well structured transition systems everywhere well structured transition systems wstss are a general class of infinite state systems for which decidability results rely on the existence of a well quasi ordering between states that is compatible with the transitions in this article we provide an extensive treatment of the wsts idea and show several new results our improved definitions allow many examples of classical systems to be seen as instances of wstss

a differential quadrature procedure for three dimensional buckling analysis of rectangular plates abstract this paper presents an application of the differential quadrature dq method for three dimensional buckling analysis of rectangular plates the governing equations of the plate model are first presented in terms of displacement stress displacement relationship and boundary conditions with three dimensional flexibility these equations are then normalised and discretised using the dq procedure example problems pertaining to the buckling of rectangular plates with generic boundary conditions are selected to illustrate the efficiency and simplicity of implementing the dq procedure the convergence characteristics of the method are first conducted based on numerical studies the dq solutions are then compared where possible with exact or approximate solutions it is found that the differential quadrature method yields accurate results for the plate problems under the current investigation in addition to the above some parametric studies are carried out by varying the plates aspect ratio boundary conditions and thickness to width ratio under axial and biaxial loading

a higher order beam finite element for bending and vibration problems abstract the finite element equations for a variationally consistent higher order beam theory are presented for the static and dynamic behavior of rectangular beams the higher order theory correctly accounts for the stress free conditions on the upper and lower surfaces of the beam while retaining the parabolic shear strain distribution the need for a shear correction coefficient is therefore eliminated full integration of the shear stiffness terms is shown to result in the recovery of the kirchhoff constraint for thin beams without introducing spurious locking constraints the accuracy of this formulation is demonstrated by using several numerical examples for the cases of small and large displacements for a hinged hinged beam the linear thickness shear mode frequency can be matched with the timoshenko frequency to yield a shear coefficient of 0 824 matching the bending frequencies between the two theories indicates a shear coefficient for the timoshenko theory that changes with mode number and slenderness ratio the influence of in plane inertia and slenderness ratio on the non linear frequency is examined for beams with a number of different support conditions

modeling via differential quadrature method three dimensional solutions for rectangular plates this paper presents the formulation and numerical analysis of the three dimensional plate model using the differential quadrature dq method the equilibrium equations stress displacement relations and boundary conditions for the three dimensional plate model are first presented these equations are then normalised and discretised using the dq procedure example problems for rectangular plates with generic boundary conditions are selected to illustrate the computational efficiency and applicability of the dq procedure the convergence characteristics of the method are first conducted based on numerical studies the solutions are then compared where possible with the analytical or exact solutions it is found that the differential quadrature method yields accurate results for the plate problems under the current investigation

three dimensional free vibrations of thick skewed cantilevered plates abstract the natural frequencies of skewed cantilevered thick plates are determined by using the ritz method the present work is the first known three dimensional study of the problem assumed displacement functions are in the form of algebraic polynomials which satisfy the fixed face conditions exactly and which are mathematically complete accurate natural frequencies are calculated for skewed thick plates having arbitrary degrees of skewness detailed numerical studies reveal interesting trends concerning the variation of frequencies with increasing skew angle results obtained by using the present method are compared with those obtained by using three dimensional finite elements

a variable kinematic ritz formulation for vibration study of quadrilateral plates with arbitrary thickness a new variable kinematic ritz method applied to free vibration analysis of arbitrary quadrilateral thin and thick isotropic plates is presented carrera s unified formulation and the versatile pb 2 ritz method are properly combined to build a powerful yet simple modeling and solution framework the proposed technique allows to generate arbitrarily accurate ritz solutions from a large variety of refined two dimensional plate theories by expanding so called ritz fundamental nuclei of the plate mass and stiffness matrices theoretical development of the present methodology is described in detail convergence and accuracy of the method are examined through several examples on thin moderately thick and very thick plates of rectangular skew trapezoidal and general quadrilateral shapes with an arbitrary combination of clamped free and simply supported edges present results are compared with existing three dimensional solutions from open literature maximum and average differences of various higher order plate theories and three dimensional results are also presented with the aim of providing useful guidelines on the choice of appropriate plate theory to get a desired accuracy on frequency parameters

another second order beam vibration theory explicit bending warping flexibility and restraint abstract a new symmetric beam bending vibration theory which explicitly includes bending warping is presented the governing differential equations are of sixth order and the boundary conditions allow enforcement of total fixity of the end of a beam the motivation for the study was the desire to determine if consideration of bending warping restraint in bending theory is as important as is torsion warping restraint in torsion theory natural frequency predictions are given and compared with other theories for constant cross section cantilevered beams of two types short deep rectangular beams and short thin shallow circular cylindrical shells the accuracy of the new theory is comparable with murty s levinson s bickford s and rehfield s theories for beams with rectangular cross sections it is also comparable with cowper s theory for general symmetric cross sections

on the absolute continuity of the blackwell measure in 1957 blackwell expressed the entropy of hidden markov chains using a measure which can be characterised as an invariant measure for an iterated function system with place dependent weights this measure called the blackwell measure plays a central role in understanding the entropy rate and other important characteristics of fundamental models in information theory we show that for a suitable set of parameter values the blackwell measure is absolutely continuous for almost every parameter in the case of binary symmetric channels

