exact closed form solution for the vibration modes of the euler bernoulli beam with multiple open cracks abstract in this study exact closed form expressions for the vibration modes of the euler bernoulli beam in the presence of multiple concentrated cracks are presented the proposed expressions are provided explicitly as functions of four integration constants only to be determined by the standard boundary conditions the enforcement of the boundary conditions leads to explicit expressions of the natural frequency equations besides the evaluation of the natural frequencies neither computational work nor recurrence expressions for the vibration modes are required the cracks that are not subjected to the closing phenomenon are modelled as a sequence of dirac s delta generalised functions in the flexural stiffness the eigen mode governing equation is formulated over the entire domain of the beam without enforcement of any continuity conditions which are already accounted for in the adopted flexural stiffness model the vibration modes of beams with different numbers of cracks under different boundary conditions have been analysed by means of the proposed closed form expressions in order to show their efficiency

periods of residual automorphic forms abstract we develop a technique for computing period integrals of noncuspidal automorphic forms applications include a formula for the integral of a square integrable automorphic form on gl n a e over gl n f gl n a f 1 for a quadratic extension e of a number field f and a characterization of residual automorphic representations on which the period integral is nonvanishing

two multiplicity free permutation representations of the general linear groupgl n q 2 soit q une puissance d un nombre premier p et soit g gl n q 2 le groupe lineaire general de degre n sur gf q 2 soit u u n q le groupe unitaire de degre n sur gf q 2 et m gl n q le groupe lineaire general sur gf q on etudie les caracteres des representations permutation de g sur les co ensembles de a la fois u et m

a unified matrix polynomial approach to modal identification abstract one important current focus of modal identification is a reformulation of modal parameter estimation algorithms into a single consistent mathematical formulation with a corresponding set of definitions and unifying concepts particularly a matrix polynomial approach is used to unify the presentation with respect to current algorithms such as the least squares complex exponential lsce the polyreference time domain ptd ibrahim time domain itd eigensystem realization algorithm era rational fraction polynomial rfp polyreference frequency domain pfd and the complex mode indication function cmif methods using this unified matrix polynomial approach umpa allows a discussion of the similarities and differences of the commonly used methods the use of least squares ls total least squares tls double least squares dls and singular value decomposition svd methods is discussed in order to take advantage of redundant measurement data eigenvalue and svd transformation methods are utilized to reduce the effective size of the resulting eigenvalue eigenvector problem as well

asai l functions and jacquet s conjecture we give a conceptually simple proof of the square integrable case of a conjecture of jacquet concerning distinguished representations of the general linear group over a local field of characteristic zero the proof is based on consideration of the rankin selberg integral representation of the generalized asai l function and utilizes global methods

complex modes and frequencies in damped structural vibrations it is demonstrated that a state space formulation of the equation of motion of damped structural elements like cables and beams leads to a symmetric eigenvalue problem if the stiffness and damping operators are self adjoint and that this is typically the case in the absence of gyroscopic forces the corresponding theory of complex modal analysis of continuous systems is developed and illustrated in relation to optimal damping and impulse response of cables and beams with discrete viscous dampers

dynamic response of a viscously damped cantilever with a viscous end condition this paper deals with the dynamical analysis of a cantilevered bernoulli euler beam subjected to distributed external viscous damping in span and with a viscous end condition by a single damper in order to evaluate the vibration characteristics of the system a procedure is presented where overdamped and underdamped modes are investigated simultaneously via the dynamic stiffness matrix of the system further the orthogonality conditions which allow the decoupling of the equations of motion in terms of principal coordinates are derived then the complex frequency response function is obtained through a formula which was established for the receptance matrix previously finally the dynamic impulse response function of the system is evaluated in the time domain comparison with the numerical results obtained via a boundary value formulation justifies the approaches used here

physically based dirac s delta functions in the static analysis of multi cracked euler bernoulli and timoshenko beams abstract dirac s delta functions enable simple and effective representations of point loads and singularities in a variety of structural problems leading very often to elegant and otherwise unworkable closed form solutions this is the case of cracked beams under static loads whose theoretical and practical significance has attracted in recent years the interest of many researchers nevertheless analytical formulations currently available for this problem are not completely satisfactory either in terms of computational efficiency when the continuity conditions must be enforced with auxiliary equations or in terms of physical consistency when the singularities in the beam s flexural rigidity are represented with dirac s delta functions having a questionable negative sign these considerations motivate the present study which offers a novel and physically based modelling of slender euler bernoulli beams and short timoshenko beams with any number and severity of cracks conducing in both cases to exact closed form solutions for validation purposes a standard finite element code is used along with two nascent deltas uniform and gaussian density functions to describe a smeared increase in the bending flexibility around the abscissa of the crack

complex modal analysis of rods with viscous damping devices abstract the complex modal analysis of rods equipped with an arbitrary number of viscous damping devices is addressed the following types of damping devices are considered external grounded spring damper attached mass spring damper and internal spring damper within a standard 1d formulation of the vibration problem the theory of generalized functions is used to model axial stress and displacement discontinuities at the locations of the damping devices by using the separate variable approach a simple solution procedure of the motion equation leads to exact closed form expressions of the characteristic equation and eigenfunctions which inherently fulfill the required matching conditions at the locations of the damping devices based on the characteristic equation a closed form sensitivity analysis of the eigensolution is implemented the displacement eigenfunctions exhibit orthogonality conditions they can be used with the complex mode superposition principle to tackle forced vibration problems and in conjunction with the stress eigenfunctions to build the exact dynamic stiffness matrix of the rod for complex modal analysis of truss structures numerical results are discussed for a variety of parameters

