axisymmetric vibration of a circular plate with double linear variable thickness abstract the rayleigh ritz method has been employed to study the axisymmetric transverse vibration of a circular plate with two different linear variations in thickness one in the central core and the other in the outer annular region the boundary has been taken either clamped or simply supported results for linearly varying thickness and uniform thickness have been obtained as special cases and are compared with those available in the literature the effects of the various parameters on the frequencies mode shapes and the nodal radii have been examined through extensive numerical results given in the form of graphs and tables

vibrations and elastic stability of thin circular plates with variable profile abstract circular plates of thicknesses varying to the functional relationho 1 r a n wherenis a positive integer are studied in the present paper uniform elastic boundary restraints are considered and the first two natural frequency coefficients corresponding to axisymmetric modes and the buckling in plane pressure are determined using simple polynomial co ordinate functions which identically satisfy the boundary conditions and the classical rayleigh ritz method an independent solution is also obtained by means of the differential quadrature technique

free vibration analysis of circular plates with variable thickness by the generalized differential quadrature rule the generalized differential quadrature rule proposed recently by these authors is applied here to the free vibration analyses of solid circular plates with radially varying thickness and elastic restraints the thickness can vary radially in any given continuous form and it varies exponentially and linearly in this work two regularity conditions corresponding to the plate center are expressed in explicit formulae since they have been inexactly or even wrongly expressed in the literature such errors are pointed out in the application of the differential quadrature techniques and in the expression of the regularity conditions at the plate center numerical results are presented for a number of plates illustrating the versatility and accuracy of the approach

on the free vibration analysis of circular plates with stepped thickness over a concentric region by the differential quadrature element method it can be seen the dqem retains all advantages of the differential quadrature method extends the applicability range of the dq method and is more convenient for treating various boundary conditions

partitioned density functional approach for a lennard jones fluid the existing classical density functional approach for nonuniform lennard jones fluid which is based on dividing the lennard jones interaction potential into a short range repulsive part and a smoothly varying long range attractive tail was improved by dividing the bulk second order direct correlation function into strongly density depending short range part and weakly density depending long range part the latter is treated by functional perturbation expansion truncated at the lowest order whose accuracy depends on how weakly the long range part depends on the bulk density the former is treated by the truncated functional perturbation expansion which is rewritten in the form of the simple weighted density approximation and incorporates the omitted higher order terms by applying lagrangian theorem of differential calculus to the reformulated form the two approximations are put into the density profile equation of the density functional theory formalism to predict the density distribution for lennard jones fluid in contact with a hard wall or between two hard walls within the whole density range for reduced temperature t 1 35 and a density point for reduced temperature t 1 the present partitioned density functional theory performs much better than several previous density functional perturbation theory approaches and a recently proposed bridge density functional approximation

a new approach to the differential quadrature method for fourth order equations a generalized and more complete methodology for treating boundary conditions in the differential quadrature method dqm is presented this improved approach eliminates the deficiencies of the type grid arrangement which represents an approximation by applying the boundary conditions exactly two kinds of basis functions chebyshev and lagrange are used for concept demonstration it is found that the new approach cures most deficiencies of the current dqm 1997 by john wiley sons ltd

axisymmetric vibration of a circular plate with exponential thickness variation abstract the rayleigh ritz method has been used to find the first four frequencies mode shapes and nodal radii for axisymmetric vibration of a circular plate when the thickness varies exponentially with the radial distance results are given for a clamped as well as simply supported boundary for various values of the parameter controlling the thickness variation convergence is ensured by working out a sufficient number of approximations comparison has been made with existing results for uniform thickness and linearly varying thickness

free vibration of plates by the high accuracy quadrature element method in this paper a highly accurate and rapidly converging hybrid approach is presented for the quadrature element method qem solution of plate free vibration problems the hybrid qem essentially consists of a collocation method in conjunction with a galerkin finite element technique to combine the high accuracy of the differential quadrature method dqm for the efficient solution of differential equations with the generality of the finite element formulation this results in superior accuracy with fewer degrees of freedom than conventional fem or fdm a series of numerical tests is conducted to assess the performance of the quadrature plate element in free vibration problems anisotropic and stepped thickness plates are investigated as well as mixed boundary conditions and point supports at the edges in all cases the results obtained are quite accurate

transverse vibrations of circular plates and membranes with intermediate supports the present paper deals with an approximate solution of the title problem in the case of a a concentric circular support and b a secant support fundamental frequency coefficients are determined by means of the rayleigh minimization procedure the modal shapes been approximated by simple polynomial co ordinate functions in the case of a circular plate with a secant support an independent solution is obtained by means of a finite element code and very good agreement is shown to exist

deriving the rosenfeld functional from the virial expansion in this article we replace the semiheuristic derivation of the rosenfeld functional of hard convex particles with the systematic calculation of mayer clusters it is shown that each cluster integral further decomposes into diagrams of intersection patterns that we classify by their loop number this extends the virial expansion of the free energy by an expansion in the loop order with the rosenfeld functional as its leading contribution rosenfeld s weight functions then follow from the derivation of the intersection probability by generalizing the equation of blaschke santalo and chern it is found that the 0 loop order can be derived exactly and reproduces the rosenfeld functional we further discuss the influence of particle dimensions topologies and geometries on the mathematical structure of the calculation

