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

forced axi symmetric response of polar orthotropic linearly tapered circular plates forced axi symmetric vibrations of polar orthotropic linearly tapered circular plates are discussed on the basis of classical plate theory ritz method has been employed to obtain the solutions the deflection function and the bending moments for forced vibrations of the plate are presented for various values of taper parameter and rigidity ratio a comparison of results with those available in literature shows an excellent agreement

non linear vibration and thermal buckling of an orthotropic annular plate with a centric rigid mass abstract a computational analysis of the non linear vibration and thermal post buckling of a heated orthotropic annular plate with a central rigid mass is examined for the cases of immovably hinged as well as clamped constraint conditions of the outer edge first based on von karman s plate theory and hamilton s principles the governing equations in terms of the displacements of the middle plane of the problem are derived then upon assuming that harmonic responses of the system exist the non linear partial differential equations are converted into the corresponding non linear ordinary differential equations through elimination of the time variable by using the kantorovich time averaging method finally by applying a shooting method the fundamental responses of the non linear vibration and thermal post buckling of the plate are numerically obtained for some prescribed values of the parameters such as the material rigidity ratio temperature rise and so on the curves of the fundamental frequency versus specified amplitude and the thermal post buckled equilibrium paths of the plate are numerically presented

renormalised solutions of nonlinear parabolic problems with l1 data existence and uniqueness in this paper we prove the existence and uniqueness of a renormalised solution of the nonlinear problem where the data f and u 0 belong to l 1 0 t and l 1 and where the function a 0 t n n is monotone but not necessarily strictly monotone and defines a bounded coercive continuous operator from the space into its dual space the renormalised solution is an element of c 0 0 t l 1 such that its truncates t k u belong to with this solution satisfies the equation formally obtained by using in the equation the test function s u where belongs to and where s belongs to c with

asymmetric non linear forced vibrations of free edge circular plates part 1 theory in this article a detailed study of the forced asymmetric non linear vibrations of circular plates with a free edge is presented the dynamic analogue of the von karman equations is used to establish the governing equations the plate displacement at a given point is expanded on the linear natural modes the forcing is harmonic with a frequency close to the natural frequency omega n of one asymmetric mode of the plate thus the vibration is governed by the two degenerated modes corresponding to omega n which are one to one internally resonant an approximate analytical solution using the method of multiple scales is presented attention is focused on the case where one configuration which is not directly excited by the load gets energy through non linear coupling with the other configuration slight imperfections of the plate are taken into account experimental validations are presented in the second part of this paper

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

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

analysis and optimization of trimorph ring transducers abstract the kirchoff love plate theory and electroelasticity theory are combined to simulate the dynamic behaviors of the trimorph ring transducers under different boundary conditions the transducer consists of an isotropic elastic ring laminated between two identical piezoelectric rings their electric current response resonant frequencies antiresonant frequencies and electromechanical coupling coefficients emccs are theoretically formulated and studied by numerical simulation also the resonant frequencies and their corresponding mode shape are simulated by the finite element modelling to verify the theoretical results finally to obtain the maximum energy conversion efficiency the dynamic emcc is optimized by varying the proportion of piezoelectric and elastic parts it is shown that the dynamic emcc depends on geometric thickness and radii ratios optimum settings for a particular transducer to reach the maximum dynamic emcc are found for different boundary conditions the trimorph ring transducer for the fixed inner and free outer surfaces boundary condition has slightly lower resonant and anti resonant frequencies and larger emccs than that for the free inner and fixed outer surfaces boundary condition does

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

three dimensional vibration analysis of a torus with circular cross section the free vibration characteristics of a torus with a circular cross section are studied by using the three dimensional small strain elasticity theory a set of three dimensional orthogonal coordinates system comprising the polar coordinate r at each circular cross section and the circumferential coordinate around the ring is developed each of the displacement components ur and w in the r and directions respectively is taken as a product of the chebyshev polynomials in the r direction and the trigonometric functions in the and directions eigenfrequencies and vibration mode shapes have been obtained via a three dimensional displacement based extremum energy principle upper bound convergence of the first seven eigenfrequencies accurate to at least six significant figures is obtained by using only a few terms of the admissible functions the eigenfrequency responses due to variation of the ratio of the radius of the ring centroidal axis to the cross sectional radius are investig

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

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

a goodness of fit approach to testing mean residual times the random residual lifetime is a random variable representing the remaining life of a system of age x 0 the mean residual life at age x is the expected value of the remaining life beyond that age which is well known and extensively studied for both testing and estimation in this article a new approach is presented for testing constant versus decreasing residual life the new test is much simpler to compute asymptotically normal and performs better than previous tests in terms of power and pitman asymptotic efficiencies for several alternatives