quasi copulas with a given sub diagonal section abstract as is well known the frechet hoeffding bounds are the best possible for both copulas and quasi copulas for every quasi copula q max x y 1 0 q x y min x y for all x y 0 1 sharper bounds hold when the quasi copulas take prescribed values e g along their diagonal or horizontal resp vertical sections here we pursue two goals first we investigate construction methods for quasi copulas with a given sub diagonal section i e with prescribed values along the straight line segment joining the points x 0 0 and 1 1 x 0 for x 0 0 1 then we determine the best possible bounds for sets of quasi copulas with a given sub diagonal section

a closed form solution of a bernoulli euler beam on a viscoelastic foundation under harmonic line loads fourier transform is used in this paper to solve the problem of steady state response of a beam on a viscoelastic foundation subjected to a harmonic line load the solution is constructed in the form of the convolution of the green function of the beam the theorem of residue is employed to evaluate the generalized integral such that a closed form solution can be achieved all the different combinations of damping and vibration frequency are discussed and analytical solutions are presented as a special case the solution of the beam on a winkler foundation is also discussed the validation of the solution is verified by considering the static solution of the beam and comparing the degraded solution to a well known result the closed form expression of the result can be used to construct algorithms for the inverse problems of non destructive testing of pavement structures using vibration devices

a fourier series solution for the transverse vibration response of a beam with a viscous boundary abstract this paper presents the generalized fourier series solution for the transverse vibration of a beam subjected to a viscous boundary the model of the system produces a non self adjoint eigenvalue like problem which does not yield orthogonal eigenfunctions therefore such functions cannot be used to calculate the coefficients of expansion in the fourier series furthermore the eigenfunctions and eigenvalues are complex valued nevertheless the eigenfunctions can be utilized if the space of the operator is extended and a suitable inner product is defined the methodology presented in this paper utilizes hilbert space methods and is applicable in general to other problems of this type as an adjunct to the theoretical discussion the results from numerical simulations are presented

esprit estimation of signal parameters via rotational invariance techniques an approach to the general problem of signal parameter estimation is described the algorithm differs from its predecessor in that a total least squares rather than a standard least squares criterion is used although discussed in the context of direction of arrival estimation esprit can be applied to a wide variety of problems including accurate detection and estimation of sinusoids in noise it exploits an underlying rotational invariance among signal subspaces induced by an array of sensors with a translational invariance structure the technique when applicable manifests significant performance and computational advantages over previous algorithms such as mem capon s mlm and music

excitation and sensing of multiple vibrating traveling waves in one dimensional structures lightly damped vibrating structures normally exhibit vibration patterns that are a combination of standing waves i e mode shapes traveling waves on the other hand occur only under special circumstances in this work the theoretical conditions under which traveling waves prevail in finite structure are investigated these conditions are highly sensitive to the geometrical and material parameters of the structure and in particular the vibration pattern is sensitive to the boundary conditions there are several combinations under which traveling waves cannot be formed and these ill posed cases are analyzed in some detail to overcome the unavoidable uncertainties in a model a tuning process based on identification and optimization of the excitation is suggested the identification process uses a parametric algorithm to estimate the wavenumbers of the measured vibrations then the waves are decomposed into traveling and standing parts and the external excitation is tuned until a pure traveling wave is formed

local e factors and characters of gl 2 introduction the representation theory of gl 2 k for k a nonarchimedean local field is somewhat more complicated than the corresponding theory for gl 2 r in particular the formulas for the characters of discrete series representation of gl 2 r have a concise closed form while the published character formulas for supercuspidal representations of gl 2 k occupy several pages 10 14 the purpose of this paper is to give a concise formula for the character of certain infinite dimensional representations of gl 2 k the representations considered are admissible in the sense that the stabilizer of a vector in the representation space is open in gl 2 k and the subspace stabilized by an open compact subgroup of gl 2 k is finite dimensional irreducible admissible representations ir of gl 2 k satisfy schur s lemma so that the center k of gl 2 k acts by multiplication by a quasicharacter there exists a locally constant character function ch defined on a dense open subgroup of gl 2 k which determines the isomorphism class of ir 7 section 7 jacquet and langlands 7 section 2 introduced factors e 10 x attached to the twist of ir by quasicharacters x of k which describe the action of r in a specific model for each separable quadratic extension l of k there exists an irreducible admissible representation bcl k 1r of gl 2 l the base change of ir to l 9 section 2 this representation of gl 2 l enters into the expression for the character the main result of this paper is the following formula recall that conjugacy classes of nonsplit cartan subgroups are parameterized by quadratic separable field extensions l of k via embeddings of l in gl 2 k

on applications of generalized functions to beam bending problems using a mathematical approach this paper seeks an eacient solution to the problem of beams bending under singular loading conditions and having various jump discontinuities for two instances the boundary value problem that describes beam bending cannot be written in the space of classical functions in the first instance the beam is under singular loading conditions such as point forces and moments and in the second instance the dependent variable s and its derivatives have jump discontinuities in the most general case we consider both instances first we study singular loading conditions and present a theorem by which the equivalent distributed force of a general class of singular loading conditions can be found as a consequence of obtaining the equivalent distributed force of a distributed moment we find a mathematical explanation for the corner condition in classical plate theory while plate theory is not the focus of this paper this explanation is interesting then beams with various jump discontinuities are considered when beams have jump discontinuities the form of the governing diaerential equations changes we find the governing diaerential equations in the space of generalized functions it is shown that for euler bernoulli beams with jump discontinuities the operator of the diaerential equation remains unchanged only the force term changes so that delta function and its distributional derivatives appear within it but for timoshenko beams with jump discontinuities in addition to changes in the force terms the operator of one of the governing diaerential equations changes we then propose a new method for solving these equations this method which we term the auxiliary beam method is to solve the governing diaerential equations not in the space of generalized functions but rather to solve them by means of solving equivalent boundary value problems in the space of classical functions the auxiliary beam method reduces the number of diaerential equations and at the same time obviates the need to solve these diaerential equations in the space of generalized functions which can be more diacult 7 2000 elsevier science ltd all rights reserved

