an extension of kesten s criterion for amenability to topological markov chains abstract the main results of this note extend a theorem of kesten for symmetric random walks on discrete groups to group extensions of topological markov chains in contrast to the result in probability theory there is a notable asymmetry in the assumptions on the base that is it turns out that under very mild assumptions on the continuity and symmetry of the associated potential amenability of the group implies that the gurevic pressures of the extension and the base coincide whereas the converse holds true if the potential is holder continuous and the topological markov chain has big images and preimages finally an application to periodic hyperbolic manifolds is given

improved stable approximants using the routh array a simple method for obtaining a stable reduced order k th order approximant g k s for a stable hlgh order n th order transfer function g s is described the method is an improvement over some previous methods 1 2 in that it not only ensures matching of the first k time moments of g s and g k s but it also ensures that the k 1 th time moment of g k s be as close as possible to the corresponding value in g s

ergodic theory for markov fibred systems and parabolic rational maps a paraboiic rational map of the riemann sphere admits a non atomic h conformal measure on its julia set where h the hausdorff dimension of the julia set and satisfies 1 2 h 2 with respect to this measure the rational map is conservative exact and there is an equivalent a finite invariant measure finiteness of the measure is characterised central limit theorems are proved in the case of a finite invariant measure and return sequences are identified in the case of an infinite one a theory of markov fibred systems is developed and parabolic rational maps are considered within this framework

the buckling of functionally graded truncated conical shells under dynamic axial loading abstract the dynamic buckling of truncated conical shells made of functionally graded materials fgms subject to a uniform axial compressive load which is a linear function of time has been studied the material properties of functionally graded shells are assumed to vary continuously through the thickness of the shell the variation of properties followed an arbitrary distribution in terms of the volume fractions of the constituents the fundamental relations the dynamic stability and compatibility equations of functionally graded truncated conical shells are obtained first applying galerkin s method these equations have been transformed to a pair of time dependent differential equation with variable coefficient and critical parameters obtained using the runge kutta method the results show that the critical parameters are affected by the configurations of the constituent materials compositional profile variations loading speed variations and the variation of the shell geometry comparing the results of this study with those in the literature validates the present analysis

buckling of a conical thin shell with variable thickness under a dynamic loading this study considers the buckling of an elastic truncated conical shell having a meridional thickness expressed by an arbitrary function subject to a uniform external pressure which is a power function of time at first the fundamental relations and donnell type dynamic buckling equation of an elastic conical shell with variable thickness have been obtained then employing galerkin s method those equations have been reduced to a time dependent differential equation with variable coefficients finally applying the ritz type variational method the critical static and dynamic loads the corresponding wave numbers dynamic factor and critical stress impulse have been found analytically using the results thus obtained the effects of the thickness variations with a power or an exponential function the variation of the semi vertex angle and the variation of the power of time in the external pressure expression are studied through pertinent computations it is observed that these factors have appreciable effects on the critical parameters of the problem in the heading

a method for optimal linear model reduction abstract this paper presents a new method for generating a reduced order model of a linear time invariant siso stable system the simplification criterion is the integral of a linear combination of the transient term of the original system step response and of a suitable number of its derivatives the reduction procedure is computationally simpler than similar procedures considered in the literature and leads to reduced order models whose step response fits satisfactorily the original one

spl gamma spl delta routh approximation for interval systems the paper presents the spl gamma spl delta routh approximation for interval systems the interval spl gamma s and spl delta s are evaluated for the higher order interval systems and then an rth order approximant is obtained by retaining the first r interval spl delta s and spl gamma s a numerical example illustrates the procedure

pade techniques for model reduction in linear system theory a survey abstract techniques of pade approximation and continued fractions have been used often in model reduction problems an extensive bibliography on this topic is given the ideas are explained for the simple situation of a scalar function where no singular blocks appear in the pade table extensions to the matrix case and the multivariable case are not explained in detail