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

non linear elliptic and parabolic equations involving measure data in this paper we prove the existence of solutions for equations of the type div a du f in a bounded open set u 0 on where a is a possibly non linear function satisfying some coerciveness and monotonicity assumptions and f is a bounded measure we also consider the equation div a du g u f in u 0 on with f l1 or f m u u 0 and the parabolic equivalent of the first elliptic equation

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

solvability for equations of motion of weak aqueous polymer solutions with objective derivative abstract in this paper we consider the initial boundary problem for equations of motion of weak aqueous polymer solutions involving the regularized jaumann s derivative we prove the weak solvability of the model in space e 1 v v l 0 t v 1 v l 2 0 t v 1 using the topological approximation approach

optimum shape design against flutter of a cantilevered column with an end mass of finite size subjected to a non conservative load abstract optimum design for dynamic stability of slender cantilevered columns subjected to a follower force due to a rocket thrust is investigated the aim is to determine the tapering of the column which maximizes the critical value of the rocket thrust at which flutter is initiated under the constraint of constant length and volume of the column the rocket thrust is assumed to be produced by a solid rocket motor mounted at the tip end of the column the rocket motor is simplified as a massive ball with the same material density as the column based on experimental evidence 1 2 it is argued that a mathematical model without damping gives the practical stability limit if internal and external damping is small and the rocket thrust acts only in a short interval of time optimum columns are determined for various sizes of the end ball rocket motor for small sizes the critical thrust can be significantly increased by optimization about eight times by practical experimental realizable values of the mass ratio mass of end ball mass of column the critical thrust can only be increased 1 3 1 4 times which is similar to the case of a pure conservative dead end load also it is found that the great sensitivity to small changes in design parameters which significantly complicates optimization of the pure beck s column is not present for practical values of it is argued then that the pure beck s column should be considered as a theoretical limit case of vanishing end mass

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

free vibration of circular and annular plates with variable thickness and different combinations of boundary conditions in this paper the first nine frequency parameters of circular and annular plates with variable thickness and combined boundary conditions are computed for different thickness to radius ratios several combined boundary conditions are considered for inner and outer edges these are free soft and hard simply supported and clamped boundary conditions three dimensional elasticity theory is used results of this paper are compared with works of other authors and the results of finite element method analysis which are in agreement data for thick circular and annular plates with linear and parabolic thickness variation and different combinations are presented for the first time

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

free vibration analysis of stepped circular mindlin plates this paper presents the first known investigation on exact vibration of circular mindlin plates with multiple step wise thickness variations a stepped circular plate is divided into multiple annular and one circular segments along the locations of the step variations the governing differential equations for harmonic vibration of annual and circular segments are derived and an analytical method based on the domain decomposition technique is developed to solve the plate vibration problem exact vibration solutions are presented for circular mindlin plates of different edge support conditions and various combinations of step wise thickness variations the influence of plate boundary conditions plate thickness ratios step location ratios and step thickness ratios on the vibration behaviour of stepped circular mindlin plates are examined the exact vibration results can serve as benchmark values for researchers to validate their numerical methods for such circular plate problems

vibration and critical speeds of a spinning annular disk of varying thickness the equation of motion of a spinning isotropic annular plate of linearly and exponentially varying thickness is formulated based on the lagrangian approach and the assumed mode method the plate is assumed to be elastic in the spinning motion and the initial stress fields in the plate are derived assuming the plane stress condition the natural frequencies and critical speeds for vibration modes consisting of radial nodal lines without any nodal circle are presented for simply supported simply supported and clamped free edge conditions

solvability of a parabolic problem with non smooth data abstract we study a weak solvability of one linear parabolic problem with a summable right hand side and non smooth coefficients we consider this problem as appropriate operator equation in some banach space methods of the semigroups theory fractional powers of operators and integral operators for solvability of this operator equation are used

three dimensional vibrations of thick linearly tapered annular plates abstract the ritz method is applied in a three dimensional 3 d analysis to obtain accurate frequencies for thick linearly tapered annular plates the method is formulated for annular plates having any combination of free or fixed boundaries at both inner and outer edges admissible functions for the three displacement components are chosen as trigonometric functions in the circumferential co ordinate and algebraic polynomials in the radial and thickness co ordinates upper bound convergence of the non dimensional frequencies to the exact values within at least four significant figures is demonstrated comparisons of results for annular plates with linearly varying thickness are made with ones obtained by others using 2 d classical thin plate theory extensive and accurate four significant figures frequencies are presented for completely free thick linearly tapered annular plates having ratios of average plate thickness to difference between outer radius a and inner radius b ratios hm l of 0 1 and 0 2 forb l 0 2 and 0 5 all 3 d modes are included in the analyses e g flexural thickness shear in plane stretching and torsional because frequency data given is exact to at least four digits it is benchmark data against which the results from other methods e g 2 d thick plate theory finite element methods and may be compared throughout this work poisson s ratiovis fixed at 0 3 for numerical calculations

