free vibration and buckling analysis of clamped rectangular plates of variable thickness by the galerkin method abstract the problem of free vibration and buckling of isotropic clamped rectangular plates of variable thickness is investigated the fourth order differential equation is solved by using galerkin s variational method the thickness of the plate varies linearly along the x axis and this variation is taken to be symmetric with respect to the middle surface the parameters considered herein for buckling and free vibration behaviour of rectangular plates of variable thickness are the plate aspect ratios taper parameters and load ratios simplicity and quick convergence is the advantage of the method in comparison with other much more laborious numerical methods which require extensive computer facilities

vibrations of circular plates with variable profile galerkin s variational approach is invoked in analyzing transverse vibrations of circular plates where the thickness varies according to the functional relation h r h0 1 r a n where n is an integer the displacement function is approximated in terms of simple polynomials which identically satisfy the boundary conditions the two lowest frequency coefficients of axisymmetric modes are determined in the present paper for several combinations of the governing mechanical parameters

consistent distribution free k sample and independence tests for univariate random variables a popular approach for testing if two univariate random variables are statistically independent consists of partitioning the sample space into bins and evaluating a test statistic on the binned data the partition size matters and the optimal partition size is data dependent while for detecting simple relationships coarse partitions may be best for detecting complex relationships a great gain in power can be achieved by considering finer partitions we suggest novel consistent distribution free tests that are based on summation or maximization aggregation of scores over all partitions of a fixed size we show that our test statistics based on summation can serve as good estimators of the mutual information moreover we suggest regularized tests that aggregate over all partition sizes and prove those are consistent too we provide polynomial time algorithms which are critical for computing the suggested test statistics efficiently we show that the power of the regularized tests is excellent compared to existing tests and almost as powerful as the tests based on the optimal yet unknown in practice partition size in simulations as well as on a real data example

minimal realization of nonlinear systems described by input output difference equations we consider a general class of nonlinear discrete time systems described by their input output i o relationship we first present the necessary and sufficient conditions for existence of a local observable state space realization of the system and an explicit algorithm for computing it in cases where the i o map and its resulting realization are nonminimal we formulate an algorithm for extracting its minimal realization whenever possible the developed theory and algorithms are illustrated by means of several examples

measuring and testing dependence by correlation of distances distance correlation is a new measure of dependence between random vectors distance covariance and distance correlation are analogous to product moment covariance and correlation but unlike the classical definition of correlation distance correlation is zero only if the random vectors are independent the empirical distance dependence measures are based on certain euclidean distances between sample elements rather than sample moments yet have a compact representation analogous to the classical covariance and correlation asymptotic properties and applications in testing independence are discussed implementation of the test and monte carlo results are also presented

brief transfer equivalence and realization of nonlinear higher order input output difference equations two fundamental modelling problems in nonlinear discrete time control systems are studied using the language of differential forms the discrete time nonlinear single input single output systems to be studied are described by input output i o difference equations i e a high order difference equation relating the input the output and a finite number of their time shifts a new definition of equivalence is introduced which generalizes the notion of transfer equivalence well known for the linear case our definition is based upon the notion of an irreducible differential form of the system and was inspired by the analogous definition for continuous time systems the second problem to be addressed is the realization problem the i o difference equation is assumed to be in the irreducible form so that one can obtain an accessible and observable realization necessary and sufficient conditions are given for the existence of a local state space realization of the irreducible i o difference equation these conditions are formulated in terms of the integrability of certain subspaces of one forms classified according to their relative degree the sufficiency part of the proof gives a constructive procedure up to finding the integrating factors and integration of the set of one forms for obtaining a locally observable and accessible state space system if the system is not in the irreducible form one has first to apply the reduction procedure to transform the system into the irreducible form

k sample anderson darling tests abstract two k sample versions of an anderson darling rank statistic are proposed for testing the homogeneity of samples their asymptotic null distributions are derived for the continuous as well as the discrete case in the continuous case the asymptotic distributions coincide with the k 1 fold convolution of the asymptotic distribution for the anderson darling one sample statistic the quality of this large sample approximation is investigated for small samples through monte carlo simulation this is done for both versions of the statistic under various degrees of data rounding and sample size imbalances tables for carrying out these tests are provided and their usage in combining independent one or k sample anderson darling tests is pointed out the test statistics are essentially based on a doubly weighted sum of integrated squared differences between the empirical distribution functions of the individual samples and that of the pooled sample one weighting adjusts for the possibly different s

