the convergence of spline collocation for strongly elliptic equations on curves most boundary element methods for two dimensional boundary value problems are based on point collocation on the boundary and the use of splines as trial functions here we present a unified asymptotic error analysis for even as well as for odd degree splines subordinate to uniform or smoothly graded meshes and prove asymptotic convergence of optimal order the equations are collocated at the breakpoints for odd degree and the internodal midpoints for even degree splines the crucial assumption for the generalized boundary integral and integro differential operators is strong ellipticity our analysis is based on simple fourier expansions in particular we extend results by j saranen and w l wendland from constant to variable coefficient equations our results include the first convergence proof of midpoint collocation with piecewise constant functions i e the panel method for solving systems of cauchy singular integral equations

numerical experiments on vibrating rectangular plates with discontinuously varying cross sections utilisation des methodes de rayleigh ritz et des elements finis etude de la plaque encastree et simplement supportee

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

a bie method for a nonlinear bvp abstract a nonlinear boundary value problem bvp governed by laplace s equation with a nonlinear boundary condition is considered this paper is concerned with the numerical solvability of a nonlinear boundary integral equation bie obtained by reformulating the nonlinear bvp we give a simple alternative to the standard collocation method for the nonlinear bie which requires less computational effort the method is a bie analogue of the product approximation method used for solving some nonlinear problems by the finite element method we obtain superconvergence of approximate solutions introduced in this paper

free vibration of a system of two elastically connected rectangular plates the free vibration problem of a system of two rectangular plates connected by a non homogeneous elastic layer is considered an integral formulation of the problem by using properties of green s functions is achieved and by application of a quadrature method to the integral equation the frequency equation of the combined system is obtained the comparison of an exact solution with the numerical results obtained by using the presented method for a system of two identical plates is given the numerical investigations have shown the effect of the area size as well as the stiffness of an elastic layer connecting the plates on the vibration frequencies of the combined systems

the flexibility function approach to vibration analysis of rectangular plates with arbitrary multiple point supports on the edges abstract the development and application of a comprehensive analytical technique for the simulation of point supports in the vibration analysis of plates have been presented in some recent studies the approach was based on simulating a point support on free edges as a zero of a flexibility function representing a fictitious elastic restraint distribution over the free edge in these earlier studies mainly a single point support on a free edge was considered in the present study this technique namely the flexibility function approach is extended to a more general class of problems of free vibrations of multiply point supported plates the versatility and the ability of this approach in simulating arbitrarily located multiple point supports on free edges is demonstrated by considering a rectangular plate with simple supports on two opposite edges and arbitrarily located multiple point supports on the other two edges which are otherwise free numerical results in the form of frequency tables and mode shape plots are presented for wide variety of problems and are compared with those obtained by using the impulse function approach based on epresenting the reactions at the point supports as a fourier series expansion of the impulse function this comparative study while presenting results from these two approaches for the first time also brings out the superiority of the flexibility function approach

simulation of classical edge conditions by finite elastic restraints in the vibration analysis of plates abstract the simulation of classical edge conditions by finite values of elastic edge restraints is a problem frequently encountered in experimental vibration analysis the support fixtures utilized in such studies always introduce undesired flexibilities or stiffnesses causing the support conditions to deviate from ideal classical ones there are also some analytical studies in which finite values of flexibilities are used in conjunction with a specific distribution over the edge to represent classically supported edges with point supports thus one may encounter in the simulation of classical edge conditions a small but finite flexibility where it is required to be zero or a large but finite flexibility where it is required to be infinity the present study attempts to answer the question how large can a small value of flexibility be and yet represent zero flexibility and how small can a large value be and yet represent infinite flexibility in the simulation of classical boundary conditions the effects of finite values and distributions of the elastic edge restraint on the natural frequencies of rectangular plates are examined and guidelines are provided in terms of their ranges and limits for their use in representing classical edge conditions based on an analysis of the errors in the edge forces and moments the values of the flexibility coefficients suitable for stress analysis are also identified

reweighting to achieve elliptically contoured covariates in regression abstract we investigate a method of constructing weights to induce elliptically contoured covariates in regression analyses much recent work in regression has identified various data analytic and model robustness advantages associated with such covariates in particular new estimation methods like sir sirii save and phd have been built around the assumption of elliptically contoured covariates finite samples of regression covariates may deviate from this ideal in practice and the method developed here termed voronoi weighting can be used to induce elliptical symmetry in such samples in a number of examples we show that reweighting cases by the voronoi method can substantially enhance various procedures for covariates that deviate from elliptical symmetry we show that voronoi weighting in conjunction with some trimming via the minimum volume ellipsoid method can be effective