on distinguished square integrable representations for galois pairs and a conjecture of prasad we prove an integral formula computing multiplicities of square integrable representations relative to galois pairs over p adic fields and we apply this formula to verify two consequences of a conjecture of dipendra prasad one concerns the exact computation of the multiplicity of the steinberg representation and the other the invariance of multiplicities by transfer among inner forms

vibration of non uniform rods and beams we show that for some non uniform rods and beams the equation of motion can be transformed into the equation of motion for a uniform rod or beam then when the ends are completely fixed the eigenvalues of the non uniform continuum are the same as those of uniform rods or beams for other end support conditions exact solutions are obtained an efficient procedure is used to analyze the free vibration of non uniform beams with general shape and arbitrary boundary conditions simple formulas are presented for predicting the fundamental natural frequency of non uniform beams with various end support conditions

wave propagation in continuous periodic structures research contributions from southampton 1964 1995 abstract after brief reference to some early studies by other investigators this paper focuses mainly on methods developed at the university of southampton since 1964 to analyze and predict the free and forced wave motion in continuous periodic engineering structures beginning with receptance methods which have been applied to periodic beams and rib skin structures it continues with a method of direct solution of the wave equation this uses floquet s principle and has been applied to beams and quasi one dimensional periodic plates and cylindrical shells sample curves of the propagation and attenuation constants pertaining to these structures are presented a limited discussion of the transfer matrix then follows after which the method of space harmonics is introduced as the method best suited to the prediction of sound radiated from a vibrating periodic structure reviewed next are some theorems and variational principles relating to periodic structures which have been developed at southampton and which form a basis for finding natural frequencies of finite structures or for computing free and forced wave notion by energy methods this has led to the finite element method in its standard and hierarchical forms being used to study wave motion in genuine two dimensional and three dimensional structures examples of this work are shown the method of phased array receptance functions is then introduced as possibly the easiest way of setting up exact equations for the propagation constants of uniform quasi one dimensional periodic structures a summary is finally presented of the limited and early work performed at southampton on simple disordered periodic structures

singularity aspects of archimedean copulas abstract calculating markov kernels of two dimensional archimedean copulas allows for very simple and elegant alternative derivations of various important formulas including kendall s distribution function and the measures of the level curves more importantly using markov kernels we prove the existence of singular archimedean copulas a with full support of the following two types i all conditional distribution functions y f x a y are discrete and strictly increasing ii all conditional distribution functions y f x a y are continuous strictly increasing and have derivative zero almost everywhere the results show that despite of their simple analytic form archimedean copulas can exhibit surprisingly singular behavior

efficiency and tuning of viscous dampers on discrete systems an approximate solution is developed to the complex eigenproblem associated with free vibrations of a discrete system with several viscous dampers in order to facilitate optimal placement and sizing of added dampers in structures the approximate solution is obtained as an interpolation between the solutions of the two limiting eigenproblems the undamped eigenproblem and the constrained eigenproblem in which each damper is replaced with a rigid link an explicit form of the approximate solution is developed for cases in which the difference between these limiting eigensolutions is sufficiently small and an iterative solution scheme is presented for cases in which the difference is larger these results allow the efficiency and tuning of viscous dampers to be investigated by solving only the two limiting real valued eigenproblems the application of the approximate formulation is illustrated for a 10 story building model with added dampers

coupled bending torsional dynamic stiffness matrix for beam elements explicit expressions for the coupled bending torsional dynamic stiffness matrix of a uniform beam element are derived in an exact sense by solving the governing differential equation of the beam implementation of the derived dynamic stiffness matrix in a space frame computer program is discussed with particular reference to an established algorithm to enable vibration analysis of coupled systems to be made the application of the theory is demonstrated by an illustrative example wherein the results for a cantilever beam with a substantial amount of coupling between bending and torsion are highlighted the correctness of the theory is confirmed to a high degree of accuracy by computed results and numerical checks

distinction of the steinberg representation for inner forms of gl n let f be a non archimedean local field of characteristic not 2 let d be a division algebra of dimension d 2 over its center f and e a quadratic extension of f if m is a positive integer to a character chi of e one can attach the steinberg representation st chi of g gl m d otimes f e let h be the group gl m d we prove that st chi is h distinguished if and only if chi f is the quadratic character eta e f md 1 where eta e f is the character of f with kernel the norms of e we also get multiplicity one for the space of invariant linear forms

modal and characteristics based approaches for modeling elastic waves induced by time dependent boundary conditions in this paper we present a characteristics based approach for solving elastic wave problems with time dependent traction boundary conditions a generalized mathematical model for this important class of problems is expressed as a set of first order linear hyperbolic partial differential equations we analyze the mathematical structure of this first order linear system verify its hyperbolicity derive its characteristic form and deduce its eigenvalues eigenvectors and riemann invariants the eigenvalues correspond to the wave speeds while the riemann invariants are used to construct a solution by the method of characteristics we benchmark the method of characteristics against several popular modal approaches two of these which we refer to as the concentrated body force method cbfm and the homogeneous eigenfunction expansion method heem were developed to simplify the well established but tedious mindlin goodman method to homogenize the boundary conditions and enable modal analysis the cbfm and heem forgo the usual formalism of linear transformations a la mindlin goodman in favor of intuitive modeling assumptions and postulated solution structures we find however that these approaches introduce an artificial stress discontinuity at the forced boundary in their reformulated problems when these reformulated problems are solved by modal analysis spurious oscillations and significant overshoot similar to the gibbs phenomenon emerge in the stress profile at the artificial discontinuity we demonstrate that these oscillations and overshoot are physical manifestations of a series solution for stress obtained from term by term differentiation that is not uniformly convergent as required by the formalism of mathematical analysis the method of characteristics solution on the other hand is exact to within machine precision yielding no artificial discontinuities spurious oscillations or unphysical overshoot unlike the modal approaches the method of characteristics solves the first order problem with time dependent boundary conditions as is without any reformulation restructuring or postulated solution structures further its solutions require no post processing no a posteriori solution treatment like l hopital s rule to accommodate resonance resonant behavior is inherently captured without the emergence of singularities no term by term differentiation to deduce stress stress is primitive in a first order velocity stress formulation of elastodynamics and no convergence tests