vibration of tapered thickness annular sector plates by spline element method abstract this paper deals with the determination of the vibrations of thin annular sector plates of tapered thickness by using the spline element method to demonstrate the accuracy of the present method several examples are solved and results are compared with those obtained by analytical methods and other numerical methods good accuracy is obtained frequencies of tapered annular sector plates with several boundary conditions are analyzed for the different sector angles and thickness parameters

on the realization of nonlinear discrete time systems abstract it is shown on the basis of a compact expression of the kernels of the discrete volterra series associated to a linear analytic discrete time system that the kernels satisfy a suitable property which enables their inductive characterization we also give a first result on the realization of a given family of functions by a linear analytic discrete time system with linear invertible drift term

adaptive estimation of a quadratic functional by model selection we consider the problem of estimating s 2 when s belongs to some separable hilbert space and one observes the gaussian process y t langles t rangle sigmal t for all t epsilon mathbb h where l is some gaussian isonormal process this framework allows us in particular to consider the classical gaussian sequence model for which mathbb h l 2 mathbb n and l t sum lambda geq1 t lambda varepsilon lambda where varepsilon lambda lambda geq1 is a sequence of i i d standard normal variables our approach consists in considering some at most countable families of finite dimensional linear subspaces of mathbb h the models and then using model selection via some conveniently penalized least squares criterion to build new estimators of s 2 we prove a general nonasymptotic risk bound which allows us to show that such penalized estimators are adaptive on a variety of collections of sets for the parameter s depending on the family of models from which they are built in particular in the context of the gaussian sequence model a convenient choice of the family of models allows defining estimators which are adaptive over collections of hyperrectangles ellipsoids l p bodies or besov bodies we take special care to describe the conditions under which the penalized estimator is efficient when the level of noise sigma tends to zero our construction is an alternative to the one by efroimovich and low for hyperrectangles and provides new results otherwise

a kernel two sample test we propose a framework for analyzing and comparing distributions which we use to construct statistical tests to determine if two samples are drawn from different distributions our test statistic is the largest difference in expectations over functions in the unit ball of a reproducing kernel hilbert space rkhs and is called the maximum mean discrepancy mmd we present two distribution free tests based on large deviation bounds for the mmd and a third test based on the asymptotic distribution of this statistic the mmd can be computed in quadratic time although efficient linear time approximations are available our statistic is an instance of an integral probability metric and various classical metrics on distributions are obtained when alternative function classes are used in place of an rkhs we apply our two sample tests to a variety of problems including attribute matching for databases using the hungarian marriage method where they perform strongly excellent performance is also obtained when comparing distributions over graphs for which these are the first such tests

axisymmetric vibrations of polar orthotropic mindlin annular plates of variable thickness abstract analysis and numerical results are presented for the axisymmetric vibrations of polar orthotropic annular plates with linear variation in thickness according to mindlin s shear theory of plates a chebyshev collocation technique has been employed to obtain the frequency equations for the transverse motion of such plates for three different boundary conditions frequencies mode shapes and moments for the first three modes of vibration have been computed for different plate parameters a comparison of frequencies with the corresponding values obtained by classical plate theory leads to some interesting conclusions

coverage adjusted entropy estimation summary data on neural coding have frequently been analyzed using information theoretic measures these formulations involve the fundamental and generally difficult statistical problem of estimating entropy we review briefly several methods that have been advanced to estimate entropy and highlight a method the coverage adjusted entropy estimator cae due to chao and shen that appeared recently in the environmental statistics literature this method begins with the elementary horvitz thompson estimator developed for sampling from a finite population and adjusts for the potential new species that have not yet been observed in the sample these become the new patterns or words in a spike train that have not yet been observed the adjustment is due to i j good and is called the good turing coverage estimate we provide a new empirical regularization derivation of the coverage adjusted probability estimator which shrinks the maximum likelihood estimate we prove that the cae is consistent and first order optimal with rate op 1 logn in the class of distributions with finite entropy variance and that within the class of distributions with finite qth moment of the log likelihood the good turing coverage estimate and the total probability of unobserved words converge at rate op 1 logn q we then provide a simulation study of the estimator with standard distributions and examples from neuronal data where observations are dependent the results show that with a minor modification the cae performs much better than the mle and is better than the best upper bound estimator due to paninski when the number of possible words m is unknown or infinite copyright q 2007 john wiley sons ltd