nonlinear buckling of cylinders under external pressure with nonaxisymmetric thickness imperfections using the comi axisymmetric shell element abstract this paper concerns the influence of thickness imperfections on the nonlinear buckling of cylinders under uniform external pressure the material is assumed to behave elastically a parametric study is performed using the comi finite element which allows to perform nonlinear analyses of shells of revolution with any kind of nonaxisymmetric initial imperfection let us assume that the perfect shell buckles with a fourier mode m and that the initial thickness imperfection is on fourier mode 1 m or 2 m as shown in a previous study on linear buckling of cylinders with thickness imperfections 1 and 2 m are the most harmful thickness imperfections we show that the nonlinear pre buckling does not affect the buckling pressures very much we then study the coupling with geometrical imperfections we show that the geometry and thickness imperfections have a multiplicative effect on the decrease in buckling load in the nonlinear range finally we show that if one uses only the measured outer radius of a shell to input initial imperfections very different nonlinear buckling pressures can be obtained under the assumptions that the imperfection is purely geometric purely thickness or a combination of both

snap through buckling reliability analysis under spatiotemporal variability and epistemic uncertainty surrogate models often provide an effective tradeoff between accuracy and efficiency during reliability analysis with expensive physics models in snap through buckling reliability analysis a surrogate model could be built for the critical buckling load as a function of loading material properties geometry and boundary conditions however in the presence of spatiotemporal variability the response surface of the critical buckling load is often highly nonlinear and irregular thus rendering commonly used response surface type surrogate modeling strategies ineffective this paper proposes a new buckling reliability analysis method based on support vector machines for structures subjected to spatiotemporal variability and in the presence of epistemic uncertainty regarding model inputs and parameters bayesian calibration is first used to quantify the epistemic uncertainty in the modeling of spatiotemporal variability under limited data upon the modeling of spatiotemporal variability and epistemic unce

amenable covers for surfaces and growth of closed geodesics abstract in this article we show that the rate of growth of closed geodesics up to translation on an amenable cover of a compact surface is the same as that on the underlying space this generalizes the result for negatively curved surfaces

a note on the model reduction problem a mixed method of model reduction is proposed it is based on the differentiation method suggested by gutman et al 1 and on the usual pade method more precisely the differentiation procedure is used to obtain the reduced order denominator thus ensuring stability preservation while the numerator is obtained by matching the first maclaurin expansion coefficients of the original system and model transfer functions the method is computationally very simple and may lead to satisfactory results as shown by an example where the original system transfer function is taken from the relevant literature

stability preservation and computational aspects of a newly proposed reduction method the stability of the reduced order models obtained using the method suggested by a lepschy et al syst contr lett vol 8 pp 405 10 may 1987 is analyzed the relation between this method and the routh approximation is pointed out some interesting properties related to the construction of the reduced order transfer functions and to the evaluation of certain quadratic integrals are derived an examples shows the practicality of the procedures

effects of initial twist and thickness variation on the vibration behaviour of shallow conical shells abstract a thorough computational investigation is presented into the effects of initial twist and thickness variation on the vibratory characteristics of cantilevered pretwisted thin shallow conical shells with generally varying thickness an energy approach with the ritz minimization procedure is employed to arrive at a governing eigenvalue equation the admissiblepb 2shape functions which comprise sets of mathematically complete two dimensional orthogonal polynomials and a basic function are introduced to account for the boundary constraints and to approximate the three dimensional displacements of the conical shell the effects of angle of twist thickness variation and geometric parameters on the vibration response are presented in a comprehensive parametric study which provides useful new design data selected vibration mode shapes are also included to enhance the existing literature it is found that an increase in the angle of twist does not necessarily increase the torsional stiffness on the contrary the fundamental frequencies is reduced in the present analysis it is also observed that non zero angle of twist and non uniform chordwise thickness variation cause the absent of vibration mode symmetry

an algorithmic method for the simplification of linear dynamic scalar systems a comprehensive method is proposed for obtaining reduced order models of a scalar linear time invariant system described by the transfer function g s the method is a viable alternative to the pade approximation technique for model order reduction it approximates the differential operations d i g s dsi proportional to the time moments by the divided difference equivalents and finally leads to linear equations in the unknown coefficients of the reduced model r s it is shown that a parameter governs the stability and the low frequency matching quality of the model heuristic criteria are given for selecting a proper the method is illustrated by some examples from the literature

amenability critical exponents of subgroups and growth of closed geodesics let gamma be a non elementary convex co compact group of isometries of a pinched hadamard manifold x we show that a normal subgroup gamma 0 has critical exponent equal to the critical exponent of gamma if and only if gamma gamma 0 is amenable we prove a similar result for the exponential growth rate of closed geodesics on x gamma these statements are analogues of classical results of kesten for random walks on groups and brooks for the spectrum of the laplacian on covers of riemannian manifolds

