with the existing ritz methods the mls ritz method is highly stable and accurate and is extremely flexible for dealing with plates of arbitrary shapes and boundary conditions

discrete singular convolution and its application to the analysis of plates with internal supports part 1 theory and algorithm this paper presents a novel computational approach the discrete singular convolution dsc algorithm for analysing plate structures the basic philosophy behind the dsc algorithm for the approximation of functions and their derivatives is studied approximations to the delta distribution are constructed as either bandlimited reproducing kernels or approximate reproducing kernels unified features of the dsc algorithm for solving differential equations are explored it is demonstrated that different methods of implementation for the present algorithm such as global local galerkin collocation and finite difference can be deduced from a single starting point the use of the algorithm for the vibration analysis of plates with internal supports is discussed detailed formulation is given to the treatment of different plate boundary conditions including simply supported elastically supported and clamped edges this work paves the way for applying the dsc approach in the following paper to plates with complex support conditions which have not been fully addressed in the literature yet

eigenfrequencies of tapered rectangular plates with intermediate line supports the free vibrations of a wide range of tapered rectangular plates with an arbitrary number of intermediate line supports in one or two directions are investigated the domain of the plate is bounded by x a a 0 1 and y b b 0 1 in the rectangular co ordinates the thickness of the plate is continuously varying and proportional to a power function xsyt a variety of tapered rectangular plates can be described by giving the taper factors s and t various values the intermediate line supports run parallel to the edges of the plate a new set of admissible functions which are the static solutions of the tapered beam with intermediate point supports or a strip taken from the plate structure in one or the other direction under a taylor series of loads is developed consistent convergency independent of the truncation factors and of the plate can be obtained by taking the midpoint of the beam as the expanding point of the taylor series unlike conventional admissible functions this set of static beam functions can appropriately vary with the thickness variation of the plate the eigenfrequency equation of the plate is derived by the rayleigh ritz approach a general computer program has been compiled it can be seen that the convergency of the numerical computation is very rapid and that the first few eigenfrequencies can be obtained with good accuracy by using only a small number of terms of the static beam functions sets of first time reported eigenfrequency data are included for future reference

mathematical modeling of vibration problem of nano sized annular sector plates using the nonlocal continuum theory via eight node discrete singular convolution transformation abstract in the present study free vibration analysis of nano sized annular sector plate is analyzed using the nonlocal continuum theory the method of discrete singular convolution dsc is used for numerical computations firstly equation of motion of thin plates is formulated via nonlocal elasticity then irregular physical domain is transformed into a rectangular domain by using geometric coordinate transformation the dsc procedures are then applied to discretization of the transformed set of governing equations and related boundary conditions the effects of nonlocal parameter mode numbers sector angle and radius ratio on the vibration frequencies are investigated in detail it is seen that the size effects are significant in vibration analysis of nano scaled annular sector plates and need to be included in the mechanical model

vibrations of mindlin rectangular plates with elastically restrained edges using static timoshenko beam functions with the rayleigh ritz method abstract a set of static timoshenko beam functions is developed as the admissible functions for the free vibration analysis of mindlin rectangular plates with uniform elastic translational and or rotational edge constraints by the use of the rayleigh ritz method this set of beam functions is made up of two parts the transverse deflection functions and rotation functions which are the static solutions of a timoshenko beam under the transverse loads of a fourier sinusoidal series distributed along the length of the beam therefore the effect of shear deformation on the admissible functions is taken into account in fact the beam is considered to be a unit width strip taken from the rectangular plate in a direction parallel to the edge of the plate and has the end supports corresponding to the edge conditions of the particular plate under consideration it can be seen that the method is sound theoretically each of the beam functions is a polynomial function of not more than third order plus a sine or cosine function for all cases and the change of the boundary supports only results in a corresponding change of the coefficients of the low order polynomial therefore a unified program with little computational efforts can be easily developed for the vibration analysis of mindlin rectangular plates with arbitrary boundary conditions and thickness span ratios the accuracy and efficiency of the proposed method are demonstrated by comparison and convergency studies finally sets of reasonably accurate natural frequencies are presented which can serve as a supplement to the database of vibration characteristics of moderately thick plates