vibration analysis of arbitrarily shaped plates using beam characteristic orthogonal polynomials in the semi analytical finite strip method abstract a semi analytical finite strip method mapping arbitrarily shaped plates into a natural co ordinate plane using serendipity functions is presented the product of normalized beam characteristic orthogonal polynomials and hermitian polynomials form the displacement function for the strip in the natural co ordinate domain flexural free vibration analysis of various shaped plates is performed results show that as long as the plate is modelled by high enough degree mapping functions for the specific applications requested the flexural frequencies obtained are in excellent agreement with those found in the literature

nonparametric k sample tests via dynamic slicing k sample testing problems arise in many scientific applications and have attracted statisticians attention for many years we propose an omnibus nonparametric method based on an optimal discretization aka slicing of continuous random variables in the test the novelty of our approach lies in the inclusion of a term penalizing the number of slices i e the resolution of the discretization so as to regularize the corresponding likelihood ratio test statistic an efficient dynamic programming algorithm is developed to determine the optimal slicing scheme asymptotic and finite sample properties such as power and null distribution of the resulting test statistic are studied we compare the proposed testing method with some existing well known methods and demonstrate its statistical power through extensive simulation studies as well as a real data example a dynamic slicing method for the one sample testing problem is further developed and studied under the same framework supplementary materials inclu

3 d vibration analysis of annular sector plates using the chebyshev ritz method abstract the three dimensional free vibration of annular sector plates with various boundary conditions is studied by means of the chebyshev ritz method the analysis is based on the three dimensional small strain linear elasticity theory the product of chebyshev polynomials satisfying the necessary boundary conditions is selected as admissible functions in such a way that the governing eigenvalue equation can be conveniently derived through an optimization process by the ritz method the boundary functions guarantee the satisfaction of the geometric boundary conditions of the plates and the chebyshev polynomials provide the robustness for numerical calculation the present study provides a full vibration spectrum for the thick annular sector plates which cannot be given by the two dimensional 2 d theories such as the mindlin theory comprehensive numerical results with high accuracy are systematically produced which can be used as benchmark to evaluate other numerical methods the effect of radius ratio thickness ratio and sector angle on natural frequencies of the plates with a sector angle from 120 to 360 is discussed in detail the three dimensional vibration solutions for plates with a re entrant sector angle larger than 180 and shallow helicoidal shells sector angle larger than 360 with a small helix angle are presented for the first time

testing for independence in arbitrary distributions summary statistics are proposed for testing the hypothesis that arbitrary random variables are mutually independent the tests are consistent and well behaved for any marginal distributions they can be used for example for contingency tables which are sparse or whose dimension depends on the sample size as well as for mixed data no regularity conditions data jittering or binning mechanisms are required the statistics are rank based functionals of cramer von mises type whose asymptotic behaviour derives from the empirical multilinear copula process approximate p values are computed using a wild bootstrap the procedures are simple to implement and computationally efficient and maintain their level well in moderate to large samples simulations suggest that the tests are robust with respect to the number of ties in the data can easily detect a broad range of alternatives and outperform existing procedures in many settings additional insight into their performance is provided through asymptotic local power calculations under contiguous alternatives the procedures are illustrated on traumatic brain injury data

free vibration of annular sector plates with edges possessing different degrees of rotational restraint abstract results for the natural frequencies of annular sector plates possessing different degrees of elastic restraint along the edges are presented the analysis is based on a numerical method developed by the author the functions in the circumferential direction satisfying the boundary conditions along the radial edges which are required in the analysis are indicated to the best of the author s knowledge no previous results exist for such plates

free vibration of a cantilever annular sector plate with curved radial edges and varying thickness abstract the free vibration of a cantilever annular sector plate with curved radial edges and varying thickness is analyzed by the ritz method for this purpose the plate is transformed into a regular sector plate with unit outer radius by a transformation of variables the transverse deflection of the transformed plate is expressed in a power series the dynamical energies of the plate are evaluated and the frequency equation of the plate is derived by the conditions for a stationary value of the lagrangian functional this method is applied to annular sector plates with symmetrically or unsymmetrically curved radial edges and also with varying thickness the natural frequencies and the mode shapes are calculated numerically and the effects of varying thickness on the vibration are studied