a well structured framework for analysing petri net extensions transition systems defined from recursive functions in p in p are introduced and named wsns or well structured nets such nets sit conveniently between petri net extensions and general transition systems in the first part of this paper we study decidability properties of wsn classes obtained by imposing natural restrictions on their defining functions with respect to termination coverability and four variants of the boundedness problem we are able to precisely answer almost all the questions which arise thus gaining much insight into old and new generalized petri net decidability results in the second part we specialize our analysis to wsns defined from affine functions which elegantly encompass most petri net extensions studied in the literature again we study decidability properties of natural classes of affine wsn with respect to the above six computational problems in particular we develop an algorithm computing limits of iterated nonnegative affine functions in order to decide the path place variant of the boundedness problem for non negative affine wsn

stationary measures for projective transformations the blackwell and furstenberg measures in this paper we study the blackwell and furstenberg measures which play an important role in information theory and the study of lyapunov exponents for the blackwell measure we determine parameter domains of singularity and give upper bounds for the hausdorff dimension for the furstenberg measure we establish absolute continuity for some parameter values our method is to analyze linear fractional iterated function schemes which are contracting on average have no separation properties that is we do not assume that the open set condition holds see hutchinson in indiana univ math j 30 713 747 1981 and in the case of the blackwell measure have place dependent probabilities in such a general setting even an effective upper bound on the dimension of the measure is difficult to achieve

three dimensional vibration analysis of a cantilevered parallelepiped exact and approximate solutions the paper investigates the hypothetical assumption of neglecting transverse normal stress in vibration analysis for cantilevered thick plates and rectangular parallelepiped the analysis solves the three dimensional elasticity energy functional including as well as excluding transverse normal stress and obtains free vibration solutions for a cantilevered parallelepiped although it is widely accepted the omission of transverse normal stress is well justified in kirchhoff love thin plate theory and higher order thick plate models the transverse normal stress effects and thickness extent to which the thick plate models apply as the thickness increases are practically unknown the inconsistency of assuming constant transverse normal displacement through thickness for thick plate models is also addressed the paper concludes that for a rectangular parallelepiped with thickness exceeding a certain limit there is considerable discrepancy if transverse normal stress is neglected

explicit invariant measures for products of random matrices we construct explicit invariant measures for a family of infinite products of random independent identically distributed elements of sl 2 c the matrices in the product are such that one entry is gamma distributed along a ray in the complex plane when the ray is the positive real axis the products are those associated with a continued fraction studied by letac seshadri z wahr verw geb 62 1983 485 489 who showed that the distribution of the continued fraction is a generalised inverse gaussian we extend this result by finding the distribution for an arbitrary ray in the complex right half plane and thus compute the corresponding lyapunov exponent explicitly when the ray lies on the imaginary axis the matrices in the infinite product coincide with the transfer matrices associated with a one dimensional discrete schrodinger operator with a random gamma distributed potential hence the explicit knowledge of the lyapunov exponent may be used to estimate the exponential rate of localisation of the eigenstates

three dimensional vibration analysis of rectangular thick plates on pasternak foundation the free vibration characteristics of rectangular thick plates resting on elastic foundations have been studied based on the three dimensional linear and small strain elasticity theory the foundation is described by the pasternak two parameter model the ritz method is used to derive the eigenvalue equation of the rectangular plate by augmenting the strain energy of the plate with the potential energy of the elastic foundation the chebyshev polynomials multiplied by a boundary function are selected as the admissible functions of the displacement functions in each direction the approach is suitable for rectangular plates with arbitrary boundary conditions convergence and comparison studies have been performed on square plates on elastic foundations with different boundary conditions it is shown that the present method has a rapid convergent rate stable numerical operation and very high accuracy parametric investigations on the dynamic behaviour of clamped square thick plates on elastic foundations have been carried out in detail with respect to different thickness span ratios and foundation parameters some results found for the first time have been given and some important conclusions have been drawn

comparative accuracy of dq and hdq methods for three dimensional vibration analysis of rectangular plates an accuracy study between the differential quadrature dq and harmonic differential quadrature hdq methods for three dimensional elasticity solutions of free vibration of rectangular plates is carried out the solution capability of the dq and hdq methods is first studied then the numerical performance of both the methods is compared it is found that the dq method displays more superior convergence characteristics over the hdq method for the lower modes of vibration however the hdq method is advantageous over the dq method for computing higher modes of vibration it is also discovered that the dq and hdq methods produce better convergent solutions than the finite element method fem when a similar number of discrete points nodes are used copyright 1999 john wiley sons ltd

numerical aspects for free vibration of thick plates part i formulation and verification abstract this paper investigates the numerical aspects for free vibration analysis of a class of thick relative thickness ratio t b 0 2 shear deformable rectangular plates with all possible combinations of edge conditions these thick plate vibration frequencies most probably cannot be accurately determined using the classical thin plate theory or the mindlin plate theory the effect of transverse shear strain has been considered by using a higher order plate theory without the need for a shear correction factor unlike some domain discretization methods this analysis assumes a single global element for the entire plate the strain and kinetic energy integrals of the global plate element are formulated and the energy functional is minimized to yield the natural frequencies a set of boundary compliant admissible shape functions is developed to obtain solutions which are unattainable using the classical trigonometric admissible functions the numerical efficiency of symmetry classification is investigated and on certain computational platforms more than 80 of the execution time can be saved while maintaining the same level of accuracy