crank nicolson quasi wavelets method for solving fourth order partial integro differential equation with a weakly singular kernel in this paper we study a novel numerical scheme for the fourth order partial integro differential equation with a weakly singular kernel in the time direction a crank nicolson time stepping is used to approximate the differential term and the product trapezoidal method is employed to treat the integral term and the quasi wavelets numerical method for space discretization our interest in the present paper is a continuation of the investigation in yang et al 33 where we study discretization in time by using the forward euler scheme the comparisons of present results with the previous ones show that the present scheme is more stable and efficient for numerically solving the fourth order partial integro differential equation with a weakly singular kernel we also tested the method proposed on several one and two dimensional problems with very promising results besides in order to demonstrate the power of the quasi wavelets method in comparison with standard discretization methods we also consider the high frequency oscillation problems with the integro differential term

quasi wavelet based numerical method for volterra integro differential equations on unbounded spatial domains in this paper we study the numerical solution of the parabolic volterra integro differential equation with a memory term on one dimensional unbounded domain a new numerical method is proposed by applying the forward euler scheme in time and the quasi wavelet based numerical scheme in space some numerical examples are presented to illustrate the efficiency and accuracy of the proposed method

finite strip elements for the dynamic analysis of orthotropic plate structures abstract a finite strip element method is presented for the dynamic analysis of orthotropic plate structures in the strip element a hierarchical interpolation is used that is a combination of finite element shape functions and trigonometric shape functions a transformation of variables is used to calculate the strip element stiffness and mass matrices this enables continuous plates and plates with point and line supports to be analyzed convergence is rapid with few hierarchical terms being required for engineering accuracy

free vibration analysis of symmetric laminated skew plates by discrete singular convolution technique based on first order shear deformation theory in this study free vibration of laminated skew plates was investigated discrete singular convolution dsc method is used for numerical solution of vibration problems the straight sided quadrilateral domain is mapped into a square domain in the computational space using a four node element by using the geometric transformation typical results are presented for different geometric parameters and boundary conditions it is concluded from the results that the skew angle have considerable influence on the variations of the frequencies with fibre orientation angle and number of layers in the laminate the results obtained by dsc method are compared with those obtained by analytical and numerical approaches it is shown that reasonable accurate results are obtained present work also indicates that the method of dsc is a promising and potential approach for computational mechanics copyright 2009 john wiley sons ltd

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

option valuation by using discrete singular convolution this paper explores the utility of a discrete singular convolution dsc algorithm for solving the black scholes equation both european and american style options which include all nontrivial plain option pricing problems are considered to test the accuracy and to examine the efficiency of the present algorithm adaptive meshes are constructed to enhance the performance of the dsc algorithm all the present results are validated either by the analytical solution or by the standard binomial tree method extensive comparisons are carried out with two standard finite difference schemes and two binomial models of high speed convergence numerical experiments reveal that the present approach is accurate efficient and reliable for financial derivative valuations

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

matched interface and boundary mib for the implementation of boundary conditions in high order central finite differences high order central finite difference schemes encounter great difficulties in implementing complex boundary conditions this paper introduces the matched interface and boundary mib method as a novel boundary scheme to treat various general boundary conditions in arbitrarily high order central finite difference schemes to attain arbitrarily high order the mib method accurately extends the solution beyond the boundary by repeatedly enforcing only the original set of boundary conditions the proposed approach is extensively validated via boundary value problems initial boundary value problems eigenvalue problems and high order differential equations successful implementations are given to not only dirichlet neumann and robin boundary conditions but also more general ones such as multiple boundary conditions in high order differential equations and time dependent boundary conditions in evolution equations detailed stability analysis of the mib method is carried out the mib method is shown to be able to deliver high order accuracy while maintaining the same or similar stability conditions of the standard high order central difference approximations the application of the proposed mib method to the boundary treatment of other non standard high order methods is also considered