monte carlo inference in econometric models with symmetric stable disturbances the paper develops markov chain monte carlo methods to perform exact posterior analysis in models with symmetric stable paretian disturbances it is shown how posterior moments and marginal densities of functions of parameters can be computed methodically by combining a gibbs sampler with metropolis independence chains the new method is shown to perform satisfactorily in constructed examples the method is also applied to a set of monthly real exchange rates and the question of difference versus trend stationarity is taken up jointly with the problem of inference about the parameter of the stable distribution

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

free vibration of polar orthotropic circular plates of variable thickness with elastically restrained edge abstract asymmetric vibrations of polar orthotropic circular plates of linearly varying thickness with elastic rigid support are discussed on the basis of the classical plate theory an approximate solution of the problem is obtained by the rayleigh ritz method using functions based on static deflection of polar orthotropic circular plates this type of approximating functions has a faster rate of convergence as compared to the polynomial co ordinate functions frequency parameters of the plate have been obtained for different values of taper parameter flexibility parameter and rigidity ratio in the first three modes of vibration a comparison of results for special cases of isotropy uniform thickness and of axisymmetric vibrations obtained by other techniques such as the finite element method and the receptance method shows excellent agreement

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

vibration and stability of annular plates in non linear creep conditions abstract this paper presents a study on the influence of the physical non linearity of material in creep conditions on vibration and stability of non uniform annular plates subjected to a follower force radially distributed at the outer edge the stability analysis requires first the calculation of a membrane stress distribution and then the application of the kinetic stability criterion making use of small superposed vibrations the differential equations of the membrane and vibration states have been integrated by means of the transfer matrix method which allowed the determination of the relationships between the real and imaginary parts of the complex frequency and compressive force characteristic curves the results have been presented in numerous figures

existence and uniqueness for a degenerate parabolic equation with l1 data in this paper we study existence and uniqueness of solutions for the boundary value problem with initial datum in l1 ut div a x du in 0 u a u on 0 u x 0 u0 x in where a is a caratheodory function satisfying the classical leray lions hypothesis a is the neumann boundary operator associated to a du the gradient of u and is a maximal monotone graph in r r with 0 0

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 annular plate concentrators with conical cross section in this paper the torsional vibration and radial vibration of isotropic metal thin annular plates with conical cross section are deduced by using bessel functions and according to electro mechanical analogy the electro mechanical equivalent circuits are obtained based on the electro mechanical equivalent circuits the resonance frequency equations and the expressions of angular and radial displacement amplitude magnifications are derived and the resonance frequencies and magnifications are solved by analytical method the relationships between torsional and radial resonance frequencies and geometrical dimensions are discussed and the relationships between angular and radial displacement amplitude magnifications and the ratio of outer radius over inner radius are analyzed modal shapes are analyzed by finite element method ansys it is shown that the values calculated by using the theory of this paper are in good agreement with the results simulated by ansys the method can serve as benchmark values for researchers to validate other variable thickness thin annular plates

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

axisymmetric vibration analysis of rotating annular plates by a 3d finite element the axisymmetric vibration of spinning isotropic annular plates is herein analyzed by a modified axisymmetric finite element due to the three dimensional elasticity nature of the present approach all the initial stresses induced by the centrifugal force are calculated and taken into account in the augmented strain energy expression while only two are considered in the conventional analyses also the whole three velocity components are considered in the inertial term instead of only one by conventional approaches natural frequencies of annular plates with different ratios of inner to outer radius ratios of thickness to radius rotational speeds and boundary conditions are derived by the present approach and are compared with those by a plate theory approach

generalized power series solutions of the vibration of classical circular plates with variable thickness these solutions represented by recursive relations of the coefficients of the infinite power series can be applied to various boundary conditions to obtain the resonance frequency spectra and mode shapes these infinite power series which are bessel functions for a particular poisson ratio and other parameters can be effectively evaluated without special difficulty for most parameters involved

pontryagin s principle for state constrained boundary control problems of semilinear parabolic equations this paper deals with state constrained optimal control problems governed by semilinear parabolic equations we establish a minimum principle of pontryagin s type to deal with the state constraints we introduce a penalty problem by using ekeland s principle the key tool for the proof is the use of a special kind of spike perturbations distributed in the domain where the controls are defined conditions for normality of optimality conditions are given

conditions for optimality in experimental designs abstract the purpose of this paper is to establish some results on optimal criteria in experimental designs some relationships between optimality criteria are shown in particular we extend results on the p criteria we prove the yeh biometrika 73 1986 701 conjecture that gives a necessary and sufficient condition for a design to be universally optimal we also give a similar result based on the eigenvalues of the information matrix