three dimensional elasticity solutions to some orthotropic plate problems abstract this paper presents a three dimensional analysis of rectangular orthotropic plates by employing the differential quadrature dq method the derivation of the governing equations from the governing equations and the stress strain relationship of the three dimensional elasticity model is detailed the constrained conditions of the orthotropic plate edges are given the governing equations and boundary conditions are first normalized and discretized according to the dq procedure example problems pertaining to the bending buckling and free vibration of orthotropic plates with generic boundary conditions are selected to illustrate the simplicity and applicability of the dq method the convergence characteristics of the dq method are first obtained based on numerical studies after which the dq solutions are compared where possible with exact solutions it is found that the dq method yields accurate results for the plate problems under investigation

three dimensional vibration analysis of thick rectangular plates using chebyshev polynomial and ritz method this paper describes a method for free vibration analysis of rectangular plates with any thicknesses which range from thin moderately thick to very thick plates it utilises admissible functions comprising the chebyshev polynomials multiplied by a boundary function the analysis is based on a linear small strain three dimensional elasticity theory the proposed technique yields very accurate natural frequencies and mode shapes of rectangular plates with arbitrary boundary conditions a very simple and general programme has been compiled for the purpose for a plate with geometric symmetry the vibration modes can be classified into symmetric and antisymmetric ones in that direction in such a case the computational cost can be greatly reduced while maintaining the same level of accuracy convergence studies and comparison have been carried out taking square plates with four simply supported edges as examples it is shown that the present method enables rapid convergence stable numerical operation and very high computational accuracy parametric investigations on the vibration behaviour of rectangular plates with four clamped edges have also been performed in detail with respect to different thickness side ratios aspect ratios and poissons ratios these results may serve as benchmark solutions for validating approximate two dimensional theories and new computational techniques in future 2002 elsevier science ltd all rights reserved

on the dimension of furstenberg measure for sl _ 2 mathbb r random matrix products let mu be a measure on sl 2 mathbb r generating a non compact and totally irreducible subgroup and let nu be the associated stationary furstenberg measure for the action on the projective line we prove that if mu is supported on finitely many matrices with algebraic entries then begin aligned dim nu min big 1 frac h mathrm mathrm rw mu 2 chi mu big end aligned where h mathrm mathrm rw mu is the random walk entropy of mu chi mu is the lyapunov exponent for the random matrix product associated with mu and dim denotes pointwise dimension in particular for every delta 0 there is a neighborhood u of the identity in sl 2 mathbb r such that if a measure mu in mathcal p u is supported on algebraic matrices with all atoms of size at least delta and generates a group which is non compact and totally irreducible then its stationary measure nu satisfies dim nu 1

free vibration of thick layered rectangular plates with point supports by finite layer method in this paper the free vibration of thick isotropic and laminated composite rectangular plates with point supports is analyzed by the finite layer method a new set of two dimensional basic functions which satisfies the kinematic boundary conditions at the edges of the plate and the zero displacement conditions at point supports is developed to describe the variation of three dimensional displacements in the plane of a thin finite layer one dimensional linear or quadratic shape functions are adopted to describe the variation of the displacements through the thickness layer the governing eigenvalue equation of the plate is derived via the conventional displacement method numerical results for the three dimensional vibration of rectangular plates with point supports are presented herein for the first time the eigenfrequencies of simply supported rectangular plates with a central point support are studied in detail by considering the variations of aspect ratio side to thickness ratio properties of materials number of laminates and stacking sequences comparison with known thin plate and mindlin plate solutions is carried out to verify the applicability and accuracy of the proposed method

free vibration analysis of three dimensional solids by bem in practical applications it is often necessary to determine the natural frequencies and mode shapes of a solid in addition to the static response under a variety of loading conditions this paper discusses the calculation of natural frequencies and mode shapes of three dimensional solids using the boundary element method the method developed is based on the use of particular integrals of the elastic equilibrium equations and employs only real arithmetic it represents an extension to three dimensions of work previously carried out for two dimensional problems in references 1 and 15 the method has been incorporated for multiregion analysis in the best3d boundary element solution technology three dimensional computer program 11 results of the boundary element calculations are compared with analytical finite element and experimental results

nondestructive determination of buckling for plates and bars including shear it will be shown that the generic integral equation for nondestructive determination of the buckling loads obtained previously baruch m integral equations for nondestructive determination of buckling loads for elastic bars and plates israel journal of technology vol 11 no 1 2 1973 pp 1 8 includes the influence of the transverse shear strains on the buckling load this can not be said for the integral equations obtained by differentiation of the generic integral equation

analytical 3 d p element for quadrilateral plates part 1 thick isotropic plate structures an analytical three dimensional 3 d p version element for the vibration analysis of arbitrary quadrilateral thick plates is presented with the additional hierarchical shape functions and analytically integrated element matrices the computed accuracy is considerably improved the computed natural frequencies of cantilever and simply supported square plates show that the convergence rate of the present element is very fast with respect to the number of hierarchical terms and it can predict very accurate modes the element is applicable to the free vibration analysis of quadrilateral polygonal plates as well as 3 d space structures the continuous wavelet transform cwt is applied for the identification of damping ratios based on the rayleigh damping model the damped vibration response is obtained a simple experiment is performed to verify the predicted vibration responses the results show that the proposed element is also efficient for the vibration response analysis of plates