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 of long span continuous rectangular kirchhoff plates with internal rigid line supports abstract exact analysis for free vibration of long span continuous rectangular plates is presented based on the classical kirchhoff plate theory using the state space approach associated with joint coupling matrices levy type solution is adopted to model the field variation in the direction perpendicular to the pair of simply supported edges the series of internal rigid line supports are parallel to the remaining pair of edges which can be of an arbitrary combination of simply supported clamped and free edges transfer relationship is derived in the span direction by the state space approach the joint coupling matrices are employed to avoid numerical instability that exists in the conventional state space approach for high frequency calculation or long span geometry numerical calculation is carried out to validate effectiveness and efficiency of the present method influence of location of internal line supports on natural frequencies of multi span plates with large aspect ratios is investigated and discussed

open loop sustained chaos and control a manifold approach we present a general method for preserving chaos in nonchaotic parameter regimes as well as preserving periodic behavior in chaotic regimes using a multifrequency phase control the systems considered are nonlinear systems driven at a base frequency multifrequency phase control is defined as the addition of small subharmonic amplitude modulation coupled with a phase shift by implementing multifrequency control stable and unstable manifold intersections in postcrisis regimes may be manipulated to sustain chaos as well as to sustain periodic behavior the theory and a preliminary experiment are demonstrated for a co 2 driven laser

the fictitious foundation approach to vibration analysis of plates with interior point supports abstract a new approach to the continuum representation of interior point supports in the vibration analysis of plates is proposed the plate is assumed to be supported by a fictitious non uniform winkler foundation the flexibility distribution of the winkler foundation represented by a flexibility function is such that it has a zero value at the point support locations but assumes large values resulting in negligible restraint over the rest of the plate domain the improvization of the point supports as a special case of the flexibility distribution of the elastic foundation allows one to solve the problem in a single domain in contrast to the multiple domain solutions available in the literature the application of this approach namely the fictitious foundation approach is demonstrated by considering the free vibration of a simply supported rectangular plate with interior point supports also presented is a single domain application of the impulse function approach to plates with interior point supports involving the representation of the concentrated reactions at the point support locations by a double fourier series expansion of the impulse function the results obtained by using these single domain approaches are compared with those obtained by using the multiple domain flexibility function approach presented in an earlier study by the authors the new approach presented in this paper namely the fictitious foundation approach for the simulation of interior point supports in plates provides a method for absorbing the discrete discontinuities in the force field in the interior of the plate into the governing differential equation and obtaining a continuum representation of the solution in a single domain of the plate

high order numerical methods to two dimensional delta function integrals in level set methods in this paper we design and analyze a class of high order numerical methods to delta function integrals appearing in level set methods in two dimensional case the methods comprise approximating the mesh cell restrictions of the delta function integral in each mesh cell the two dimensional delta function integral can be rewritten as a one dimensional ordinary integral with the smooth integrand being a one dimensional delta function integral and thus is approximated by applying standard one dimensional high order numerical quadratures and high order numerical methods to one dimensional delta function integrals proposed in x wen high order numerical methods to a type of delta function integrals j comput phys 226 2007 1952 1967 we establish error estimates for the method which show that the method can achieve any desired accuracy by assigning the corresponding accuracy to the sub algorithms and has better accuracy under an assumption on the zero level set of the level set function which holds generally numerical examples are presented showing that the second to fourth order methods implemented in this paper achieve or exceed the expected accuracy and demonstrating the advantage of using our high order numerical methods

dsc solution for flow in a staggered double lid driven cavity a benchmark quality solution is presented for flow in a staggered double lid driven cavity obtained by using the wavelet based discrete singular convolution dsc the proposed wavelet based algorithm combines local methods flexibility and global methods accuracy and hence is a promising approach for achieving the high accuracy solution of the navier stokes equations block structured grids with pseudo overlapping subdomains are employed in the present simulation a third order runge kutta scheme is used for the temporal discretization quantitative results are presented apart from the qualitative fluid flow patterns the prevalence of rich features of flow morphology such as two primary vortex patterns merged single primary vortex patterns and secondary eddies makes this problem very attractive and interesting the problem is quite challenging for the possible existence of numerically induced asymmetric flow patterns and elliptic instability important computational issues like consistence convergence and reliability of the numerical scheme are examined the dsc algorithm is tested on the single lid driven cavity flow and the taylor problem with a closed form solution the double lid driven cavity simulations are cross validated with the standard second order finite volume method copyright 2003 john wiley sons ltd