on the boundary element method for the signorini problem of the laplacian for the laplace equation with signorini boundary conditions two equivalent boundary variational inequality formulations are deduced we investigate the discretization by a boundary element galerkin method and obtain quasi optimal asymptotic error estimates in the underlying sobolev spaces an algorithm based on the decomposition coordination method is used to solve the discretized problems numerical examples confirm the predicted rate of convergence

transverse vibrations of the elastically connected rectangular double membrane compound system abstract the free and forced vibrations of a system of two rectangular membranes attached together by a winkler elastic layer are studied analytically the motion of the system is described by two non homogeneous partial differential equations the solutions of the free vibrations are obtained by the bernoulli fourier method solving the boundary value problem the natural frequencies and the mode shape functions are found the initial value problem is also solved the free vibrations of the double membrane system are realised by synchronous and asynchronous deflections the forced vibrations of membranes subjected to arbitrarily distributed continuous loads are determined by using the classical method of the expansion in a series of the normal modes of vibrations discussing the vibrations caused by the harmonic exciting forces it is shown that the dynamic absorption phenomenon appears therefore the double membrane system can be used as a dynamic vibration absorber as a numerical example the vibrations of the system consisting of two identical membranes subjected to harmonic uniform distributed load are treated in detail

dynamic response of a double euler bernoulli beam due to a moving constant load in this paper the dynamic response of a double beam system traversed by a constant moving load is studied the system consists of two elastic homogeneous isotropic euler bernoulli beams the two simply supported prismatic beams are identical parallel one upon the other and connected continuously by a viscoelastic layer the dynamic deflections of both beams are given in analytical closed forms the effects of the moving speed of the load and the damping and the elasticity of the viscoelastic layer on the dynamic responses of the beams are investigated in detail also several plots of the deflections of the beams are given and discussed for different values of speed parameter damping ratio and stiffness parameter furthermore the force transmitted between the beams is determined and the effects of the system parameters on this force are studied plots of the maximum responses of the beams are presented

a new approach for the continuum representation of point supports in the vibration analysis of beams abstract the formulation of a new approach for the representation of point supports in the analysis of plates and its application to various problems of point supported plates was presented in earlier studies the application of this approach to the vibration analysis of beams with intermediate point supports is presented in this paper this approach is based on the use of a flexibility function representing the distribution of a fictitious elastic foundation of the beam which is such that it has a zero value at the point support location but assumes large values resulting in negligible restraint over the rest of the span of the beam the application of this approach is demonstrated by considering the free vibration of a simply supported beam with point supports the results obtained by using this approach are compared with those obtained by using the method based on the representation of the concentrated reaction at the point support location by a fourier series expansion of the impulse function the fictitious foundation approach for the simulation of intermediate point supports presented in this paper provides a method of absorbing the discrete discontinuities in the force field in the interior of the beam and obtaining a continuum representation in a single domain namely that of a simply supported beam

comparison of model misspecification diagnostics using residuals from least mean of squares and least median of squares fits abstract this article explores model misspecification diagnostics based on least squares and least median of squares fits it shows that in some circumstances least median of squares methods or any other estimator with the exact fit property fail to reveal an incorrectly specified mean function but least squares methods succeed

a new approach for the representation of a point support in the analysis of plates abstract a new approach for the representation of a point support in the analysis of plates is presented it is based on the use of a flexibility function representing the distribution of a fictitious elastic restraint over the boundary which is such that it has a zero value at the point support location but assumes large values resulting in negligible restraint over the free boundary the application of this flexibility function approach is demonstrated by considering the free vibrations of rectangular plates with two opposite edges simply supported and mid point supports on the other two edges which are otherwise free the results obtained by using this approach are compared with those obtained by using the method based on the representation of the concentrated force at the point support by a fourier series expansion of the impulse function it is shown that the flexibility function approach as compared to the impulse function approach gives a slightly faster convergence and yields results which are generally very accurate it is also shown that the flexibility function approach has the scope to simulate practical point support conditions in which the support reaction is spread over a definite band

free transverse vibrations of an elastically connected rectangular plate membrane complex system abstract this paper theoretically analyzes undamped free transverse vibrations of an elastically connected rectangular plate membrane system solutions of the problem are formulated by using the navier method natural frequencies of the system in the form of two infinite sequences are determined normal mode shapes of vibration expressing two kinds of vibration synchronous and asynchronous are presented the initial value problem is also solved in a numerical example the effect of membrane tension on the natural frequencies of this mixed system is discussed