3 d vibration analysis of generalized super elliptical plates using chebyshev ritz method the three dimensional free vibration of generalized super elliptical plates is analysed based on the exact small strain and linear elasticity theory the ritz method is applied to derive the frequency equation the triplicate chebyshev polynomial series form the backbones of the admissible functions as modified by a characteristic boundary function to ensure the satisfaction of geometric boundary conditions of the plate utilizing the symmetry of the plate under consideration eight distinct vibration modes can be classified and individually solved while maintaining the same level of accuracy the accuracy of the present method has been examined by the convergence and comparison studies the effect of geometric parameters on vibration behaviour of the generalized super elliptical plates with free and fixed perimeters have been studied for different powers thickness ratios and aspect ratios

on the three dimensional vibrations of the cantilevered rectangular parallelepiped a solution is presented for the three dimensional problem of determining the free vibration frequencies and mode shapes for a rectangular parallelepiped which is completely fixed on one face and free on the other five faces this problem apparently is previously unsolved in the published literature the ritz method is used with displacements assumed in the form of algebraic polynomials convergence is studied numerical results are given for the first five frequencies of each of the four symmetry classes of vibration for five thick parallelepiped configurations including the cube contour plots are exhibited for the modal displacements of the cube the effects of varying poisson s ratio are also observed

a new rectangular beam theory abstract a new theory for beams of rectangular cross section which includes warping of the cross sections is presented in the present work by satisfying the shear free conditions on the lateral surfaces of the beam a pair of coupled equations of motion are obtained such that no arbitrary shear coefficient is required it is shown that the uncoupled equation for the transverse displacement is the same as the corresponding equation in timoshenko beam theory provided that for the timoshenko equation the shear coefficient is taken to be 5 6 this value lies within the range of values 0 822 0 870 appearing in the literature for the beam of rectangular cross section results for two typical static examples are given for both the new theory and timoshenko beam theory these results are compared with the solutions of the comparable problems in the linear theory of elasticity for the end loaded cantilever beam the new theory predicts the same result for the neutral surface deflection as does the linear theory of elasticity while timoshenko beam theory underestimates the shear correction term by 20 for the uniformly loaded and simply supported case both beam theories provide the same overestimate of the central deflection when compared with the theory of elasticity solution

high order theory of homogeneous plate flexure the need for higher order models to obtain accurate estimates to transverse shear and normal stresses and strains is well known in this paper a higher order shear deformation theory with provision for cubic variation of in plane displacements and parabolic variation of the normal displacement has been considered for detailed study numerical results have been obtained for infinite plate strip simply supported on opposite edges and infinitely long in the other direction subjected to sinusoidal static load displacements strains and stresses are compared with the exact solution results by the classical plate theory levinson s theory and a higher order theory based on partial deflections are also included this study shows that the present model can predict all displacements strains and stresses reasonably accurately further it is also noted that the statically equivalent estimates to transverse stresses from classical theory and the corresponding strains also agree closely with the exact solution

algorithmic analysis of programs with well quasi ordered domains over the past few years increasing research effort has been directed towards the automatic verification of infinite state systems this paper is concerned with identifying general mathematical structures which can serve as sufficient conditions for achieving decidability we present decidability results for a class of systems called well structured systems which consist of a finite control part operating on an infinite data domain the results assume that the data domain is equipped with a preorder which is a well quasi ordering such that the transition relation is monotonic a simulation with respect to the preorder we show that the following properties are decidable for well structured systems reachability whether a certain set of control states is reachable other safety properties can be reduced to the reachability problem eventuality whether all executions eventually reach a given set of control states represented as afp in ctl simulation whether there exists a simulation between a finite automaton and a well structured system the simulation problem will be shown to be decidable in both directions we also describe how these general principles subsume several decidability results from the literature about timed automata relational automata petri nets and lossy channel systems

static analysis of thick rectangular laminated plates three dimensional elasticity solutions via differential quadrature element method this article presents the first endeavor to develop the differential quadrature element method for static solution of three dimensional elasticity equations of thick rectangular laminated composite plates the domain decomposition technique is employed to decompose a laminated plate into elements according to material layers the differential quadrature dq method is then applied to each element where the material properties are continuous to form the element weighting coefficient matrix and element force vector the discretized element weighting coefficient matrices and element force vectors are assembled together to form the global weighting coefficient matrix and global force vector for the whole plate using connection conditions the solution for the entire plate is obtained by solving the final algebraic equation system detailed formulations and numerical procedures are presented and the convergence characteristics of the method are investigated the numerical results are then compared where possible with the analytical solutions to verify the present solutions consequently some new numerical results are computed and analyzed using the present numerical method for laminated rectangular plates with different boundary conditions which are not solvable directly by the global dq method