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

some statistical methods for random process data from seismology and neurophysiology examples are presented of statistical techniques for the analysis of random process data and of their uses in the substantive fields of seismology and neurophysiology the problems addressed include frequency estimation for decaying cosinusoids signal estimation association measurement causal connection assessment estimation of speed and direction and structural modeling the techniques employed include complex demodulation nonlinear regression probit analysis deconvolution maximum likelihood singular value decomposition fourier analysis and averaging

free axisymmetric vibration of laminated transversely isotropic annular plates based on the basic equations of three dimensional theory of elasticity this paper establishes the state space equation of the axisymmetric vibration of laminated annular plates composed of transversely isotropic layers taking advantage of the finite hankel transform four exact solutions are obtained for four different types of boundary conditions the calculating methods of frequencies and mode shapes are presented lastly numerical results are given to validate the present method

buckling and vibration of polar orthotropic circular plate resting on winkler foundation buckling and vibrational behavior of polar orthotropic circular plates of linearly varying thickness is presented on the basis of classical plate theory the plate is resting on winkler type foundation an approximate solution has been obtained by ritz method which employs basis functions based upon static deflection of polar orthotropic plates the effect of elastic foundation and that of orthotropy on the natural frequency of plate has been illustrated for different values of taper parameter flexibility parameter in plane force and nodal diameter the critical buckling load for clamped and simply supported plates have been obtained a comparison of results with those available in literature has been presented

modification of fundamental vibration modes of circular plates with free edges for an isotropic circular plate with constant thickness and free edges its fundamental vibration mode takes the form of a twisting mode with two nodal diameters i e n 2 in certain applications it may be necessary to have an axisymmetric shape for the fundamental vibration mode i e mode shape with no nodal diameter n 0 in this paper we show that such an axisymmetric vibration mode can be realized by increasing the bending rigidity of the outer rim of the circular plate by using a larger thickness or by using a material with a larger young s modulus or both we also determine the critical flexural rigidity of the outer rim that will trigger this vibration mode change from n 2 type to n 0 type for a given rim width the ability to alter the mode shape of circular plates with free edges has useful applications in sensing and actuating devices and large pontoon type floating circular structures

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

forced asymmetric response of linearly tapered circular plates the eigenfunction method is used to analyze the asymmetric response of linearly tapered circular plates subjected to transverse loads uniformly distributed over an annular sectorial area of the plate the analysis is based on the classical plate theory numerical results are presented graphically for the transverse deflection and stresses of the plate for various combinations of plate and loading parameters results obtained as a particular case for a plate of constant thickness subjected to an off center half sine pulse point load are compared with previously published results and found to match exactly

a general approximate solution of the problem of free vibrations of annular plates of stepped thickness abstract an approximate solution to the title problem is proposed for the case in which the inner boundary of the circular plate is free and the outer edge is elastically restrained against rotation the displacement amplitude is approximated by means of a superposition of simple polynomial co ordinate functions which satisfy identically the boundary conditions at the outer edge only and which yield excellent accuracy in the case of simply connected circular plates the optimized rayleigh ritz method is then used to generate the frequency determinant minimizing the eigenvalues with respect to an exponential parameter contained in each polynomial co ordinate function a comparison with eigenvalues obtained using a finite element solution is also presented and good agreement is shown to exist

asymmetric vibrations and elastic stability of polar orthotropic circular plates of linearly varying profile abstract asymmetric vibration of polar orthotropic circular plates of linearly varying thickness subjected to hydrostatic in plane force are discussed on the basis of classical plate theory an approximate solution of the problem has been obtained by the ritz method which employs functions based upon the static deflection of polar orthotropic plates this method has a faster rate of convergence as compared to the polynomial co ordinate functions frequency parameters of the plate with elastically restrained edge conditions are presented for the three modes of vibrations for various values of taper parameter rigidity ratio flexibility parameter and buckling load parameter the critical buckling loads for elastically restrained edge conditions have been obtained a comparison of results with those available in the literature shows an excellent agreement