the use and interpretation of residuals based on robust estimation abstract residual plots and diagnostic techniques are important tools for examining the fit of a regression model in the case of least squares fits plots of residuals provide a visual assessment of the adequacy of various aspects of the fitted model an important question is whether plots of robust residuals can be interpreted in the same manner as their least squares counterparts this article addresses this problem for two popular classes of robust estimates m estimates and gm estimates of the mallows and schweppe types first order properties of the residuals and fitted values are derived under correct and misspecified models these properties are insightful on the general interpretability of robust residual plots and on their ability to detect curvature in misspecified models the results of a simulation study consisting of tests for randomness and curvature in residual plots supports these theoretical properties standardization of robust residuals is also presented

solution of nonlinear elliptic equations with boundary singularities by an integral equation method a boundary integral equation bie formulation is presented for the numerical solution of certain two dimensional nonlinear elliptic equations subject to nonlinear boundary conditions by applying the kirchoff transformation all nonlinear aspects are first transferred to the boundary of the solution domain then the accurate solution of problems in which there are boundary singularities is demonstrated by including the analytic nature of the singular solution in only those regions nearest the singularity because of this only a minor modification of the classical nonlinear bie is required and this results in a substantial improvement in the accuracy of the numerical results throughout the entire solution domain

on the boundary element method for some nonlinear boundary value problems here we analyse the boundary element galerkin method for two dimensional nonlinear boundary value problems governed by the laplacian in an interior or exterior domain and by highly nonlinear boundary conditions the underlying boundary integral operator here can be decomposed into the sum of a monotoneous hammerstein operator and a compact mapping we show stability and convergence by using leray schauder fixed point arguments due to petryshyn and necas

transverse vibrations of elastically connected double string complex system part i free vibrations this paper analyzes the forced transverse vibrations of an elastically connected double string complex continuous system the general solutions of forced vibrations of strings subjected to arbitrarily distributed continuous loads are found by using the method of expansion in a series of the mode shape functions different cases of exciting loadings are analyzed the action of stationary harmonic loads and moving concentrated forces is considered vibrations caused by the harmonic exciting forces are discussed and conditions of resonance and dynamic vibration absorption are formulated thus the string type dynamic absorber can be used to suppress the excessive vibrations of corresponding string systems the dynamic string type damper is a new concept of a continuous dynamic vibration absorber cdva it is shown that a corresponding two degree of freedom discrete system is an analogue of an elastically connected double string complex system theoretical analysis is illustrated by a numerical example

regression diagnostics for rank based methods abstract residual plots and diagnostic techniques have become important tools in examining the least squares fit of a linear model in this article we explore the properties of the residuals from a rank based fit of the model we present diagnostic techniques that detect outlying cases and cases that have an influential effect on the rank based fit we show that the residuals from this fit can be used to detect curvature not accounted for by the fitted model furthermore our diagnostic techniques inherit the excellent efficiency properties of the rank based fit over a wide class of error distributions including asymmetric distributions we illustrate these techniques with several examples

a new approach for numerical modal analysis using the element free method a novel approach in analysing the vibration of elastic body systems is presented and discussed in this paper this method uses a meshless spatial approximation based only on nodes which constitutes an advantage over the finite element method as it is applicable to an elastic body with arbitrary shape it also has advantages over the classical rayleigh ritz method and its extensions the paper is organized as follows in section 2 hamilton s principle is used for obtaining the equations of motion for a three dimensonal simply connected elastic body in section 3 the development of weighted base functions for the moving least squares interpolant is described in section 4 the mass and stiffness matrices are derived using the previous results in section 5 a system synthesis description is given in which we also develop the approach used for integrating the boundary conditions finally in section 6 the theoretical results are validated by case studies chosen to highlight various features of the approach including optimization of the shape function parameters the particle method has already been used for structural dynamics liu et al international journal for numerical methods in engineering 1995 38 1655 1679 but for free vibration of beams and plates to the authors knowledge this paper is the first application of the element free method to modal analysis copyright c 1999 john wiley sons ltd

forced transverse vibrations of an elastically connected complex rectangular simply supported double plate system abstract the paper deals with forced transverse vibrations of an elastically connected rectangular double plate system this complex continuous system can represent a certain simplified model of a three layered structure consisting of two parallel thin plates separated by an elastic massless layer of a winkler type undamped motion of the system excited by arbitrarily distributed continuous loadings subjected transversely to both plates are governed by a linear set of two coupled non homogeneous partial differential equations based on the kirchhoff love plate theory the forced vibration problem is solved generally by the application of the modal expansion method in the case of simply supported boundary conditions for plates on the basis of general solutions obtained three particular cases of the action of exciting stationary harmonic loads are considered an analysis of harmonic responses of the system makes it possible to determine conditions of resonance and dynamic vibration absorption a numerical example is given to illustrate the theory presented