dynamic buckling of cylindrical shells subject to an axial impact in a symplectic system this paper discusses the dynamic pre buckling of finite cylindrical shells in the propagation and reflection of axial stress waves by introducing the hamiltonian system into dynamic buckling of structures the problem can be described mathematically in a symplectic space the solutions of hamiltonian dual equations shown in canonical variables are obtained the problem is reduced to the determination of eigenvalues and eigensolutions with the former indicating critical buckling loads and the latter buckling modes numerical example presented shows phenomena of axisymmetric and non axisymmetric dynamic buckling subject to impacts of axial load

a unified derivation and critical review of modal approaches to model reduction six of the most commonly used modal reduction techniques are represented by means of signal flow diagrams connecting inputs and state variables in this representation the derivation and the cross comparison of the various methods are greatly facilitated each method is then analysed to determine key characteristics i e i steady state agreement ii initial value agreement iii independence of the reduced model on the choice of retained state variables and inputs and iv eigen vector orientation realistic large scale systems are used to evaluate the static and dynamic characteristics of each model reduction method numerically these studies reveal some important and often unrecognized weaknesses of several traditional techniques and confirm the strength of the newly developed technique of litz

frequency domain reduction of linear systems using schwarz approximation a frequency domain approach for reducing linear time invariant systems is presented which produces stable approximations of stable systems the method is based upon the schwarz canonical form and is shown to have a continued fraction representation a link between this method and the popular routh approximation is also given further the schwarz approximation is combined with a moments matching technique to improve steady state responses to step and polynomial inputs examples are given to illustrate the methods

free vibration of a conical shell with variable thickness abstract an analysis is presented for the free vibration of a truncated conical shell with variable thickness by use of the transfer matrix approach the applicability of the classical thin shell theory is assumed and the governing equations of vibration of a conical shell are written as a coupled set of first order differential equations by using the transfer matrix of the shell once the matrix has been determined by quadrature of the equations the natural frequencies and the mode shapes of vibration are calculated numerically in terms of the elements of the matrix under any combination of boundary conditions at the edges the method is applied to truncated conical shells with linearly parabolically or exponentially varying thickness and the effects of the semi vertex angle truncated length and varying thickness on the vibration are studied

the patterson measure for geometrically finite groups with parabolic elements new and old we study the patterson measure on the limit set of a geometrically finite kleinian group with parabolic elements using the conformality of the patterson measure in combination with basic hyperbolic geometry a global shadow lemma is obtained this macroscopic measure estimate is exploited to derive a khintchine type theorem which is then used for a finer analysis of the density of the limit set in terms of hausdorff measure

critical exponents of normal subgroups the spectrum of group extended transfer operators and kazhdan distance abstract for a pinched hadamard manifold x and a discrete group of isometries of x the critical exponent is the exponential growth rate of the orbit of a point in x under the action of we show that the critical exponent for any family n of normal subgroups of 0 has the same coarse behaviour as the kazhdan distances for the right regular representations of the quotients 0 the key tool is to analyse the spectrum of transfer operators associated to subshifts of finite type for which we obtain a result of independent interest

the effect of material and thickness variability on the buckling load of shells with random initial imperfections abstract the effect of material and thickness imperfections on the buckling load of isotropic shells is investigated in this paper for this purpose the concept of an initial imperfect structure is introduced involving not only geometric deviations of the shell structure from its perfect geometry but also a spatial variability of the modulus of elasticity as well as the thickness of the shell the initial geometric imperfections are described as a two dimensional uni variate 2d 1v stochastic field with statistical properties that are either based on an available data bank of measured initial imperfections or assumed in cases where no experimental data is available in order to describe the non homogeneous characteristics of the initial imperfections the spectral representation method is used in conjunction with an autoregressive moving average model with evolutionary power spectra based on a statistical analysis of the experimentally measured imperfections in cases where no experimental results is available the initial imperfections are assumed to be homogeneous and their impact on the buckling load is investigated on the basis of worst case scenarios with respect to the correlation length parameters of the stochastic fields the elastic modulus and the shell thickness are described as 2d 1v non correlated homogeneous stochastic fields while the stochastic stiffness matrix of the shell elements is formulated using the local average method the monte carlo simulation method is used to calculate the variability of the buckling load while for the determination of the limit load of the shell a stochastic formulation of the elastoplastic and geometrically non linear tric facet triangular shell element is implemented