vibration confinement in a general beam structure during harmonic excitations abstract in the present paper the green s function is utilized to provide a simple exact and direct analytical method for analysis of a beam structure of generic boundary conditions with attached springs and or finite masses the aim is to confine the vibration in a certain part of the structure the beam equation is based on the timoshenko beam theory with corrections for shear deformation and rotary inertia effects in the analysis the beam is driven by a harmonic external excitation the attached springs are modeled as simple reactions that provide transverse forces to the beam while each added mass provides a transverse force in addition to a moment at its location these forces moments act as secondary forces moments that reduce the response caused by the external force numerical simulations are conducted to find the optimal masses and or springs that confine the vibration in a certain chosen region the results were compared to that obtained from euler bernoulli beam theory beams that are excited by a bi harmonic force as well as dual excitation forces are analyzed in addition the case when the beams are excited near resonances is discussed also a method is proposed to impose a node at any desired location along the structure

distinguished representations shintani base change and a finite field analogue of a conjecture of prasad abstract let e f be a quadratic extension of fields and g a connected quasi split reductive group over f let g o p be the opposition group obtained by twisting g by the duality involution considered by prasad assume that the field f is finite let be an irreducible generic representation of g e when is a shintani base change lift of some representation of g o p f we give an explicit nonzero g f invariant vector in terms of the whittaker vector of this shows particularly that is g f distinguished when the field f is p adic the paper also proves that the duality involution takes an irreducible admissible generic representation of g f to its contragredient as a special case of this result all generic representations of g 2 f 4 or e 8 are self dual

dynamic analysis of a multi span uniform beam carrying a number of various concentrated elements abstract this paper employs the numerical assembly method nam to determine the exact frequency response amplitudes of a multiple span beam carrying a number of various concentrated elements and subjected to a harmonic force and the exact natural frequencies and mode shapes of the beam for the case of zero harmonic force first the coefficient matrices for the intermediate concentrated elements pinned support applied force left end support and right end support of a beam are derived next the overall coefficient matrix for the whole vibrating system is obtained using the numerical assembly technique of the conventional finite element method fem finally the exact dynamic response amplitude of the forced vibrating system corresponding to each specified exciting frequency of the harmonic force is determined by solving the simultaneous equations associated with the last overall coefficient matrix the graph of dynamic response amplitudes versus various exciting frequencies gives the frequency response curve for any point of a multiple span beam carrying a number of various concentrated elements for the case of zero harmonic force the above mentioned simultaneous equations reduce to an eigenvalue problem so that natural frequencies and mode shapes of the beam can also be obtained

multi cracked euler bernoulli beams mathematical modeling and exact solutions localized flexibility models of cracks enable one for simple and effective representation of the behavior of damaged beams and frames important applications such as the determination of closed form solutions and the development of diagnostic methods of analysis have attracted the interest of many researchers in recent years nevertheless certain fundamental questions have not been completely clarified yet one of these issues concerns with the mechanical justification of the macroscopic model of rotational elastic spring commonly used to describe the presence of an open crack in a beam under bending deformation two main analytical formulations have been recently proposed to take into account the singularity generated by the crack the crack is represented by suitable dirac s delta functions either in the beam s flexural rigidity or in the beam s flexural flexibility both approaches require some caution due to mathematical subtleties of the analysis motivated by these considerations in this paper we propose a justification of the rotational elastic spring model of an open crack in a beam in bending deformation we show that this localized flexibility model of a crack is the variational limit of a family of one dimensional beams when the flexural stiffness of these beams tends to zero in an interval centered at the cracked cross section and simultaneously the length of the interval vanishes in a suitable way we also show that the static and dynamic problem for the flexibility model of cracked beam can be formulated within the classical context of the theory of distributions avoiding the hindrances encountered in previous approaches to the problem in addition the proposed treatment leads to a simple and efficient determination of exact closed form solutions of both static and dynamic problems for beams with multiple cracks

test vectors for finite periods and base change abstract let e f be a quadratic extension of finite fields by a result of gow an irreducible representation of g gl n e has at most one non zero h invariant vector up to multiplication by scalars when h is gl n f or u n e f if does have an h invariant vector it is said to be h distinguished it is known from the work of gow that h distinction is characterized by base change from u n e f due to kawanaka when h is gl n f resp from gl n f due to shintani when h is u n e f assuming is generic and h distinguished we give an explicit description of the h invariant vector in terms of the bessel function of let be a non degenerate character of n g n h and let b be the normalized bessel function of on the whittaker model for the h average w 1 h h h h b of the bessel function we prove that w i n dim dim gl n e gl n f u n e f where is the irreducible representation of u n e f resp gl n f that base changes to when h is gl n f resp u n e f as an application we classify the members of a generic l packet of sl n e that admit invariant vectors for sl n f finally we prove a p adic analogue of our result for square integrable representations in terms of formal degrees by employing the formal degree conjecture of hiraga ichino ikeda 19

on differential properties of copulas we clarify the problem of the existence of functions obtained as particular restrictions of the first partial derivatives of a quasi copula and we show their role for characterizing the 2 increasing property the question of the existence of the one sided first partial derivatives of a copula along an affine section of the real unit square is discussed and new results and several examples are provided