measuring dependence powerfully and equitably given a high dimensional data set we often wish to find the strongest relationships within it a common strategy is to evaluate a measure of dependence on every variable pair and retain the highest scoring pairs for follow up this strategy works well if the statistic used a has good power to detect non trivial relationships and b is equitable meaning that for some measure of noise it assigns similar scores to equally noisy relationships regardless of relationship type e g linear exponential periodic in this paper we define and theoretically characterize two new statistics that together yield an efficient approach for obtaining both power and equitability to do this we first introduce a new population measure of dependence and show three equivalent ways that it can be viewed including as a canonical smoothing of mutual information we then introduce an efficiently computable consistent estimator of our population measure of dependence and we empirically establish its equitability on a large class of noisy functional relationships this new statistic has better bias variance properties and better runtime complexity than a previous heuristic approach next we derive a second related statistic whose computation is a trivial side product of our algorithm and whose goal is powerful independence testing rather than equitability we prove that this statistic yields a consistent independence test and show in simulations that the test has good power against independence taken together our results suggest that these two statistics are a valuable pair of tools for exploratory data analysis

transverse vibrations of a trapezoidal cantilever plate of variable thickness n atural frequencies of a trapezoidal cantilever plate of variable thickness which model an aircraft wing structure approximately are determined using energy techniques characteristic orthogonal polynomials in two variables are constructed to describe the structural deflections which are used in the rayleigh ritz method to obtain the natural frequencies the fundamental natural frequencies for different parameter values are also obtained using a deflection function containing an optimized exponent the first technique can be used to obtain the natural frequencies and corresponding mode shapes for the preliminary design of aircraft wing structures

application of the spline element method to analyze vibration of annular sector plates abstract this paper deals with the vibrations of isotropic annular sector plates with arbitrary boundary conditions using the spline element method to demonstrate the accuracy of the methods several examples are solved and results are compared with those obtained by analytical methods and by other numerical methods good accuracy is obtained frequencies of annular sector plates with free edges and with point supports are presented

dynamic realizations of sufficient sequences let u 1 u 2 cdots be a sequence of observed random variables and t 1 u 1 t 2 u 1 u 2 cdots be a corresponding sequence of sufficient statistics a sufficient sequence under certain regularity conditions the sufficient sequence defines the input output map of a time varying discrete time nonlinear system this system provides a recursive way of updating the sufficient statistic as new observations are made conditions are provided assuring that such a system evolves in a state space of minimal dimension several examples are provided to illustrate how this notion of dimensional minimality is related to other properties of sufficient sequences the results can be used to verify the form of the minimum dimension discrete time nonlinear filter associated with the autoregressive parameter estimation problem

a new coefficient of correlation abstract is it possible to define a coefficient of correlation which is a as simple as the classical coefficients like pearson s correlation or spearman s correlation and yet b consistently es

on the free transverse vibration of annular and circular thin sectorial plates subject to certain complicating effects abstract the rayleigh ritz method with orthogonally generated polynomials as admissible functions is used to obtain an eigenvalue equation for the free transverse vibration of thin annular sectorial plates circular sectorial plates are treated with this equation by permitting the inner radius to become negligibly small the plates may be of isotropic or polar orthotropic material of uniform or radially and or circumferentially varying thickness and may include interior circumferential or radial line supports numerical values for the natural frequency parameters of several different plates are presented and compared with previously published values where available

differential quadrature method for vibration analysis of shear deformable annular sector plates this paper presents differential quadrature solutions for free vibration analysis of moderately thick annular sector plates based on the mindlin first order shear deformation theory numerical characteristics of the differential quadrature method are illustrated through solving selected annular sector plates with different boundary conditions relative thickness ratios inner to outer radius ratios and various sector angles parametric studies in terms of the vibration frequency parameters are thoroughly investigated

free vibrations of rectangular plates of exponentially varying thickness and with a free edge abstract transverse vibrations of the structural system described in the title are analyzed by using classical plate theory and employing two different methodologies the recently developed optimized kantorovich approach and a finite element algorithmic procedure it is shown that the fundamental frequency coefficients obtained by using both techniques for a rather wide variation of the governing geometric parameters are in very good agreement lower frequency coefficients of the plate system determined by means of the finite element method are also presented