3 d theory versus 2 d approximate theory of free orthotropic isotropic plate and shell vibrations part 1 derivation of governing equations in part 1 of the paper the basic assumptions of the shells with added masses considered are introduced they serve for a derivation of the governing equations which are analyzed in part 2 of the paper

handling infinitely branching well structured transition systems abstract most decidability results concerning well structured transition systems apply to the finitely branching variant yet some models inserting automata petri nets are naturally infinitely branching here we develop tools to handle infinitely branching wsts by exploiting the crucial property that in the ideal completion of a well quasi ordered set downward closed sets are finite unions of ideals then using these tools we derive decidability results and we delineate the undecidability frontier in the case of the termination the maintainability and the coverability problems coverability and boundedness under new effectiveness conditions are shown decidable

analyticity of entropy rate of hidden markov chains we prove that under mild positivity assumptions the entropy rate of a hidden markov chain varies analytically as a function of the underlying markov chain parameters a general principle to determine the domain of analyticity is stated an example is given to estimate the radius of convergence for the entropy rate we then show that the positivity assumptions can be relaxed and examples are given for the relaxed conditions we study a special class of hidden markov chains in more detail binary hidden markov chains with an unambiguous symbol and we give necessary and sufficient conditions for analyticity of the entropy rate for this case finally we show that under the positivity assumptions the hidden markov chain itself varies analytically in a strong sense as a function of the underlying markov chain parameters

a continuum three dimensional vibration analysis of thick rectangular plates abstract this paper presents a continuum three dimensional ritz formulation for the vibration analysis of homogeneous thick rectangular plates with arbitrary combinations of boundary constraints this model is formulated on the basis of the linear three dimensional small deformation elasticity theory to predict the vibratory responses of these thick rectangular plates the displacement fields in the transverse and in plane directions are expressed by sets of orthogonally generated polynomial functions these shape functions are intrinsically a product of a class of orthogonal polynomial functions and a basic function which are chosen to satisfy the essential geometric boundary conditions at the outset sets of frequency data for plates with various aspect ratios and thickness ratios have been presented these data are used to examine the merits and limitations of the classical plate theory and mindlin plate theory by direct comparisons finally using the three dimensional continuum approach sets of first known deformed mode shapes have been generated thus helping to understand the vibratory motion furthermore these results may also serve as the benchmark to further research into the refined plate theories

a generalization of shear deformation theories for axisymmetric multilayered shells a generalization of geometrically linear shear deformation theories for small elastic strains is presented for multilayered axisymmetric shells of general shape without any assumption other than neglecting the transverse normal strain the shear is taken into account by using a function f which is introduced in the assumed kinematics the boundary value problem is derived from the principle of virtual power with the shear function f in the kinematics all equations are directly applicable to kirchhoff love first order shear deformation third order shear deformation theories and obviously the proposed generalized shear deformation theory by using a certain sine shear function no shear correction factors are needed with the proposed generalization of shear deformation theories a numerical evaluation of the new theory is presented and compared with the above classic theories for a simply supported thick laminated cylindrical shell under an internal pressure

warping displacement of timoshenko beam model abstract a refined timoshenko beam model which takes into account warping of the cross sections is presented the model extends saint venant s theory of uniform torsion to the generic loading of a beam in a coherent manner the use of kinetic and kinematic assumptions virtual work expression of full elasticity problem and the principle of virtual work in derivation brings the presentation to the usual context of engineering models a new definition of the warping displacement in terms of a variational problem is one of the outcomes boundary value problems for the stretch shear bending and torsion loading modes are also given analytic and numeric solutions to warping displacements refined constitutive equations and correction factors for circular rectangle triangle and open annular cross sections of isotropic material are compared with expressions in literature as an interesting detail shear correction factors are found to be purely geometrical quantities which contradicts many findings in literature

refined one dimensional formulations for laminated structure analysis this paper proposes one dimensional formulations based on hierarchical expansions of the unknown displacement variables for the analysis of multilayered structures made of anisotropic composite layers the hierarchical technique shows variable kinematic properties and it is based on the carrera unified formulation two different classes of refined theories are proposed the first expands the unknown variables in terms of power polynomials of the cross sectional coordinates it consists of a taylor like expansion the second class of onedimensional theories uses lagrange polynomials lagrange expansion and subdomain discretizations of the cross section and it leads to only pure displacements as the unknown variables taylor like expansion is used to develop equivalent single layer formulations and lagrange expansion is used to construct both equivalent single layer and layerwise descriptions the finite element method is employed to develop numerical applications using the carrera unified formulation finite element matrices are obtained in terms of a few fundamental nuclei that are formally independent of all the considered one dimensional formulations a number of numerical examples are given concerning on beams plates and more complex structures comparisons with results from plate and solid models are provided the following has been concluded 1 the proposed formulation represents a reliable compact and accurate method to develop refined one dimensional models 2 the present one dimensional models are very effective at detecting both global and local responses of composite structures 3 shell and solidlike results are obtained with a significant reduction in the computational costs