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

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

finite volume formulation of the mib method for elliptic interface problems the matched interface and boundary mib method has a proven ability for delivering the second order accuracy in handling elliptic interface problems with arbitrarily complex interface geometries however its collocation formulation requires relatively high solution regularity finite volume method fvm has its merit in dealing with conservation law problems and its integral formulation works well with relatively low solution regularity we propose an mibfvm to take the advantages of both mib and fvm for solving elliptic interface problems we construct the proposed method on cartesian meshes with vertex centered control volumes a large number of numerical experiments are designed to validate the present method in both two dimensional 2d and three dimensional 3d domains it is found that the proposed mibfvm achieves the second order convergence for elliptic interface problems with complex interface geometries in both l and l2 norms

fourier bessel analysis of patterns in a circular domain this paper explores the use of the fourier bessel analysis for characterizing patterns in a circular domain a set of stable patterns is found to be well characterized by the fourier bessel functions most patterns are dominated by a principal fourier bessel mode n m which has the largest fourier bessel decomposition amplitude when the control parameter r is close to a corresponding non trivial root n m of the bessel function moreover when the control parameter is chosen to be close to two or more roots of the bessel function the corresponding principal fourier bessel modes compete to dominate the morphology of the patterns 2001 elsevier science b v all rights reserved

high resolution conjugate filters for the simulation of flows this paper proposes a hermite kernel realization of the conjugate filter oscillation reduction cfor scheme for the simulation of fluid flows the hermite kernel is constructed by using the discrete singular convolution dsc algorithm which provides a systematic generation of low pass filter and its conjugate high pass filters the high pass filters are utilized for approximating spatial derivatives in solving flow equations while the conjugate low pass filter is activated to eliminate spurious oscillations accumulated during the time evolution of a flow as both low pass and high pass filters are derived from the hermite kernel they have similar regularity time frequency localization effective frequency band and compact support fourier analysis indicates that the cfor hermite scheme yields a nearly optimal resolution and has a better approximation to the ideal low pass filter than previous cfor schemes thus it has better potential for resolving natural high frequency oscillations from a shock extensive one and two dimensional numerical examples including both incompressible and compressible flows with or without shocks are employed to explore the utility test the resolution and examine the stability of the present cfor hermite scheme small ratio of point perwavelength ppw is achieved in advancing a wavepacket and resolving a shock entropy wave interaction the present results for the advection of an isentropic vortex compare very favorably to those in the literature

vibration analysis of multi span plates having orthogonal straight edges abstract an accurate numerical technique is developed for flexural vibration of rectangular and l shaped plates continuous over rigid supports with arbitrary number of spans a set of orthogonally generated two dimensional plates function is used in the rayleigh ritz method to determine the natural frequencies of the plate systems several numerical examples are presented and the results obtained where possible are compared with the known solutions in the literature the present method is proven to be extremely versatile in solving a broad class of the aforementioned problems

discrete singular convolution for the sine gordon equation abstract this paper explores the utility of a discrete singular convolution dsc algorithm for the integration of the sine gordon equation the initial values are chosen close to a homoclinic manifold for which previous methods have encountered significant numerical difficulties such as numerically induced spatial and temporal chaos a number of new initial values are considered including a case where the initial value is exactly on the homoclinic orbit the present algorithm performs extremely well in terms of accuracy efficiency simplicity stability and reliability

on the numerical solution of the sine gordon equation in this the first of two papers on the numerical solution of the sine gordon equation we investigate the numerical behavior of a double discrete completely integrable discretization of the sine gordon equation for certain initial values in the vicinity of homoclinic manifolds this discretization admits an instability in the form of grid scale oscillations we clarify the nature of the instability through an analytical investigation supported by numerical experiments in particular a perturbation analysis of the associated linear spectral problem shows that the initial values used for the numerical experiments lie exponentially close to a homoclinic manifold this paves the way for the second paper where we use the non linear spectrum as a basis for comparing different numerical schemes