contributions to the model reduction problem a new method of model reduction is introduced based on the differentiation of polynomials the reciprocals of the numerator and denominator polynomials of the high order transfer function are differentiated suitably many times to yield the coefficients of the reduced order transfer function an error analysis shows the accuracy of the method and an eighth order example illustrates it the method is computationally very simple and is equally applicable to unstable and nonminimum phase systems

transverse vibrations of an orthotropic rectangular plate of linearly varying thickness and with a free edge fil bambill diana virginia consejo nacional de investigaciones cientificas y tecnicas centro cientifico tecnologico conicet bahia blanca argentina universidad nacional del sur departamento de ingenieria argentina

a pb 2 ritz formulation for flexural vibration of shallow cylindrical shells of rectangular planform abstract this paper presents a free flexural vibration analysis of shallow cylindrical shells of rectangular planform with arbitrary combinations of free simply supported and clamped boundaries the pb 2 ritz method previously used in the plate analysis by one of the authors is now extended to shallow shell studies the ritz approach along with the in plane and transverse displacements assumed in the form of orthogonal polynomials is used to formulate the problems numerical results for the vibration frequencies for wide ranges of aspect ratio shallowness ratio and thickness ratio are presented several selected contour plots of the mode shapes for six different combinations of boundary conditions are presented as usual the accuracy of the present method is illustrated by convergence tests and comparison with the well established results from the literature

an improvement in the routh pade approximation techniques a method for approximating high order stable systems via lower order stable models is presented it is an improvement over previous routh pade methods since the denominator polynomial of the model transfer function even if based on the elements of a routh array contains two free parameters a systematic procedure is illustrated for evaluating besides the numerator coefficients such denominator parameters in order to ensure a good fit in the pade sense and a suitable stability margin

a sampling based approach for probabilistic design with random fields an original technique to incorporate random fields non intrusively in probabilistic design is presented the approach is based on the extraction of the main features of a random field using a limited number of experimental observations snapshots an approximation of the random field is obtained using proper orthogonal decomposition pod for a given failure criterion an explicit limit state function lsf in terms of the coefficients of the pod expansion is obtained using a support vector machine svm an adaptive sampling technique is used to generate samples and update the approximated lsf the coefficients of the orthogonal decomposition are considered as random variables with distributions determined from the snapshots based on these distributions and the explicit lsf the approach allows for an efficient assessment of the probabilities of failure in addition the construction of explicit lsf has the advantage of handling discontinuous responses two test problems are used to demonstrate the proposed methodology used for the calculation of probabilities of failure the first example involves the linear buckling of an arch structure for which the thickness is a random field the second problem concerns the impact of a tube on a rigid wall the planarity of the walls of the tube is considered as a random field

buckling of an axially compressed cylindrical shell of variable thickness abstract this paper focuses on the buckling of cylindrical shells with small thickness variations two important cases of thickness variation pattern are considered asymptotic formulas up to the second order of the thickness variation parameter e are derived by the combination of the perturbation and weighted residual methods the expressions obtained in this study reduce to koiter s formulas when only the first order term of the thickness variation parameter is retained in the analysis results from the asymptotic formulas are compared with those obtained through the purely numerical techniques of the finite difference method and the shooting method

an improvement on routh approximation technique a modification of the routh approximant is introduced which results in a considerable improvement over the conventional routh approximation technique since some amount of arbitrariness is available in the time moment expressions of the conventional routh approximant it can be utilized to minimize the step response error while preserving the stability and moment matching property of the conventional routh approximant a numerical example illustrates the procedure

improved routh pade spl acute approximants a computer aided approach a geometric programming based computer aided method to derive a reduced order rth order approximant for a given stable siso linear continuous time system is presented in this method stability and the first r time moments markov parameters are preserved as well as the errors between a set of subsequent time moments markov parameters of the system and those of the model are minimized