application of generalized differential quadrature rule in blasius and onsager equations the generalized differential quadrature rule gdqr proposed recently by the authors is applied here to third order non linear differential equations of the blasius type and to sixth order linear onsager differential equations high 3rd order differential equations in fluid mechanics are dealt with without using point techniques the half space domain is simplified in a practical way accurate results are obtained for both kinds of problems the wide applicability of the gdqr in high order differential equations is manifested further through this work copyright 2001 john wiley sons ltd

transverse vibrations of a circular annular plate with an intermediate circular support and a free inner edge the present study deals with the determination of the fundamental frequency of transverse vibration

vibrating circular plates with stepped thickness over a concentric circular region a general approximate solution natural frequencies corresponding to axi and antisymmetric modes of vibration of the structural elements described in the title are studied using the optimized rayleigh ritz approach it is assumed that the plates are elastically restrained against translation and rotation the plate amplitude is approximated in terms of polynomial coordinate functions that satisfy the boundary conditions each one containing an undetermined exponential parameter that allows for the minimization of the eigenvalues under investigation

exact vibration solutions for circular mindlin plates with multiple concentric ring supports this paper presents an analytical approach to investigate the vibration behaviour of circular mindlin plates with multiple concentric ring supports a circular plate is first divided into multiple annular segments and a circular segment at the locations of the ring supports the governing differential equations and the solutions of these equations for the annular and circular segments based on the mindlin plate theory are presented a homogenous equation system governing the vibration of circular mindlin plates with ring supports is derived by imposing the essential and natural boundary and segment interface conditions the first known exact vibration frequencies for circular mindlin plates with multiple concentric ring supports are obtained and the modal shapes of displacement fields and stress resultants for several selected cases are presented the influence of the ring support locations plate boundary conditions and plate thickness ratios on the vibration behaviour of circular plates is discussed

fluid structure from density functional theory we treat various common fluid models like the inverse power asakura oosawa and lennard jones potentials within the soft fundamental measure theory sfmt we show that this recently proposed density functional approach is able to predict the pair correlations in the fluid phase reliably compared to computer simulations explicit expressions for certain quantities of sfmt are given namely for the weight functions and the fundamental measures these technical tools permit practical calculations for a large class of inhomogeneous systems

vibration analysis of beams using the generalized differential quadrature rule and domain decomposition abstract this study dealt with domain decomposition in the recently proposed generalized differential quadrature rule in detail the authors concentrated on the free vibration of multispan and stepped euler beams and beams carrying an intermediate or end concentrated mass since compatibility conditions should be implemented in a strong form at the junction of the subdomains concerned the fem techniques used for internal moments and shear forces must not be used compatibility conditions and their differential quadrature expressions were explicitly formulated a peculiar phenomenon was found in differential quadrature applications that equal length subdomains gave more accurate results than unequal length ones using the same number of subdomain grids various examples were presented and very accurate results have been obtained

application of differential quadrature to transport processes the methodology and numerical solution of problems concerning transport processes via the method of differential quadrature are presented application of the method is demonstrated by solving a simple one dimensional time dependent transient diffusion process involving an irreversible reaction without any flux across the end boundary in addition the same technique is used for the first time to the authors knowledge to solve a steady state problem for this purpose a convection diffusion problem involving an irreversible reaction is considered the demonstration is carried out in two ways 1 using the bellman et al technique which employs approximation formulas for higher order partial derivatives derived by iterating the linear quadrature approximation for the first order partial derivative and 2 using individual quadratures to approximate the partial derivatives of first as well as higher orders as suggested by mingle both approaches give the same results however the latter saves an appreciable amount of iterative computing effort despite the fact that it requires separate weighting coefficients for each individual quadrature since the technique of differential quadrature can produce solutions with sufficient accuracy even when using as few as three discrete points both the programming task and computational effort are alleviated considerably for these reasons the differential quadrature approach appears to be very practical in solving a variety of problems related to transport phenomena

transport theory of granular swarms the transport of trace granular gas swarm in a carrier granular fluid is studied by means of the boltzmann lorentz kinetic equation time dependent perturbation theory is used to follow the evolution of the granular swarm from an arbitrary initial distribution a nonhydrodynamic extension of the diffusion equation is derived with transport coefficients that are time dependent and implicitly depend on the wave vector transport coefficients of any order are obtained as velocity moments of the solutions of the corresponding kinetic equations derived from the boltzmann lorentz equation for the special case of the initial distribution of swarm particles transport coefficients are identified as time derivatives of the moments of the number density finally the granular particle transport theory is extended by the introduction of the concept of non particle conserving collisions