eigenfrequencies of line supported rectangular plates abstract a set of series consisting of a combination of free vibrating beam functions and polynomials is used as the admissible functions in the rayleigh ritz method to study the problem of the flexural vibration of thin uniform thickness orthotropic rectangular plates which may be continuous over several supports in one or two directions in practice which kind of free vibrating beam functions are used is determined by the boundary conditions of the plate the starting order of the beam eigenfunctions and the number of terms in the polynomials in each direction depend on the number of intermediate line supports in that direction the coefficients of the polynomials are decided by the boundary conditions of the plate and the locations of the line supports some numerical results are given for the simply supported and or clamped rectangular plates with two and three spans in one and two directions it is demonstrated that the method may be used to tackle such plate problems and has considerable accuracy and fast convergence compared with the available results the difficulty of application not being greater than any other methods

free vibration analysis of continuous rectangular plates vibration characteristics of rectangular plates continuous over full range line supports or partial line supports have been studied by using a discrete method concentrated loads with heaviside unit functions and dirac delta functions are used to simulate the line supports the fundamental differential equations are established for the bending problem of the continuous plate by transforming these differential equations into integral equations and using the trapezoidal rule of the approximate numerical integration the solution of these equations is obtained green function which is the solution of deflection of the bending problem of plate is used to obtain the characteristic equation of the free vibration the effects of the line support the variable thickness and aspect ratio on the frequencies and mode shapes are considered by comparing the numerical results obtained by the present method with those previously published the efficiency and accuracy of the present method are investigated

stochastic bifurcation in a driven laser system experiment and theory we analyze the effects of stochastic perturbations in a physical example occurring as a higher dimensional dynamical system the physical model is that of a class b laser which is perturbed stochastically with finite noise the effect of the noise perturbations on the dynamics is shown to change the qualitative nature of the dynamics experimentally from a stochastic periodic attractor to one of chaoslike behavior or noise induced chaos to analyze the qualitative change we apply the technique of the stochastic frobenius perron operator l billings et al phys rev lett 88 234101 2002 to a model of the experimental system our main result is the identification of a global mechanism to induce chaoslike behavior by adding stochastic perturbations in a realistic model system of an optics experiment in quantifying the stochastic bifurcation we have computed a transition matrix describing the probability of transport from one region of phase space to another which approximates the stochastic frobenius perron operator this mechanism depends on both the standard deviation of the noise and the global topology of the system our result pinpoints regions of stochastic transport whereby topological deterministic dynamics subjected to sufficient noise results in noise induced chaos in both theory and experiment

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

free vibration of a solid plate of arbitrary shape lying on an arbitrarily shaped ring support this paper is concerned with a method for solving problems of vibrating plates of arbitrary shape lying on arbitrarily shaped inner ring supports to treat the inner ring support the reaction force of the support is assumed to be an external unknown force the exact solution of the equation of motion in polar co ordinates is applied the boundary conditions along the edge and the support are satisfied directly by means of the fourier expansion collocation method which has bee developed in the author s previous reports numerical calculations have been carried out for a solid polygonal plate on an annular ring support and a solid circular plate on a elliptical ring support

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

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

triggering and enhancing chaos with a prescribed target lyapunov exponent using optimized perturbations of minimum power the objective of the present work is to propose a method for nonfeedback anticontrol of chaos with perturbations of minimum power for a preset control goal the noted lorenz system is employed as the test model for chaotification with the target state specified by a prescribed positive value of the largest lyapunov exponent lle lambda over 0 periodic and quasiperiodic perturbations are used as control signals and the signals parameters are optimized using a genetic algorithm under restriction of minimum power performance of the optimized signals in triggering chaos at an ordered state fixed point or periodic as well as further enhancing chaoticity at a chaotic state is explored the present numerical experiments reveal the following interesting physics about chaotification in general the power for chaotification increases with the preset value of lambda and quasiperiodic signals can achieve the control goal with a lower power than periodic ones given the same increment of lle from that of the uncontrolled state lambda1 0 i e deltalambda lambda lambda1 0 the further enhancement of chaoticity in a chaotic state needs a higher control power than the triggering of chaos from an ordered state the minimum power required for chaotification of an ordered state increases relatively slowly for lower lambda over but increases drastically as the preset target lle reaches a certain critical value most strikingly the numerical experiments demonstrate that this critical value of lambda corresponds to lle of the nearest chaotic state in the neighborhood of the uncontrolled state robustness of applying the present method in the presence of external noise is also demonstrated