on the asymptotic convergence of collocation methods we prove quasioptimal and optimal order estimates in various sobolev norms for the approximation of linear strongly elliptic pseudodifferential equations in one independent variable by the method of nodal collocation by odd degree polynomial splines the analysis pertains in particular to many of the boundary element methods used for numerical computation in engineering applications equations to which the analysis is applied include fredholm integral equations of the second kind certain first kind fredholm equations singular integral equations involving cauchy kernels a variety of integro differential equations and two point boundary value problems for ordinary differential equations the error analysis is based on an equivalence which we establish between the collocation methods and certain nonstandard galerkin methods we compare the collocation method with a standard galerkin method using splines of the same degree showing that the galerkin method is quasioptimal in a sobolev space of lower index and furnishes optimal order approximation for a range of sobolev indices containing and extending below that for the collocation method and so the standard galerkin method achieves higher rates of convergence

projection methods for a class of hammerstein equations here some new convergence results for a class of hammerstein equations are given a particular example appearing in the solution of a steady state heat conduction problem with a nonlinear boundary condition was recently studied by ruotsalainen and wendland numer math 53 1988 pp 299 314 using the galerkin approximation and by ruotsalainen and saranen jcam 28 1989 pp 339 348 using collocation this paper improves the convergence results in both of these works the general result also applies to some time dependent nonlinear model problems

a meshless galerkin scheme for the approximate solution of nonlinear logarithmic boundary integral equations utilizing radial basis functions abstract this paper presents a computational scheme to solve nonlinear logarithmic singular boundary integral equations these types of integral equations arise from boundary value problems of laplace s equations with nonlinear robin boundary conditions the discrete galerkin method together with the inverse multiquadric radial basis functions established on scattered points is utilized to approximate the solution the discrete galerkin method for solving boundary integral equations results from the numerical integration of all integrals in the method the proposed scheme uses a special accurate quadrature formula via the nonuniform gauss legendre integration rule to compute logarithm like singular integrals appeared in the scheme since the numerical method developed in the current paper does not require any mesh generations on the boundary of the domain it is meshless and does not depend to the domain form we also investigate the error analysis of the proposed method illustrative examples show the reliability and efficiency of the new scheme and confirm the theoretical error estimates

on the interpretation of regression plots abstract a framework is developed for the interpretation of regression plots including plots of the response against selected covariates residual plots added variable plots and detrended added variable plots it is shown that many of the common interpretations associated with these plots can be misleading the framework also allows for the generalization of standard plots and the development of new plotting paradigms a paradigm for graphical exploration of regression problems is sketched

free transverse vibrations of elastically connected simply supported double beam complex system abstract in this paper the free vibration analysis of two parallel simply supported beams continuously joined by a winkler elastic layer is presented the motion of the system is described by a homogeneous set of two partial differential equations which is solved by using the classical bernoulli fourier method the natural frequencies of the system are determined the initial value problem is considered to find the final form of the free vibrations the free vibrations of an elastically connected double beam complex system are realized by synchronous and asynchronous deflections the presented theoretical analysis is illustrated by a numerical example in which the effect of physical parameters characterizing the vibrating system on the natural frequencies is investigated

robust nonparametric methods the terms nonparametric statistics and distributionfree methods have historically referred to a collection of statistical tests whose null distributions do not depend on the underlying distribution of the data the area has been expanded to include estimates and confidence intervals derived from the tests and includes asymptotically distribution free tests for complex models as well it is now generally recognized that these statistical methods are highly efficient over large sets of possible models and are robust as well this was not always the case the earliest work was by hotelling and pabst in 1936 references to works in this paragraph can be found in the books cited in the next paragraph on rank correlation and by friedman in 1937 on rank tests in a two way design followed in 1945 with the introduction of the signed rank and rank sum tests by wilcoxon in 1947 mann and whitney extended the ideas of wilcoxon all of these rank tests were considered quick and dirty but not competitive with the presumably more efficient t tests this perspective was about to change in 1948 pitman developed efficiency concepts in a set of lecture notes that although never published were widely disseminated during the 1950s and 1960s lehmann working with hodges and with his students at berkeley showed that rank tests are surprisingly efficient and robust in fact the wilcoxon rank tests are essentially efficient at the normal model and can be much more efficient than least squares methods when the underlying distribution of the data has heavy tails in the early 1960s hodges and lehmann derived estimates and confidence intervals from rank test statistics and also introduced aligned rank tests for use in the regression model in 1967 hajek and sid published their seminal book on the theory of rank tests it is impossible to mention all of the contributions to this early development hence we cite several key mono