free vibration analysis of mindlin sector plates numerical solutions by differential quadrature method abstract in this paper the free vibration analysis of moderately thick sector plates based on mindlin s first order shear deformation theory is examined the solutions to this problem are determined using the differential quadrature dq method for numerical evaluation the dq formulations for free vibration of the mindlin sector plates in two dimensional polar co ordinate system are derived to demonstrate the accuracy of the dq method convergence and comparison studies are carried out in parametric study the first eight frequency parameters are computed for sector plates with different boundary conditions relative thickness ratios and sector angles 30 360 the effects of sector angle and relative thickness ratio on the frequency parameters are discussed

adapting to unknown smoothness via wavelet shrinkage abstract we attempt to recover a function of unknown smoothness from noisy sampled data we introduce a procedure sureshrink that suppresses noise by thresholding the empirical wavelet coefficients the thresholding is adaptive a threshold level is assigned to each dyadic resolution level by the principle of minimizing the stein unbiased estimate of risk sure for threshold estimates the computational effort of the overall procedure is order n log n as a function of the sample size n sureshrink is smoothness adaptive if the unknown function contains jumps then the reconstruction essentially does also if the unknown function has a smooth piece then the reconstruction is essentially as smooth as the mother wavelet will allow the procedure is in a sense optimally smoothness adaptive it is near minimax simultaneously over a whole interval of the besov scale the size of this interval depends on the choice of mother wavelet we know from a previous paper by the authors that traditional smoot

fisher exact scanning for dependency abstractwe introduce a method called fisher exact scanning fes for testing and identifying variable dependency that generalizes fisher s exact test on 2 2 contingency tables to r c contingency tables and continuous sample spaces fes proceeds through scanning over the sample space using windows in the form of 2 2 tables of various sizes and on each window completing a fisher s exact test based on a factorization of fisher s multivariate hypergeometric mhg likelihood into the product of the univariate hypergeometric likelihoods we show that there exists a coarse to fine sequential generative representation for the mhg model in the form of a bayesian network which in turn implies the mutual independence up to deviation due to discreteness among the fisher s exact tests completed under fes this allows an exact characterization of the joint null distribution of the p values and gives rise to an effective inference recipe through simple multiple testing procedures such as sidak and bonferroni

a consistent multivariate test of association based on ranks of distances summary we consider the problem of detecting associations between random vectors of any dimension few tests of independence exist that are consistent against all dependent alternatives we propose a powerful test that is applicable in all dimensions and consistent against all alternatives the test has a simple form is easy to implement and has good power

equitability mutual information and the maximal information coefficient how should one quantify the strength of association between two random variables without bias for relationships of a specific form despite its conceptual simplicity this notion of statistical equitability has yet to receive a definitive mathematical formalization here we argue that equitability is properly formalized by a self consistency condition closely related to data processing inequality mutual information a fundamental quantity in information theory is shown to satisfy this equitability criterion these findings are at odds with the recent work of reshef et al reshef dn et al 2011 science 334 6062 1518 1524 which proposed an alternative definition of equitability and introduced a new statistic the maximal information coefficient mic said to satisfy equitability in contradistinction to mutual information these conclusions however were supported only with limited simulation evidence not with mathematical arguments upon revisiting these claims we prove that the mathematical definition of equitability proposed by reshef et al cannot be satisfied by any nontrivial dependence measure we also identify artifacts in the reported simulation evidence when these artifacts are removed estimates of mutual information are found to be more equitable than estimates of mic mutual information is also observed to have consistently higher statistical power than mic we conclude that estimating mutual information provides a natural and often practical way to equitably quantify statistical associations in large datasets

numerical experiments on the determination of natural frequencies of transverse vibrations of rectangular plates of non uniform thickness abstract a comparison of natural frequencies of transverse vibration of thin rectangular plates of non uniform thickness with different combinations of boundary conditions is presented in this paper as obtained by using the following methodologies 1 the rayleigh ritz method with characteristic orthogonal polynomial shape functions 2 the rayleigh ritz method with a shape function which includes two exponents that are to be determined by minimizing the fundamental frequency coefficient 3 the optimized kantorovich method which has been proposed rather recently 4 the finite element method the results are presented in tabular form and discussed

method for the global analysis of non linear parametrized systems a method for the global analysis of non linear systems is presented which provides a framework for the analysis of both continuous and discrete time non linear systems for the diverse range of model types by extending a numerical approach to enable the analysis of non linear parametrized non linear systems a global perspective is achieved that is difficult to obtain using analytical methods alone simple examples are used to illustrate how the method characterizes the system stability at the same time as detecting typical qualitative bifurcation phenomena a non linear feedback system is analysed in order to show how the approach provides both qualitative and quantitative information over a defined region of the system parameter space the method proves to be a powerful tool which can be used to probe the non linear characteristics of a system