quasi wavelet based numerical method for a class of partial integro differential equation abstract in this paper we study the numerical solution of initial boundary problem for a class of partial integro differential equations the quasi wavelet method is proposed to handle the spatial derivatives while the forward euler method is used to discretize the temporal derivatives detailed discrete schemes are given and some numerical experiments are included to demonstrate the effectiveness of the discrete technique the comparisons of the present numerical results with the exact analytical solutions show that the quasi wavelet based numerical method has distinctive local property and can achieve accurate results

vibration of triangular plates point supports mixed edges and partial internal curved supports a numerical method which is a hybrid form of the rayleigh ritz method and the lagrangian multiplier method is presented in this paper for the vibration analysis of general triangular plates with complicated supported conditions these support conditions include internal clamped or simple point supports mixed periphery boundary conditions and partial internal curved supports several plate examples are used to illustrate the method apart from the limiting cases of some of these triangular plates with point supports where existing results are available for comparison the frequency parameters presented in this paper are new they should be valuable to designers in some industrial applications

free vibration analysis of symmetrically laminated thin composite plates by using discrete singular convolution dsc approach algorithm and verification this study presents a detailed procedure for the implementation of a discrete singular convolution dsc approach to the free vibration analysis of composite plates based on classical laminated plate theory clpt the approach performs a numerical solution of differential equation of motion by using a grid discretization based on distribution theory and wavelets in the paper firstly computational algorithm of the dsc method is presented then the accuracy of the computer code developed is verified by comparing dsc solutions with the exact results of simply supported isotropic thin beams fully simply supported one layer isotropic and specially orthotropic plates and also some symmetrically laminated thin composite plates orientated to become specially orthotropic besides dsc predictions for laminated composite plates with different boundary conditions and ply numbers for which there is no analytical solution are compared with those of several distinguished works available in the literature it is noteworthy that dsc results completely match with the exact solutions and are in perfect agreement with those of compared studies

free vibration of generally supported rectangular kirchhoff plates state space based differential quadrature method the title problem is investigated using the differential quadrature method based on the state space formalism the plates with mixed boundary conditions may cross over one way internal rigid line supports that impose zero transverse displacement constraints differential quadrature procedure is applied in the direction of line supports while exact solution is sought in the transfer domain perpendicular to the line supports using the state space method to avoid numerical instability in the transfer matrix method joint coupling matrices are introduced mainly according to the continuity conditions at line joints natural frequencies of rectangular kirchhoff plates with general boundary conditions are calculated and compared with the results from other methods effects of location of internal line supports and the mixed boundary conditions on the frequency parameters are discussed copyright 2006 john wiley sons ltd

numerical methods for multiple inviscid interfaces in creeping flows we present new highly accurate and efficient methods for computing the motion of a large number of two dimensional closed interfaces in a slow viscous flow the interfacial velocity is found through the solution to an integral equation whose analytic formulation is based on complex variable theory for the biharmonic equation the numerical methods for solving the integral equations are spectrally accurate and employ a fast multipole based iterative solution procedure which requires only o n operations where n is the number of nodes in the discretization of the interface the interface is described spectrally and we use evolution equations that preserve equal arclength spacing of the marker points we assume that the fluid on one side of the interface is inviscid and we discuss two different physical phenomena bubble dynamics and interfacial motion driven by surface tension viscous sintering applications from buoyancy driven bubble interactions the motion of polydispersed bubbles in an extensional flow and the removal of void spaces through viscous sintering are considered and we present large scale fully resolved simulations involving o 100 closed interfaces

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