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

free transverse vibrations of an elastically connected rectangular simply supported double plate complex system abstract in this paper the free transverse vibrations of a system of two rectangular simply supported thin plates connected by a homogeneous winkler elastic layer are investigated analytically the small vibrations of the system are described by a set of two partial differential equations based on the kirchhoff love plate theory next the homogeneous equations of motion are solved by using the classical navier method the natural frequencies of the system in the form of two infinite sequences are determined and the corresponding mode shapes of vibration are shown as a consequence an elastically connected double plate complex system executes two kinds of the free vibrations synchronous and asynchronous the initial value problem is then considered to find the final form of the free vibrations the theoretical analysis presented is illustrated by a numerical example in which the free vibrations of a system of two identical plates are discussed in detail

free vibrations of elastically restrained non uniform plates abstract a simple and efficient method is presented to examine the levy type solutions for the free vibration of elastically restrained rectangular plates resting on a non uniform elastic winkler foundation under the action of constant in plane forces both the thickness of the plate and stiffness of the elastic foundation are uniform along one axis and variable along the other axis the frequency equation is derived and concisely expressed in terms of the four fundamental solutions of the governing characteristic differential equation if the closed form fundamental solutions of the system are not available then approximate fundamental solutions can be obtained through a numerical algorithm which is shown to be efficient convenient and accurate the results are compared with those in the literature finally the influence of the elastically restrained boundary conditions on the natural frequencies is investigated

free transverse vibrations of an elastically connected complex beam string system abstract the present work is devoted to theoretical vibration analysis of a complex mixed continuous system undamped free transverse vibrations of an elastically connected beam string system are considered solutions of the problem are formulated by using the modal expansion method two infinite sequences of the natural frequencies corresponding to two possible kinds of vibration motions synchronous and asynchronous are determined in a numerical example illustrating the theory presented the effect of string tension force on the natural frequencies of the system is investigated in detail

using the wpg method for solving integral equations of the second kind abstract in this paper we use the wavelet petrov galerkin wpg method based on discontinuous orthogonal multiwavelets for solving fredholm integral equations of the second kind that yields linear system that the condition number of its coefficient matrix is bounded and for showing efficiency of method we use numerical examples

the use of flexibility functions with negative domains in the vibration analysis of asymmetrically point supported rectangular plates a new approach for the simulation of point supports as zeroes of a flexibility function representing a fictitious positive elastic restraint distribution over the boundary was presented in an earlier study concerned mainly with rectangular plates with symmetric point supports this paper is concerned with the extension of this flexibility function approach to more general cases of asymmetrically point supported rectangular plates which have simple supports on two opposite edges first it is shown that sufficiently large negative values of the flexibility of the elastic restraint can simulate the free edge conditions accurately based on this and with use of flexibility functions which cross over from positive to negative values or vice versa over the plate boundary it is shown that zeroes of the function at arbitrary point support locations can be easily obtained extensive numerical results are obtained for various combinations of boundary conditions plate aspect ratios and types and locations of point supports the results show that the flexibility function approach can handle with ease arbitrary locations of point supports by using flexibility functions having both positive and negative domains a comparative study of this approach with the impulse function approach based on the representation of the reaction at the point support as a fourier series expansion of the impulse function is also presented to bring out the superiority of the flexibility function approach

models prior information and bayesian analysis abstract formulation of models for observations and prior densities for their parameters is an important activity in many sciences in the present paper after a discussion of this area of activity entropy based methods are employed to derive many central econometric and statistical models and noninformative and informative prior densities for their parameters in an explicit reproducible manner examples are provided to illustrate the general procedures in particular maxent is employed to produce linear and nonlinear regression and autoregression models hierarchical models time varying parameter models etc then maximal data information prior mdip densities for hyperparameters common parameters in different likelihood functions multinomial parameters etc are derived also the mdip approach is utilized to produce prior odds for alternative hypotheses or models

free vibrations of elastically connected stretched beams abstract a general theory for the determination of natural frequencies and mode shapes for a set of elastically connected axially loaded euler bernoulli beams is developed a normal mode solution is applied to a set of non dimensional coupled partial differential equations the natural frequencies are the eigenvalues of a matrix of differential operators the matrix operator is shown to be self adjoint leading to an orthogonality condition for the mode shapes in the special case of identical beams it is shown that the natural frequencies are organized into sets of intramodal frequencies in which each mode shape is a product of a spatial mode and a discrete mode an exact solution is available for the general case however the natural frequencies and mode shapes are then determined using a complicated numerical method a rayleigh ritz method using mode shapes of the corresponding unstretched beams is developed as an alternative