controlling the false discovery rate a practical and powerful approach to multiple testing summary the common approach to the multiplicity problem calls for controlling the familywise error rate fwer this approach though has faults and we point out a few a different approach to problems of multiple significance testing is presented it calls for controlling the expected proportion of falsely rejected hypotheses the false discovery rate this error rate is equivalent to the fwer when all hypotheses are true but is smaller otherwise therefore in problems where the control of the false discovery rate rather than that of the fwer is desired there is potential for a gain in power a simple sequential bonferronitype procedure is proved to control the false discovery rate for independent test statistics and a simulation study shows that the gain in power is substantial the use of the new procedure and the appropriateness of the criterion are illustrated with examples

estimation of entropy and mutual information we present some new results on the nonparametric estimation of entropy and mutual information first we use an exact local expansion of the entropy function to prove almost sure consistency and central limit theorems for three of the most commonly used discretized information estimators the setup is related to grenander s method of sieves and places no assumptions on the underlying probability measure generating the data second we prove a converse to these consistency theorems demonstrating that a misapplication of the most common estimation techniques leads to an arbitrarily poor estimate of the true information even given unlimited data this inconsistency theorem leads to an analytical approximation of the bias valid in surprisingly small sample regimes and more accurate than the usual 1 n formula of miller and madow over a large region of parameter space the two most practical implications of these results are negative 1 information estimates in a certain data regime are likely contaminated by bias even if bias corrected estimators are used and 2 confidence intervals calculated by standard techniques drastically underestimate the error of the most common estimation methods finally we note a very useful connection between the bias of entropy estimators and a certain polynomial approximation problem by casting bias calculation problems in this approximation theory framework we obtain the best possible generalization of known asymptotic bias results more interesting this framework leads to an estimator with some nice properties the estimator comes equipped with rigorous bounds on the maximum error over all possible underlying probability distributions and this maximum error turns out to be surprisingly small we demonstrate the application of this new estimator on both real and simulated data

equivalence of distance based and rkhs based statistics in hypothesis testing we provide a unifying framework linking two classes of statistics used in two sample and independence testing on the one hand the energy distances and distance covariances from the statistics literature on the other maximum mean discrepancies mmd that is distances between embeddings of distributions to reproducing kernel hilbert spaces rkhs as established in machine learning in the case where the energy distance is computed with a semimetric of negative type a positive definite kernel termed distance kernel may be defined such that the mmd corresponds exactly to the energy distance conversely for any positive definite kernel we can interpret the mmd as energy distance with respect to some negative type semimetric this equivalence readily extends to distance covariance using kernels on the product space we determine the class of probability distributions for which the test statistics are consistent against all alternatives finally we investigate the performance of the family of distance kernels in two sample and independence tests we show in particular that the energy distance most commonly employed in statistics is just one member of a parametric family of kernels and that other choices from this family can yield more powerful tests

consistent nonparametric tests of independence three simple and explicit procedures for testing the independence of two multi dimensional random variables are described two of the associated test statistics l1 log likelihood are defined when the empirical distribution of the variables is restricted to finite partitions a third test statistic is defined as a kernel based independence measure two kinds of tests are provided distribution free strong consistent tests are derived on the basis of large deviation bounds on the test statistics these tests make almost surely no type i or type ii error after a random sample size asymptotically level tests are obtained from the limiting distribution of the test statistics for the latter tests the type i error converges to a fixed non zero value and the type ii error drops to zero for increasing sample size all tests reject the null hypothesis of independence if the test statistics become large the performance of the tests is evaluated experimentally on benchmark data

axisymmetric vibrations of polar orthotropic annular plates of variable thickness in this study of the free axisymmetric vibrations of polar orthotropic annular plates of linearly varying thickness on the basis of the classical theory of plates the chebyshev collocation technique has been employed to solve the differential equation governing the transverse motion of such plates frequencies mode shapes and moments have been computed for three different boundary conditions for various values of the rigidity ratios the radii ratio and the taper parameter for the first two modes of vibration the results for isotropic annular plates of uniform and non uniform thickness show good agreement with those available in the literature