asymptotic stability of the euler bernoulli beam with boundary control abstract we show that under appropriate conditions a euler bernoulli beam clamped at one end with boundary controls at the other end can be made uniformly exponentially stable the method can also be applied to multibeam structures with controls either at the end or somewhere along the structure

numerical solution for differential equations of duffing type non linearity using the generalized differential quadrature rule the generalized differential quadrature rule gdqr proposed recently by the authors is applied for the first time to second and fourth order initial value differential equations with duffing type non linearity procedures are given in detail to convert these non linear differential equations into a set of linear algebraic equations in an iterative loop using the frechet derivative the effectiveness of the gdqr for obtaining the periodic solution of the duffing equation has been demonstrated through a number of examples it is also shown that the use of the frechet derivative makes it easier for the gdqr to handle non linearity the wide applicability of the gdqr is manifested further through this work

high accuracy plane stress and plate elements in the quadrature element method in this paper a high accuracy and rapid convergence hybrid approach is developed for the quadrature element method qem solution of two dimensional plane stress and plate bending problems the hybrid qem essentially consists of a collocation method in conjunction with a galerkin finite element technique to combine the high accuracy of the differential quadrature method dqm with the generality of finite element formulations this results in superior accuracy with fewer degrees of freedom than conventional fem or fdm the present method also extends the general application of the collocation numerical approach to fourth order governing equation systems here the influence of collocation point location is investigated a series of numerical tests is conducted in order to assess the performance of the quadrature plane stress and plate elements in static problems

regulation of a geometrically exact flexible beam manipulator abstract the rest to rest maneuver of a single link flexible manipulator using the geometrically exact nonlinear beam model is considered it is shown that with the joint torque only a simple linear feedback law derived based on a lyapunov type method stabilizes the highly nonlinear coupled system described by a set of integro partial differential equations with coupled nonlinear boundary conditions

lyapunov functions and the control of the euler bernoulli beam a controller for the euler bernoulli beam is derived using the complete distributed model along with a lyapunov function approach model structure is therefore preserved in the control law whose parameters can be used to balance two different types of behaviour the gross motion of the beam and the vibration superimposed on it in the limiting case of a rigid beam these two types of behaviour become indistinguishable and so the controller reduces to a proportional feedback law this approach also guarantees that the controller provides asymptotic trajectory tracking for smooth initial conditions also since it is not constrained to linear systems it could in principle be used for multi link flexible robot systems

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

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

the generalized differential quadrature rule for initial value differential equations abstract the generalized differential quadrature rule gdqr proposed recently by the authors is applied here to solve initial value differential equations of the 2nd to 4th order differential quadrature expressions are derived based on the gdqr for these equations the hermite interpolation functions are used as trial functions to obtain the explicit weighting coefficients for an easy and efficient implementation of the gdqr the numerical solutions for example problems demonstrate that the gdqr has high efficiency and accuracy a detailed discussion on the present method is presented by comparing with other existing methods the present method can be extended to other types of differential equation systems

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

application of differential quadrature to static analysis of structural components the numerical technique of differential quadrature for the solution of linear and non linear partial differential equations first introduced by bellman and his associates is applied to the equations governing the deflection and buckling behaviour of one and two dimensional structural components separate transformations are used for higher order derivatives as suggested by mingle thus extending the method to treat fourth order equations and to include multiple boundary conditions in the respective co ordinate directions results are obtained for various boundary and loading conditions and are compared with existing exact and numerical solutions by other methods the application of differential quadrature to this class of problems is seen to lead to accurate results with relatively small computational effort

the generalized differential quadrature rule for fourth order differential equations the generalized differential quadrature rule gdqr proposed here is aimed at solving high order differential equations the improved approach is completely exempted from the use of the existing point technique by applying multiple conditions in a rigorous manner the gdqr is used here to static and dynamic analyses of bernoulli euler beams and classical rectangular plates numerical error analysis caused by the method itself is carried out in the beam analysis independent variables for the plate are first defined the explicit weighting coefficients are derived for a fourth order differential equation with two conditions at two different points it is quite evident that the gdqr expressions and weighting coefficients for two dimensional problems are not a direct application of those for one dimensional problems the gdqr are implemented through a number of examples good results are obtained in this work copyright 2001 john wiley sons ltd

modeling stabilization and control of serially connected beams many flexible structures consist of a large number of components coupled end to end in the form of a chain in this paper we consider the simplest type of such structures which is formed by n seri

density functional theory for hard particles in n dimensions recently it has been shown that the heuristic rosenfeld functional can be derived from the virial expansion for particles overlapping in one center here we generalize this approach to any number of intersections starting from the virial expansion in ree hoover diagrams it is shown in the first part that each intersection pattern corresponds to exactly one infinite class of diagrams determining their automorphism groups we sum over all its elements and derive a generic functional the second part shows that this functional factorizes into a convolute of integral kernels for each intersection center we derive this kernel for n dimensional particles in the n dimensional flat euclidean space the third part focuses on three dimensions and determines the functionals for up to four intersection centers comparing the leading order to rosenfeld s result we close by proving a generalized form of the blaschke santalo chern equation of integral geometry