a closed form solution of a longitudinal bar with a viscous boundary condition abstract a closed form solution of a longitudinal bar with a viscous boundary condition subjected to point loading is developed in this paper a new series solution is formulated that allows the time and space modes of the beam to decouple this expansion yields explicit eigenvalues and eigenvectors a frequency domain example is presented and the results are compared with finite element solutions of the same problem it is shown that the closed form solution is computationally more efficient than a finite element solution additionally the truncation error at lower frequencies is shown to be extremely small the method is easily implemented and can provide time and frequency domain solutions to this class of problems

representations over p adic fields of the finite general linear and unitary groups let p be a prime and let k denote the field of p adic numbers let q pm be a power of p and let gf q denote the finite field with q elements k has a unique unramified extension k of degree m whose associated residue class field is isomorphic to gf q k is obtained by adjoining a primitive root of unity of order q 1 to k for a description of these facts see for example theorem 2 p 54 and proposition 16 p 77 of s now consider the general linear group g gl n q of degree n over gf q part of the purpose of this paper is to show that if we consider representations of g over extension fields of k the field k is a minimal splitting field for g similarly if u u n q is the corresponding unitary group the characters of u take values in k moreover if p and q are sufficiently large the representations themselves are realizable in k and are unitary with respect to the involution of k over k we also discuss the number of representations of g and u that are realizable in given subfields of km and k our proofs rely mainly on a well known permutation lemma of brauer and give no indication of how these k representations might be constructed in practice we also note here that analogous results on the p adic representations of other classical groups do not appear to hold in complete generality this can already be seen in the case of the group sl 2 p certain of whose irreducible characters take values in a quadratic ramified extension of k

free and forced vibrations of stepped rods and coupled systems abstract analytical and closed form frequency responses of the longitudinal vibration of n stepped rods as well as the coupled system of multi stepped rods and lumped elements with non classical boundary conditions are proposed in this paper the closed form frequency equation for these systems is also obtained in this article a new two way state flow model based on the dynamics of the rod is developed in addition to the state flow model developed for lumped elements concentrated mass and spring and damper the exact frequency response of both stepped rod and the coupled system can be directly written out according to the graph theory since the results are analytical and closed form they can be directly implemented for analytical and numerical analysis without resorting to complex operations such as inversion recursive calculation or iteration computation moreover the derived equations are feasible not only for the multi stepped and multi stage rods but also for the coupled system of multi stepped rods and lumped elements finally the results were checked using multi stepped rods with classical and non classical boundary conditions as well as a combination of stepped rods and lumped elements to demonstrate the efficiency of this method

a galerkin method for distributed systems with non local damping in this paper a non local damping model including time and spatial hysteresis effects is used for the dynamic analysis of structures consisting of euler bernoulli beams and kirchoff plates unlike ordinary local damping models the damping force in a non local model is obtained as a weighted average of the velocity field over the spatial domain determined by a kernel function based on distance measures the resulting equation of motion for the beam or plate structures is an integro partial differential equation rather than the partial differential equation obtained for a local damping model approximate solutions for the complex eigenvalues and modes with non local damping are obtained using the galerkin method numerical examples demonstrate the efficiency of the proposed method for beam and plate structures with simple boundary conditions for non local and non viscous damping models and different kernel functions

eliminating the modal truncation problem encountered in frequency responses of viscoelastic systems increasing the number of degrees of freedom used in finite element analysis for mechanical and structural systems with viscoelastic damping the need to consider the modal truncation problem of viscoelastic systems is more than ever before the higher modes may be unnecessary to obtain in dynamic analysis for engineering applications for viscoelastic systems the modal truncation problem may be more frequently encountered since the nonviscous modes are difficult or even impossible to be found accurately even if a small scaled problem is considered for some eigensolution methods this study aims at eliminating the influence of the higher modes on the frequency responses of viscoelastically damped systems a method is presented by making the equilibrium equations of motion into a subspace equation spanned in terms of the columns of a projection basis obtained by considering the use of the contribution of the lower modes and the first two terms of the neumann expansion of the contribution of the unavailable modes finally three example studies are provided to illustrate the effectiveness of the derived results it is shown that the proposed method can reduce the modal truncation error significantly

a hitchhiker s guide to quasi copulas abstract this paper presents a review of the concept of an n quasi copula starting from the characterization of functions that can be derived from operations on random variables we recall several other characterizations and properties that have been proven in the literature highlighting the differences between the bivariate case and the higher dimensional case additionally we recall several applications of n quasi copulas such as their role in the study of bounds on sets of n copulas we also recall various classes of n quasi copulas that have been studied in the literature finally we present some questions that have not yet been answered in the literature

transient response of one dimensional distributed systems a closed form eigenfunction expansion realization abstract the exact and closed form transient response of general one dimensional distributed dynamic systems subject to arbitrary external initial and boundary disturbances is determined non self adjoint operators characterizing damping gyroscopic and circulatory effects and eigenvalue dependent boundary conditions are considered through introduction of augmented operators a closed form modal expansion of the displacement and internal forces of the distributed system is derived the eigenfunction expansion is realized in a spatial state formulation which systematically yields exact eigensolutions eigenfunction normalization coefficients and modal co ordinates the proposed method is illustrated on a cantilever beam with end mass viscous damper and spring

complex modal analysis of a flexural vibrating beam with viscous end conditions abstract the complex mode superposition method for the dynamical analysis of a simply supported beam with two rotational dampers attached at its end is presented first a numerical procedure for the evaluation of complex frequencies and modes of vibration has been worked out second the appropriate orthogonality conditions have been established in order to decouple the equation of motion the complex mode superposition method has then been used for the dynamic analysis in the time and frequency domains finally some numerical applications under impulsive and harmonic transverse accelerations of both ends have been reported in order to illustrate the effects of the dampers on the response amplitude