dynamics of transversely vibrating beams using four engineering theories abstract in this paper the full development and analysis of four models for the transversely vibrating uniform beam are presented the four theories are the euler bernoulli rayleigh shear and timoshenko first a brief history of the development of each beam model is presented second the equation of motion for each model and the expressions for boundary conditions are obtained using hamilton s variational principle third the frequency equations are obtained for four sets of end conditions free free clamped clamped hinged hinged and clamped free the roots of the frequency equations are presented in terms of normalized wave numbers the normalized wave numbers for the other six sets of end conditions are obtained using the analysis of symmetric and antisymmetric modes fourth the orthogonality conditions of the eigenfunctions or mode shape and the procedure to obtain the forced response using the method of eigenfunction expansion is presented finally a numerical example is shown for a non slender beam to signify the differences among the four beam models

derivatives of entropy rate in special families of hidden markov chains consider a hidden markov chain obtained as the observation process of an ordinary markov chain corrupted by noise recently zuk et al showed how in principle one can explicitly compute the derivatives of the entropy rate of at extreme values of the noise namely they showed that the derivatives of standard upper approximations to the entropy rate actually stabilize at an explicit finite time we generalize this result to a natural class of hidden markov chains called black holes we also discuss in depth special cases of binary markov chains observed in binary symmetric noise and give an abstract formula for the first derivative in terms of a measure on the simplex due to blackwell

reduction and covering of infinite reachability trees abstract we present a structure for transition systems with which the main decidability results on petri nets can be generalized to structured transition systems we define the reduced reachability tree of a structured transition system it allows one to decide the finite reachability tree problem also called the finite termination problem and the finite reachability set problem a general definition of the coverability set is given and the procedure of karp and miller is extended for well structured transition systems we show then that the coverability problem is a decidable problem in the framework of well structured transition systems finally we introduce structured set of terminal states and we show that the finite reachability tree problem and the finite reachability set problem are decidable coverability is an open problem for structured transition systems with a structured set of terminal states

frequency analysis of symmetrically laminated plates with free edges abstract this paper is concerned with the estimation of natural frequencies of undamaged symmetrically laminated plates rectangular circular annular and elliptical having completely free edges the rayleigh ritz energy approach is employed here to obtain the approximate natural frequencies and the associated mode shapes the plates are considered to be thin and to undergo small deflections satisfying kirchhoff s hypothesis a complete power series is used as admissible functions for in plane and out of plane displacements in the numerical examples the accuracy of the present results is compared with the other analytical results available in the literature the effects of the shape and size of the plate number of plies and the fiber orientation on the natural frequencies flexural mode of symmetrically laminated plates are documented the mode shape corresponding to each frequency has been identified in this paper

on the optimality of symbol by symbol filtering and denoising we consider the problem of optimally recovering a finite alphabet discrete time stochastic process x sub t from its noise corrupted observation process z sub t in general the optimal estimate of x sub t will depend on all the components of z sub t on which it can be based we characterize nontrivial situations i e beyond the case where x sub t z sub t are independent for which optimum performance is attained using symbol by symbol operations a k a singlet decoding meaning that the optimum estimate of x sub t depends solely on z sub t for the case where x sub t is a stationary binary markov process corrupted by a memoryless channel we characterize the necessary and sufficient condition for optimality of symbol by symbol operations both for the filtering problem where the estimate of x sub t is allowed to depend only on z sub t sub t spl les t and the denoising problem where the estimate of x sub t is allowed dependence on the entire noisy process it is then illustrated how our approach which consists of characterizing the support of the conditional distribution of the noise free symbol given the observations can be used for characterizing the entropy rate of the binary markov process corrupted by the binary symmetric channel bsc in various asymptotic regimes for general noise free processes not necessarily markov general noise processes not necessarily memoryless and general index sets random fields we obtain an easily verifiable sufficient condition for the optimality of symbol by symbol operations and illustrate its use in a few special cases for example for binary processes corrupted by a bsc we establish under mild conditions the existence of a spl delta sup 0 such that the say what you see scheme is optimal provided the channel crossover probability is less than spl delta sup finally we show how for the case of a memoryless channel the large deviations ld performance of a symbol by symbol filter is easy to obtain thus characterizing the ld behavior of the optimal schemes when these are singlet decoders and constituting the only known cases where such explicit characterization is available

three dimensional vibration analysis of cantilevered skew plates three dimensional 3 d free vibration of cantilevered thick skew plates is analyzed based on the exact linear and small strain elasticity theory the skew domain of the plate is mapped onto a cubic domain a set of triplicate chebyshev polynomials multiplied by a boundary function is developed as the trial functions of each displacement components using the ritz method the eigenvalue equation is derived from the strain energy and kinetic energy of the plate the vibration modes are divided into the antisymmetric and symmetric ones in the thickness direction therefore can be studied individually the convergence study shows that the first eight frequency parameters for each mode categories can be obtained with an accuracy of at least four significant figures the effect of geometric parameters such as skew angle aspect ratio and span thickness ratio on frequency parameters is studied the results are compared with those obtained by using the algebraic polynomials as trial functions and the 3 d finite element solutions respectively it is shown that the chebyshev polynomials can provide better numerical stability than the algebraic polynomials especially for the plates with large skew angle the present results can serve as the benchmark data for the accuracy evaluation of other computational techniques