new modified multi level residue harmonic balance method for solving nonlinearly vibrating double beam problem abstract in this study a new modified multi level residue harmonic balance method is presented and adopted to investigate the forced nonlinear vibrations of axially loaded double beams although numerous nonlinear beam or linear double beam problems have been tackled and solved there have been few studies of this nonlinear double beam problem the geometric nonlinear formulations for a double beam model are developed the main advantage of the proposed method is that a set of decoupled nonlinear algebraic equations is generated at each solution level this heavily reduces the computational effort compared with solving the coupled nonlinear algebraic equations generated in the classical harmonic balance method the proposed method can generate the higher level nonlinear solutions that are neglected by the previous modified harmonic balance method the results from the proposed method agree reasonably well with those from the classical harmonic balance method the effects of damping axial force and excitation magnitude on the nonlinear vibrational behaviour are examined

computational vibration and buckling analysis of microtubule bundles based on nonlocal strain gradient theory abstract a nonlocal strain gradient model is proposed to study buckling and vibrational responses of microtubules in axons with attention to different size effect parameters based on finite element method supporting effects of surrounding cytoplasm and map tau proteins are considered microtubules are modeled as elastically connected improved timoshenko nano beams resting on a two parameter pasternak foundation differential equations are discretized using galerkin method finally two eigenvalue problems are solved to achieve critical buckling loads and frequencies of single and doubled microtubule systems the nonlocal strain gradient model is employed in order to show both hardening and softening effects of structural stiffness based on relative magnitudes of nanoscale parameters influence of size effects including nonlocal nanoscale parameter gradient coefficient and surface effects are examined for various boundary conditions and some benchmark results are reported it is observed that these effects are more prominent at higher modes based on presented numerical results map tau proteins strengthen doubled microtubule systems to bear 11 7 more buckling load than a single microtubule furthermore vibration frequencies of microtubules depend on their physical surrounding condition in cell such as cell matrix and membrane and since microtubules could be employed as biosensors this property may be used in order to detect malignant tumors based on vibrational damping

free vibrations of periodically point supported rectangular plates abstract the basis and formulation of a new approach namely the flexibility function approach based on simulating point supports on free edges as zeros of a flexibility function representing a fictitious elastic restraint distribution over the edges was recently presented 1 2 its application to a variety of problems of free vibrations of point supported rectangular plates was presented subsequently 3 4 the present study provides an extension of its application to the problem of periodically point supported plates it is shown that by the use of a simple flexibility function the problem of periodically point supported plates can be easily analyzed numerical results for a range of problem parameters have been obtained which bring out the effect of the number of point supports on the natural frequencies edge displacements and edge reactions they also provide a quantitative estimate of the errors associated with the approximation of a large number of discrete supports by a continuous support condition or vice versa results have also been obtained for some typical problem parameters by using the impulse function approach based on representing the reactions at the point supports as fourier series expansion of the impulse function the comparison of the results clearly illustrates the fact that the flexibility function approach gives results which converge faster requires significantly less computation time and provides accurate results

high breakdown rank regression abstract a weighted rank estimate is proposed that has 50 breakdown and is asymptotically normal at rate n based on this theory inferential procedures including asymptotic confidence and tests and diagnostic procedures such as studentized residuals are developed the influence function of the estimate is derived and shown to be continuous and bounded everywhere in x y space examples show that robustness against outlying high leverage clusters may approach that of the least median of squares while retaining more stability against inliers the estimator uses weights that correct for both factor and response spaces a monte carlo study shows that the estimate is more efficient than the generalized rank estimates which are generalized r estimates with weights that only correct for factor space when weights are constant the estimate reduces to the regular wilcoxon rank estimate

analysis of vibrating rectangular plates of discontinuously varying thickness by means of the kantorovich extended method abstract the title problem is solved by using a polynomial co ordinate function in the x direction where the discontinuity in the thickness variation occurs and which contains an exponential parameter use of a variational approach allows for the determination of a differential equation in the y direction which contains the fundamental eigenvalue of the problem since the eigenvalue is a function of the optimization parameter by minimizing it with respect to one finds an optimized value of the fundamental frequency coefficient