an exact generalised function approach to frequency response analysis of beams and plane frames with the inclusion of viscoelastic damping abstract this paper concerns the frequency response analysis of beams and plane frames with an arbitrary number of kelvin voigt viscoelastic dampers typical external and internal dampers are considered as grounded translational tuned mass rotational and axial dampers for bending and axial vibrations respectively using the theory of generalised functions within a 1d formulation of equations of motion exact closed form expressions are derived for beam dynamic green s functions and frequency response functions under arbitrary polynomial load for any number of dampers for a plane frame exact global frequency response matrix and load vector are built with size depending only on the number of beam to column nodes for any number of dampers and point polynomial loads along the frame members from the nodal displacement solution the exact frequency response in all frame members is also obtained in closed analytical form numerical applications show many of the advantages of the proposed method

a unified solution for longitudinal wave propagation in an elastic rod this paper proposes a unified analytical solution of the wave equation governing the propagation of the longitudinal stress wave in an elastic rod within a single formula derived by using the laplace transform and inverse transform the solution covers the contributions of the external excitations the nonzero initial conditions and the inhomogeneous boundary conditions altogether including such boundary conditions that the dependent variables at the ends of the rod are restricted with an equation the proposed formula particularly suitable for transient problems could be regarded as an exact interpolation function in the time domain provided the rod works as a component in a complex system etc four examples are presented to show the applications of the solution

twisted relative trace formulae with a view towards unitary groups we introduce a twisted relative trace formula which simultaneously generalizes the twisted trace formula of langlands et al in the quadratic case and the relative trace formula of jacquet and lai certain matching statements relating this twisted relative trace formula to a relative trace formula are also proven including the relevant fundamental lemma in the biquadratic case using recent work of jacquet lapid and their collaborators and the rankin selberg integral representation of the asai l function obtained by flicker using the theory of jacquet piatetskii shapiro and shalika we give the following application let e f be a totally real quadratic extension with gal e f let u be a quasi split unitary group with respect to a cm extension m f and let u res e f u under suitable local hypotheses we show that a cuspidal cohomological automorphic representation of u whose asai l function has a pole at the edge of the critical strip is nearly equivalent to a cuspidal cohomological automorphic representation of u that is u distinguished in the sense that there is a form in the space of admitting a nonzero period over u this provides cohomologically nontrivial cycles of middle dimension on unitary shimura varieties analogous to those on hilbert modular surfaces studied by harder langlands and rapoport

an exact modal analysis approach to vibration analysis of structures with mass spring subsystems and rotational joints abstract a novel exact modal analysis approach is presented for vibration analysis of plane continuous structures which are coupled with discrete mass spring subsystems and include elastic rotational joints modelling local flexibility using the theory of generalised functions to handle the discontinuities of the response variables every continuous member with any number of mass spring subsystems and joints is treated as a two node element for which a 6 6 exact dynamic stiffness matrix is obtained in closed form as a result the global dynamic stiffness matrix is built by a standard finite element assembling procedure with size depending only on the number of nonzero nodal degrees of freedom of member to member nodes upon deriving pertinent orthogonality conditions for the modes the system response under arbitrary loads is obtained by modal impulse and modal frequency response functions under the assumption of proportional damping the solutions are exact and can be used as benchmark for classical finite element solutions the approach is formulated for various mass spring subsystems acting in transverse and axial directions relative to every member

dynamic analysis of a uniform cantilever beam carrying a number of elastically mounted point masses with dampers abstract the free and forced vibration analyses of a uniform cantilever beam carrying a number of spring damper mass systems with arbitrary magnitudes and locations were made by means of the analytical and numerical combined method ancm first of all a method was presented to replace each spring damper mass system by a massless equivalent spring damper system with effective spring constant keffand effective damping coefficient ceffso that the ancm is available for the title problem next the equation of motion for the constrained beam with spring damper mass systems attached was derived by using the natural frequencies and normal mode shapes of the unconstrained beam without carrying any attachments incorporating the expansion theorem finally the eigenvalues and the forced vibration responses of the constrained beam were determined by conventional numerical methods to confirm the reliability of the presented theory all the numerical results obtained from the ancm were compared with the corresponding ones obtained from the conventional finite element method fem and good agreement was achieved the influence of the damping magnitude of each spring damper mass system on the eigenvalues and the forced vibration responses of the constrained beam was studied because the order of the overall property matrices for the equation of motion of the constrained beam derived from the ancm is much lower than that from the conventional fem the storing memory and the cpu time required by the ancm are much less than those required by the fem

closed form 2 d angle estimation with rectangular arrays in element space or beamspace via unitary esprit the uca esprit is a closed form algorithm developed for use in conjunction with a uniform circular array uca that provides automatically paired source azimuth and elevation angle estimates the 2 d unitary esprit is presented as an algorithm providing the same capabilities for a uniform rectangular array ura in the final stage of the algorithm the real and imaginary parts of the ith eigenvalue of a matrix are one to one related to the respective direction cosines of the ith source relative to the two major array axes the 2 d unitary esprit offers a number of advantages over other proposed esprit based closed form 2 d angle estimation techniques first except for the final eigenvalue decomposition of a dimension equal to the number of sources it is efficiently formulated in terms of real valued computation throughout second it is amenable to efficient beamspace implementations that are presented third it is applicable to array configurations that do not exhibit identical subarrays e g two orthogonal linear arrays finally the 2 d unitary esprit easily handles sources having one member of the spatial frequency coordinate pair in common simulation results are presented verifying the efficacy of the method

modal analysis of multi span timoshenko beams connected or supported by resilient joints with damping the present paper proposes an exact modelling and modal analysis method for non uniform multi span beam type structure supported and or connected by resilient joints with damping to this end an exact dynamic matrix for a timoshenko beam element is derived by means of the spatial domain laplace transform a generalized modal analysis method is also proposed and applied to the derivation of frequency response and time response formulas for general beam structures three examples are provided for validating and or illustrating the proposed method in the first numerical example the proposed method is compared with fem the second example deals with a three stepped beam structure supported by joints with damping property in the final example a dynamic analysis of a multi span beam under moving load is demonstrated the numerical study proves that the proposed method is useful for the dynamic analysis of multi span beam type structures