vibrations of cantilevered skewed plates with corner stress singularities in conjunction with classical thin plate theory the ritz trial space of assumed transverse displacement functions consists of algebraic polynomials which are mathematically complete and corner functions which account for the singular behaviour of bending stresses at the reentrant corner

relationships between classical and shear deformation theories of axisymmetric circular plates the exact relationships between the deflections slopes rotations shear forces and bending moments of a third order theory and those of the classical theory and the first order shear deformation theory for axisymmetric bending of isotropic circular plates are developed the relationships enable one to obtain the solutions of the third order theory from any known classical or first order theory solutions of axisymmetric circular plates for any set of boundary conditions and transverse loads the relationships may also be used to develop finite element models of axisymmetric bending of circular plates according to the first order and third order theories

vibration and buckling of deep beam columns on two parameter elastic foundations natural frequencies and buckling stresses of a deep beam column on two parameter elastic foundations are analyzed by taking into account the effect of shear deformation depth change the transverse displacement w can vary in the depth direction of beam columns and rotatory inertia by using the method of power series expansion of displacement components a set of fundamental dynamic equations of a one dimensional higher order theory for thin rectangular beam columns subjected to axial stress is derived through hamilton s principle several sets of truncated approximate theories are applied to solve the eigenvalue problems of a simply supported deep elastic beam column in order to assure the accuracy of the present theory convergence properties of the minimum natural frequency and the buckling stress are examined in detail it is noted that the present approximate theories can predict the natural frequencies and buckling stress of deep beam columns on elastic foundations accurately compared with the timoshenko beam theory and the classical beam theory

harmonic measures for distributions with finite support on the mapping class group are singular kaimanovich and masur showed that a random walk on the mapping class group for an initial distribution whose support generates a nonelementary subgroup when projected into teichmuller space converges almost surely to a point in the space pmf of projective measured foliations on the surface this defines a harmonic measure on pmf here we show that when the initial distribution has finite support the corresponding harmonic measure is singular with respect to the natural lebesgue measure class on pmf

on the hausdorff dimension of invariant measures of weakly contracting on average measurable ifs we consider measures which are invariant under a measurable iterated function system with positive place dependent probabilities in a separable metric space we provide an upper bound of the hausdorff dimension of such a measure if it is ergodic we also prove that it is ergodic iff the related skew product is

three dimensional free vibration analysis of isotropic rectangular plates using the b spline ritz method abstract this paper presents three dimensional free vibration analysis of isotropic rectangular plates with any thicknesses and arbitrary boundary conditions using the b spline ritz method based on the theory of elasticity the proposed method is formulated by the ritz procedure with a triplicate series of b spline functions as amplitude displacement components the geometric boundary conditions are numerically satisfied by the method of artificial spring to demonstrate the convergence and accuracy of the present method several examples with various boundary conditions are solved and the results are compared with other published solutions by exact and other numerical methods based on the theory of elasticity and various plate theories rapid stable convergences as well as high accuracy are obtained by the present method the effects of geometric parameters on the vibrational behavior of cantilevered rectangular plates are also investigated the results reported here may serve as benchmark data for finite element solutions and future developments in numerical methods

free vibrations of a simply supported rectangular plate an exact elasticity solution abstract an exact three dimensional solution for the free vibrations of simply supported rectangular plates of arbitrary thickness within the linear theory of elastodynamics is given in this paper the solution obtained in a semi inverse fashion as was the solution of the elastostatic problem for such plates satisfies all of the boundary conditions of the problem in a pointwise manner it is found that there are two types of modes of oscillation possible which are consistent with the kinematic assumptions made to find the semi inverse solution other modes of oscillation may exist in the three dimensional theory of elastodynamics for such plates but our kinematic assumptions would not be consistent with such modes the two types of modes found are analogous to the flexural modes of classical plate theory and the thickness twist modes here called breathing modes of mindlin plate theory some numerical results are given which indicate that the predictions of mindlin plates are uncannily good approximations to the flexural frequencies given by the present three dimensional analysis even for very thick plates however the predictions of mindlin plate theory for the thickness twist or breathing frequencies are not nearly so good these discrepancies are discussed briefly in an appendix

normal modes in a continuum model of vocal fold tissues the ritz method is used to calculate eigenmodes and eigenfrequencies in a continuum model of the vocal folds the investigation represents a rectification and extension of previous studies emphasizing the indispensability of utilizing natural boundary conditions when computing the characteristic modes of a system concurring with previous assertions two of the lower order eigenmodes are theorized to play a major role in facilitating self oscillation of the folds during phonation one mode related to vertical phasing is shown to have a more direct control over glottal convergence divergence than indicated in previous calculations unlike lumped element models the continuum model predicts that the eigenfrequencies of the two modes are closely spaced over an extensive range of tissue sizes and stiffnesses this finding may help explain why the two modes entrain so naturally over a wide range of phonatory adjustments in human phonation

deformation of short composite beam using refined theories high order flexural theories for short laminated composite beams subjected to mechanical and thermal loading are presented the formulation allows for warping of the cross section of the beam and eliminates the need for using arbitrary shear correction coefficients as in other theories based on higher order shear deformation theories the governing equations are obtained using the principle of virtual work pvw the justification for use of higher order shear deformation theories is established for short and composite beams where cross sectional warping is predominant