analytic solution to free vibration of rectangular plates abstract the analytical strip method asm is presented for the free flexural vibration problem of rectangular plates with intermediate flexible supports and different edge conditions orthotropic plates and plates having single or multiple step variation in thickness are considered the plate is divided into strips the number of which depends on the geometric discontinuities the solution employs the classical method of separation of variables and the deflection for each plate strip is expressed in a single trigonometric series results are presented and when possible compared with previously published ones

damping of beam vibrations by means of a thin constrained viscoelastic layer evaluation of a new theory abstract in this paper a new one dimensional theory of beams damped by means of a thin viscoelastic film is presented based upon a prescribed piecewise linear longitudinal displacement field and a shear stress field satisfying continuity conditions at the interfaces the beam formulation of the proposed theory is derived in order to demonstrate the accuracy of this beam model numerical tests were carried out by using the finite element method the present results are compared with well known analytical finite element with the msc nastran computer program and experimental solutions under various material temperature and boundary conditions it is found that the proposed theory is very simple and efficient in predicting the dynamic response of beams that are damped by means of a thin viscoelastic film

least median of squares regression abstract classical least squares regression consists of minimizing the sum of the squared residuals many authors have produced more robust versions of this estimator by replacing the square by something else such as the absolute value in this article a different approach is introduced in which the sum is replaced by the median of the squared residuals the resulting estimator can resist the effect of nearly 50 of contamination in the data in the special case of simple regression it corresponds to finding the narrowest strip covering half of the observations generalizations are possible to multivariate location orthogonal regression and hypothesis testing in linear models

the least trimmed differences regression estimator and alternatives abstract this article proposes and studies the performance in theory and practice of the least trimmed differences ltd linear regression estimator the estimator minimizes the sum of the smallest quartile of the squares of the differences in each pair of residuals we obtain the breakdown point maxbias curve and large sample properties of a class of estimators including the ltd as special case the ltd estimator has a 50 breakdown point and gaussian efficiency of 66 substantially higher than other common high breakdown estimators such as least median of squares and least trimmed squares the ltd estimator is difficult to compute but can be performed using a feasible solution algorithm half sample jackknifing is effective in producing standard errors in simulations we find the ltd to be more stable than other high breakdown estimators in an example the ltd still shows instability like other high breakdown estimators when there are small changes in the data

partial residual plots based on robust fits in seeking information concerning the functional relationship between additional predictors and a response partial residual plots are useful graphical tools for identifying the unknown function usually these plots are based on least squares ls fitting the sensitivity of ls fitting to outliers though can distort their partial residuals making the identification of the unknown function difficult to impossible furthermore in this setting the unknown function can be nonlinear points that are located in areas of extreme curvature can act as outliers resulting in similar distortion in this article partial residual plots based on highly efficient robust fits are discussed and their firstorder behavior is determined based on this discussion robust partial residuals will be far less distorted than their ls counterparts in the presence of outliers and hence will be more powerful in identifying the unknown function furthermore a measure of precision efficiency is developed to compare partial res

on the convergence of the collocation method for nonlinear boundary integral equations abstract recently galerkin and collocation methods have been analysed for some nonlinear boundary integral equations for the collocation method it has been assumed that the nonlinearity is asymptotically linear in this paper we remove this restriction we shall prove the convergence of the collocation method for nonlinear boundary integral equations when the nonlinearity has a polynomial growth condition in addition to this the optimal order error estimates follow in l q norm

on the collocation method for a nonlinear boundary integral equation abstract in this paper we study a potential problem with a nonlinear boundary condition using the green representation formula for a harmonic function we reformulate the nonlinear boundary value problem as a nonlinear boundary integral equation we shall give a brief discussion of the solvability of the integral equation the aim of this paper however is to analyse the collocation method for finding an approximate solution to this equation using the theory of a proper and a stable mappings we prove the unique solvability of the collocation equations and the asymptotic error estimates to do this we assume that the nonlinearity is strongly monotone

free vibration analysis of elastically connected multiple beams by using the adomian modified decomposition method abstract the adomian modified decomposition method amdm is employed in this paper to investigate the free vibrations of n elastically connected parallel euler bernoulli beams which are continuously joined by a winkler type elastic layer the proposed amdm method can be used to analyze the vibration of beam system consisting of an arbitrary number of beams by using boundary conditions the natural frequencies and corresponding mode shapes can be easily obtained simultaneously the numerical results for different boundary conditions beam numbers and the stiffness of the winkler type elastic layer are presented it is shown that the amdm offers an accurate and effective method of free vibration analysis of multiple connected beams with arbitrary boundary conditions