three dimensional vibrations of hollow cones and cylinders with linear thickness variations a three dimensional method of analysis is presented for determining the free vibration frequencies and mode shapes of hollow cones and cylinders with variable thickness displacement components us uz and u in the meridional normal and circumferential directions respectively are taken to be sinusoidal in time periodic in and algebraic polynomials in the s and z directions potential strain and kinetic energies of the cones and cylinders are formulated and upper bound values of the frequencies are obtained by minimizing the frequencies as the degree of the polynomials is increased frequencies converge to the exact values novel numerical results are presented for thick linearly tapered hollow cones and cylinders with completely free boundaries convergence to four digit exactitude is demonstrated for the first five frequencies of the cones and cylinders the method is applicable to thin cones and cylinders as well as thick and very thick ones

dynamic buckling of a cylindrical shell with variable thickness subject to a time dependent external pressure varying as a power function of time in this study the dynamic buckling of an elastic cylindrical shell with variable thickness subject to a uniform external pressure which is a power function of time has been considered initially the fundamental relations and donnell type dynamic buckling equation of an elastic cylindrical shell with variable thickness have been obtained then employing galerkin s method these equations have been reduced to a time dependent differential equation with variable coefficients finally applying a special ritz type method the critical static and dynamic loads the corresponding wave numbers and dynamic factor have been found analytically using those results the effects of the variation of the thickness with a linear a parabolic or an exponential function in the axial direction and the effect of the variation of the power of time in the external pressure expression are studied using pertinent computations it is observed that these effects change appreciably the critical parameters of the problem the present method has been verified comparing the results of the present work and those of previous works in the literature for a shell with constant thickness subject to a uniform external pressure varying linearly with time

viability of methods for generating stable reduced order models various methods for generating stable reduced order models are shown to have a serious disadvantage in that the reduced model may approximate the nondominant poles of the system and hence lead to erroneous approximations an example is given to compare these methods with the standard pade approximation method for which this disadvantage does not exist

stable partial pade approximations for reduced order trnsfer functions while the pade approximation can often be used to produce good reduced order transfer functions the method suffers from the disadvantage that a stable reduced order model is not always obtained for an original model that is stable a method is described for obtaining stable partial pade approximation reduced order models the method permits the determination of the effect of changes in the coefficients in the partial pade approximation on the poles of the reduced order transfer function by means of standard root locus plots

some further observations on the differentiation method of modal reduction the differentiation method of model reduction is shown to be equivalent to forming successive ratios of multipoint taylor polynomial approximation of the numerator and denominator of the transfer function respectively this reformulation allows the method to be applied entirely through a routh type array structure strong links are seen to exist between the method and other stability preserving methods via this routh type structure

on model reduction by modified cauer form a simple algorithm for obtaining the continued fraction quotients in the modified cauer form mcf from the given system matrices in companion form is presented in the sequel the triple of all lower order models in companion form is directly obtained a matrix method of obtaining the time moments and markov parameters from the mcf quotients is also outlined finally it is shown that system reduction by matching a set of mcf quotients is equivalent to system reduction by matching a set of time moments and markov parameters

a method for linear model reduction using the input independent equation error the paper deals with the order reduction problem for single input single output linear dynamical systems combining the uniform approximation approach with the equation error formulation a simplification method is proposed which leads to input independent optimal models by a relatively simple calculation procedure

bayesian calibration of computer models we consider prediction and uncertainty analysis for systems which are approximated using complex mathematical models such models implemented as computer codes are often generic in the sense that by a suitable choice of some of the model s input parameters the code can be used to predict the behaviour of the system in a variety of specific applications however in any specific application the values of necessary parameters may be unknown in this case physical observations of the system in the specific context are used to learn about the unknown parameters the process of fitting the model to the observed data by adjusting the parameters is known as calibration calibration is typically effected by ad hoc fitting and after calibration the model is used with the fitted input values to predict the future behaviour of the system we present a bayesian calibration technique which improves on this traditional approach in two respects first the predictions allow for all sources of uncertainty including the remaining uncertainty over the fitted parameters second they attempt to correct for any inadequacy of the model which is revealed by a discrepancy between the observed data and the model predictions from even the best fitting parameter values the method is illustrated by using data from a nuclear radiation release at tomsk and from a more complex simulated nuclear accident exercise

invariant radon measures for horocycle flows on abelian covers we classify the ergodic invariant radon measures for horocycle flows on d covers of compact riemannian surfaces of negative curvature thus proving a conjecture of m babillot and f ledrappier an important tool is a result in the ergodic theory of equivalence relations concerning the reduction of the range of a cocycle by the addition of a coboundary