bem analysis of free vibration problems using polynomial particular integrals abstract the development of a boundary element method for free vibration analysis using particular solutions is discussed the formulation presented is based on treating the forcing function in the governing differential equation as an initially unknown distributed body force within the domain the volume integral due to this body force is then eliminated by approximating the inertia force by global interpolation and polynomial function representations and finding particular solutions for the governing inhomogeneous equations the resulting non symmetric system matrix is solved by using a modified arnoldi s algorithm that takes advantage of the special structure of the substructured boundary element method the techniques described here are embedded in a computer program gpbest and the numerical examples arc solved by using this computer code

on the three dimensional vibration analysis of simultaneously skewed and twisted cantilevered parallelepipeds the natural frequencies of simultaneously skewed and twisted cantilevered parallelepipeds are determined using the ritz method the present work is the first known three dimensional study of the problem assumed displacement functions are in the form of algebraic polynomials which satisfy the fixed face conditions exactly and which are mathematically complete reasonably accurate natural frequencies are calculated for low aspect ratio thick parallelepipeds having arbitrary degrees of twist and skewness detailed numerical studies show that a three dimensional analysis is essential in monitoring complicated coupled mode sensitivities in the variation of non dimensional natural frequencies with increasing skew and twist angles and thickness ratio results obtained using the present method are compared with those obtained in a detailed three dimensional finite element analysis where the suitability and limitations of s version solid element discretizations are clearly brought out

up to lowest 100 frequencies of rectangular plates using jacobi polynomials and tsndt abstract this paper finds up to lowest 100 free vibration frequencies of isotropic and linearly elastic plates with thickness to side length ratio varying from 0 001 to 0 5 by using the ritz method a third order shear and normal deformable plate theory tsndt and weighted jacobi polynomials as admissible functions that are mutually orthogonal and exactly satisfy essential boundary conditions the numerical method is stable even for 18th degree polynomials as basis functions it is shown that this approach requires fewer degrees of freedom than those in the traditional finite element method fem to find converged lowest 100 frequencies and the corresponding mode shapes no shear correction factor is employed in the tsndt the presently computed results agree well with those from either analytical or numerical solutions of the corresponding 3 dimensional linearly elastic problems obtained with the commercial fe software abaqus furthermore results for plates made of an incompressible material can be computed by setting poisson s ratio 0 49

absolutely continuous convolutions of singular measures and an application to the square fibonacci hamiltonian author s damanik d gorodetski a solomyak b abstract 2015 we prove for the square fibonacci hamiltonian that the density of states measure is absolutely continuous for almost all pairs of small coupling constants this is obtained from a new result we establish about the absolute continuity of convolutions of measures arising in hyperbolic dynamics with exact dimensional measures

beam theory for strongly orthotropic materials abstract this paper presents a displacement based model for orthotropic beams under plane linear elasticity based on the only kinematic assumption of transverse inextensibility any given axial and transverse loading as well as boundary conditions at the beam ends are considered the solution is decomposed into the principal and the residual part corresponding to the interior and the boundary problems which are obtained by series expansions of polynomial functions and eigenfunctions respectively it is proved that the proposed one dimensional theory gives both interior and boundary exact two dimensional elasticity solutions for strongly orthotropic materials i e for ratio between shear modulus and axial young modulus approaching zero for isotropic and orthotropic materials the accuracy of the beam model is also analysed and compared with that of other theories in particular the complementary energy error of the interior solution with respect to two dimensional elasticity is evaluated the asymptotic estimate of the characteristic decay length of end effects given in choi and horgan j appl mech asme 44 424 430 1977 by two dimensional analysis is reobtained and the range of validity of boundary solution is discussed the numerical results presented agree very well with exact and finite element solutions even in the neighbourhood of clamped cross sections where the solution is mainly governed by the boundary problem

on the two frequency spectra of timoshenko beams abstract this paper is concerned with the question of whether there are indeed two distinct spectra of frequencies for the transverse vibrations of timoshenko beams as has been claimed by a number of prior authors for the case of the simply supported beam and more recently for beams supported in an arbitrary manner elementary analysis leads to the conclusion that there is only a single frequency spectrum in the particular case of the simply supported beam the two frequency spectra viewpoint may be expedient as a device to compute frequencies but does not serve otherwise to explain the complex dynamical behavior of timoshenko beams

on coupled longitudinal and lateral vibrations of elastic rods abstract in this paper the coupled longitudinal and lateral vibrations of a rectangular parallelepiped composed of a uniform isotropic elastic body are examined the one dimensional model for the body was developed by green naghdi and several of their co workers it is based on a cosserat or directed rod theory the frequency spectrum is found to divide naturally into three regions which are separated by degenerate cases when the cross section of the body is square a natural splitting of the modes occurs one half of this split involves motions coupling the axial extension and symmetric lateral deformation of the body the other half involves asymmetric lateral deformations the cases of a free free rod and a cantilevered rod are discussed and the results compared to existing works in the literature which use the three dimensional theory of elasticity to model the vibrations