vibration of beams with arbitrary discontinuities and boundary conditions abstract a general solution of the vibration of an euler bernoulli beam with arbitrary type of discontinuity at arbitrary number of locations is presented in this paper to account for the discontinuity term induced by various additional elements on the beam heaviside s function is used to express the modal displacement of the whole beam by a single function this general modal displacement function is then solved by using laplace transformation this general solution consists of four types of basic modal shapes induced by four corresponding types of discontinuity terms at the discontinuity points various discontinuity terms are obtained and expressed by the boundary values of the modal displacement in a recursive way consequently the modal displacement can be determined by examining only the conditions on the boundary in such a way the present solution reduces the vibration of beams with arbitrary discontinuities to the same order of the case without discontinuity point to demonstrate the efficiency and applicability of the present method three application examples are presented calculation example shows that the lead zirconate titanate pzt actuator should be placed as close to the fixed end as possible to achieve the best excitation effect on a cantilever beam a new method to calculate the driving point anti resonance frequency is also proposed numerical results suggest that the variation of driving point anti resonance frequency can be used to determine the location and size of crack in beams due to the generic nature of the solution and the problem the present method can be utilized in smart structures modeling and structural health monitoring of beam type structures

the exact explicit dynamic stiffness matrix of multi cracked euler bernoulli beam and applications to damaged frame structures abstract in this paper the closed form expression of the exact dynamic stiffness matrix of an euler bernoulli beam in the presence of an arbitrary number of concentrated cracks is derived the procedure adopted for the evaluation of the dynamic stiffness matrix is based on the availability of the exact closed form solution of the vibration modes of the multi cracked beam derived by the same authors in a previous paper the knowledge of the exact explicit dynamic stiffness matrix of the multi cracked beam makes the direct evaluation of the exact global dynamic stiffness matrix of damaged frame structures possible furthermore it allows the exact evaluation of the frequencies and the corresponding vibration modes consistent with the distributed parameter model through the application of the well known wittrick williams algorithm some numerical applications relative to the evaluation of frequencies and the corresponding mode shapes of multi cracked framed structure are reported furthermore the closed form solution has been validated by comparing with some exact results available in the literature for a simple single cracked frame finally further new results for a multi cracked frame have been compared with those obtained by a finite element simulation

a level set approach for damage identification of continuum structures based on dynamic responses abstract the present paper aims to propose a novel approach for damage identification of continuum structures based on their dynamic performances the main idea is resorting to the level set model which is used to describe the shape and topology of the damage regions implicitly the original natural frequency based inverse problem is thus transferred into a generalized shape optimization problem which can be tackled by solving an evolution type hamilton jacobi equation compared to traditional approaches the distinctive advantage of the proposed approach is that it can deal with damage regions of complex shapes in a convenient way numerical examples demonstrate the effectiveness of the proposed approach

dynamics of multiple cracked prismatic beams with uncertain but bounded depths under deterministic and stochastic loads abstract dynamic response of cracked beams changes with respect to undamaged ones due to the change in mechanical properties moreover usually the crack characteristics crack size crack position applied stress etc are assumed to be known however in practice they possess considerable scatter of uncertainty the aim of this paper is to evaluate the time varying upper and lower bounds of the response of damaged beams with multiple cracks subjected to deterministic or stochastic excitations assuming uncertain crack depths as interval variables in this study the analysis is performed adopting a finite element model for the damaged beam extended to the case where multiple non propagating cracks are presented in order to provide the bounds of the response the authors propose an approach developed in the time domain starting from the derivation of the bounds of the interval eigenvalues evaluated as solution of two appropriate deterministic eigenvalue problems to assess the efficiency and the accuracy of the presented method a damaged cantilever prismatic aluminum beam with multiple uncertain but bounded cracks is examined the bounds of the free end displacement and variance are calculated and compared with the exact solution via combinatorial procedure the proposed results show a high level of accuracy for both increasing amplitude value of interval deviation and increasing number of uncertain parameters

on euler bernoulli discontinuous beam solutions via uniform beam green s functions abstract the bending problem of euler bernoulli discontinuous beams is dealt with the purpose is to show that uniform beam green s functions can be used to build efficient solutions for beams with internal discontinuities due to along axis constraints and flexural stiffness jumps specifically upon deriving the equilibrium equation in the space of generalized functions first it is seen that the original bending problem may be recast as linear superposition of a principal and an auxiliary bending problem both involving a uniform reference beam and homogeneous boundary conditions then based on the green s functions of the reference beam closed form solutions are developed for the principal beam response while the auxiliary beam response is obtained by solving in general r 2 s algebraic equations written at the discontinuity locations being r the number of discontinuities due to along axis constraints and s the number of flexural stiffness jumps in this manner an appreciable reduction of computational effort is achieved as compared to alternative analytical solutions in the literature

longitudinal wave propagation part i comparison of rod theories abstract the paper introduces new four spectral elements for analysis of longitudinal wave propagation in structures the developed elements are based on the elementary love mindlin herrmann and three mode theories certain differences in wave propagation behaviour are observed for the analysed models for lower excitation frequencies the results obtained for all models are similar and from a practical point of view the spectral element based on the love theory is adequate for high frequency excitation these differences are considerable and only the mindlin herrmann or three mode models give correct results

on the frequency response function of a damped cantilever simply supported in span and carrying a tip mass abstract this paper deals with the determination of the frequency response function of a cantilevered bernoulli euler beam which is viscously damped by a single damper the beam is simply supported in span and carries a tip mass the frequency response function is obtained through a formula that was established for the receptance matrix of discrete linear systems subjected to linear constraint equations by considering the simple support as a linear constraint imposed on generalized co ordinates the comparison of the numerical results obtained via a boundary value problem formulation justifies the approach used here