the numerical solution of a nonlinear hypersingular boundary integral equation in this paper we consider a direct hypersingular integral approach to solve harmonic problems with nonlinear boundary conditions by using a practical variant of the galerkin boundary element method the proposed approach provides an almost optimal balance between the order of convergence and the numerical effort of work to compute the approximate solution numerical examples confirm the theoretical results

lp estimates of boundary integral equations for some nonlinear boundary value problems recently galerkin and collocation methods have been analyzed for boundary integral equation formulations of some potential problems in the plane with nonlinear boundary conditions and stability results and error estimates in theh 1 2 norm have been proved ruotsalainen and wendland and ruotsalainen and saranen we show that these results extend tol p setting without any extra conditions these extensions are proved by studying the uniform boundedness of the inverses of the linearized integral operators and then considering the nonlinear equations the fact that inh 1 2 setting the nonlinear operator is a homeomorphism with lipschitz continuous inverse plays a crucial role optimal error estimates for the galerkin and collocation method inl p space then follow

boundary element methods for potential problems with nonlinear boundary conditions galerkin boundary element methods for the solution of novel first kind steklov poincare and hypersingular operator boundary integral equations with nonlinear perturbations are investigated to solve potential type problems in two and three dimensional lipschitz domains with nonlinear boundary conditions for the numerical solution of the resulting newton iterate linear boundary integral equations we propose practical variants of the galerkin scheme and give corresponding error estimates we also discuss the actual implementation process with suitable preconditioners and propose an optimal hybrid solution strategy

adapting for the missing link we consider the fitting of generalized linear models in wich the link function is assumed to be unknown and propose the following computational method first estimate regression coefficients using the canonical link then estimate the link via a kernel smoother treating the direction in the predictor space determined by the regression coefficients as known then reestimate the direction using the estimated link and alternate between these two steps we show that under fairly general conditions n 1 2 consistent estimates of the direction are obtained a small monte carlo study is presented

robust and high breakdown fits of polynomial models a common strategy for fitting a polynomial regression model is to use a combination of residual plots and significance tests on the regression coefficients in this article we consider whether this strategy can be used effectively for fits based on two classes of robust estimatesnamely m estimates and gm estimates we show that the asymptotic relative efficiency of mallows type high breakdown gm estimates can be quite low for detecting curvature in polynomial models furthermore the gm residual plots may also be of little help in detecting curvature an example and a simulation study illustrate the discussion

vibrations of double string complex system under moving forces closed solutions in this paper the dynamic response of a double string system traversed by a constant or a harmonically oscillating moving force is considered the force is moving with a constant velocity on the top string the strings are identical parallel one upon the other and continuously coupled by a linear winkler elastic element the classical solution of the response of a double string system subjected to a force moving with a constant velocity has a form of an infinite series the main goal of this paper is to show that in the considered case a part of the solution can be presented in a closed analytical form instead of an infinite series the presented method of finding the solution in a closed analytical form is based on the observation that the solution of the system of partial differential equations in the form of an infinite series is also a solution of an appropriate system of ordinary differential equations

on the convergence of the galerkin method for nonsmooth solutions of integral equations it is shown that the stability region of the galerkin method includes solutions not lying in the conventional energy space optimal order error estimates for these nonsmooth solutions are derived the new result is compared with the classical statement by means of the basic potential problem

buckling and vibration of laminated composite plates using various plate theories analytical and finite element solutions of the classical first order and third order laminate theories are developed to study the buckling and free vibration behavior of cross ply rectangular composite laminates under various boundary conditions

unmasking multivariate outliers and leverage points comment detecting outliers in a multivariate point cloud is not trivial especially when there are several outliers the classical identification method does not always find them because it is based on the sample mean and covariance matrix which are themselves affected by the outliers to avoid this masking effect we propose to compute distances based on very robust estimates of location and covariance in the case of regression data the outliers also may be unmasked by using a highly robust regression method a new display is proposed in which the robust regression residuals are plotted versus the robust distances

high breakdown point estimates of regression by means of the minimization of an efficient scale abstract a new class of robust estimates estimates is introduced the estimates have simultaneously the following properties a they are qualitatively robust b their breakdown point is 5 and c they are highly efficient for regression models with normal errors they are defined by minimizing a new scale estimate applied to the residuals asymptotically a estimate is equivalent to an m estimate with a function given by a weighted average of two functions one corresponding to a very robust estimate and the other to a highly efficient estimate the weights are adaptive and depend on the underlying error distribution we prove consistency and asymptotic normality and give a convergent iterative computing algorithm finally we compare the biases produced by gross error contamination in the estimates and optimal bounded influence estimates