strong approximation of copulas abstract we introduce strong convergence with regard to approximation of copulas this new type of convergence is useful in dealing with the product of darsow nguyen and olsen for copulas we also provide tools for constructing strong approximations of copulas by using partitions of unity

on a conjecture of jacquet about distinguished representations of gl n in this paper we prove a conjecture of jacquet about supercuspidal representations of gln k distinguished by gln k or by un k for k a quadratic unramified extension of a non archimedean local field k

involutions acting on representations for a group g with order 2 automorphism we consider irreducible representations v of g such that where is the contragredient representation of this isomorphism gives rise to a nondegenerate bilinear form on v which is invariant unique up to scalar and consequently is either symmetric or skew symmetric for such a representation we study the question of when this form is symmetric and when it is skew symmetric we begin with recalling a method of prasad 13 in the case that is trivial and g is a finite group of lie type we apply a theorem of klyachko to obtain results for all representations of many of the groups sl n fq improving the results of prasad which were for generic representations in section 3 we start by generalizing lemma 1 to the case of any order 2 automorphism in lemma 2 we are able to apply this to get another proof of a theorem of gow 5 for the group gl n fq and the transposeinverse automorphism and in section 4 we are also able to apply lemma 2 to distinguished representations and gelfand pairs in section 5 we find a generating set for a finite group g given that we know certain information about the representations of g satisfying finally in section 6 we turn to the case of a locally compact totally disconnected group we adapt the methods of section 2 along with approximation by compact open subgroups to obtain an equivalent result of theorem 4 of gow for gl n f where f is a nonarchimedean local field

a new analytical technique for vibration analysis of non proportionally damped beams abstract vibrating linear mechanical systems in particular continuous systems are often modelled considering proportional damping distributions only although in many real situations this simplified approach does not describe the dynamics of the system with sufficient accuracy in this paper an analytical method is given to take into account the effects of a more general viscous damping model referred to as non proportional damping on a class of vibrating continuous systems a state form expansion applied in conjunction with a transfer matrix technique is adopted to extract the eigenvalues and to express the eigenfunctions in analytical form i e complex modes corresponding to non synchronous motions numerical examples are included in order to show the efficiency of the proposed method non proportional damping distributions of different type such as internal and external lumped or distributed viscous damping are tested on non homogeneous euler bernoulli beams in bending vibration with different boundary conditions finally a discussion on root locus diagrams behaviour and on modal damping ratio significance for non proportionally damped systems is presented

copulas with continuous strictly increasing singular conditional distribution functions abstract using iterated function systems induced by so called modifiable transformation matrices t and tools from symbolic dynamical systems we first construct mutually singular copulas a t with identical possibly fractal or full support that are at the same time singular with respect to the lebesgue measure 2 on 0 1 2 afterwards the established results are utilized for a simple proof of the existence of singular copulas a t with full support for which all conditional distribution functions y f x a t y are continuous strictly increasing and have derivative zero almost everywhere this result underlines the fact that conditional distribution functions of copulas may exhibit surprisingly irregular analytic behavior finally we extend the notion of empirical copula to the case of non i i d data and prove uniform convergence of the empirical copula e n corresponding to almost all orbits of a markov process usually referred to as chaos game to the singular copula a t several examples and graphics illustrate both the chosen approach and the main results

analytical modeling of viscoelastic dampers for structural and vibration control different approaches to the mathematical modeling of viscoelastic dampers are addressed and their theoretical basis and performance are compared the standard mechanical model smm comprising linear springs and dashpots is shown to accurately describe the broad band rheological behavior of common viscoelastic dampers and be more efficient than other models such as the fractional derivative model and the modified power law the smm renders a prony series expression for the modulus and compliance functions in the time domain and the remarkable mathematical efficiency associated with the exponential basis functions of a prony series greatly facilitates model calibration and interconversion while cumbersome nonlinear regression is usually required for other models a simple collocation or least squares method can be used to fit the smm to available experimental data the model allows viscoelastic material functions to be readily determined either directly from the experimental data or through interconversion from a function established in another domain numerical examples on two common viscoelastic dampers demonstrate the advantages of the smm over fractional derivative and power law models detailed computational procedures for fitting and interconversion are discussed and illustrated published experimental data from a viscoelastic liquid damper and a viscoelastic solid damper are used in the examples

vibration analysis for a coupled beam sdof system by using the recurrence equation method this paper presents the vibration analysis of a coupled system composed of a beam and a single degree of freedom sdof system the harmonic responses of this kind of system are formulated by means of the recurrence equation method in addition the natural characteristics of the system are also analyzed numerical examples of the undamped system are given and compared with the published results and an excellent correlation shows that the study work in this paper is correct

forced vibration of euler bernoulli beams by means of dynamic green functions abstract a method for determining the dynamic response of prismatic damped euler bernoulli beams subjected to distributed and concentrated loads is presented the method yields exact solutions in closed form and may be used for single and multi span beams single and multi loaded beams and statically determinate and indeterminate beams also green functions for various beams with different homogenous and elastic boundary conditions are given in order to demonstrate the use of the green functions method several examples are given some of the obtained results are compared with those given in the references

analysis of non homogeneous timoshenko beams with generalized damping distributions abstract this paper presents a study on the effects of generalized damping distributions on non homogeneous timoshenko beams on the basis of some fundamentals of modal analysis for damped continuous systems applied to the particular case of the timoshenko beam model the eigenproblem is solved by applying a method combining a state space representation with a transfer matrix technique yielding closed form expressions for the eigenfunctions after validation by means of numerical examples using the finite element method response functions in both the time and the frequency domain are discussed and compared according to different damping distributions