transverse vibrations of tensioned pipes conveying fluid with time dependent velocity abstract in this study the transverse vibrations of highly tensioned pipes with vanishing flexural stiffness and conveying fluid with time dependent velocity are investigated two different cases the pipes with fixed fixed end and fixed sliding end conditions are considered the time dependent velocity is assumed to be a harmonic function about a mean velocity these systems experience a coriolis acceleration component which renders such systems gyroscopic the equation of motion is derived using hamilton s principle and solved analytically by direct application of the method of multiple scales a perturbation technique the natural frequencies are found increasing the ratio of fluid mass to the total mass per unit length increases the natural frequencies the principal parametric resonance cases are investigated in detail stability boundaries are determined analytically it is found that instabilities occur when the frequency of velocity fluctuations is close to two times the natural frequency of the constant velocity system when the velocity fluctuation frequency is close to zero no instabilities are detected up to the first order of perturbation numerical results are presented for the first two modes

a moufang loop the exceptional jordan algebra and a cubic form in 27 variables abstract let i be the exceptional 27 dimensional jordan algebra over c its automorphism group is the lie group f4 c and this group is known to have a finite subgroup al where a is a self centralizing elementary abelian of order 27 l sl 3 3 and l normalizes a as an a module i decomposes into a direct sum of 1 dimensional spaces i x which afford the 27 distinct linear characters x a hom a c x these spaces satisfy i x i y i xy let e 2 i 3 there are a basis of i of the form ex for x a and a function g a a f 3 such that exey 2 e x y g x y exy where c x y 0 if x and y are linearly dependent and c x y 1 otherwise identifying a with f 33 we write x x1 x2 x3 and y y1 y2 y3 a function g which has the above properties is g x y x1 x2 x3 x3 y1 y2 x2 x3 y1 x1 y2 y3 the elements ex x a generate the infinite commutative loop l 2 m nex m z n z 3 x a under jordan multiplication the loop s is not moufang but has as quotient a moufang loop m of order 81 and exponent 3 conversely the loop m may be constructed from scratch using g and used to define the jordan algebra i using the formula this gives a new existence proof for a simple 27 dimensional jordan algebra over fields of characteristic not 2 or 3 with a primitive cube root of unity in characteristic 3 we get the group algebra of a we discuss some finite groups associated to m and the lie groups f4 c and 3e6 c and compare the analogous situation with the loop o 16 the cayley numbers and lie groups g2 c and d4 c we also get a new construction of the cubic form in 27 variables whose group is 3e6 c and an easy and natural construction of the exotic 3 local subgroup 31 3 3 sl 3 3

on the transversal vibrations of a conveyor belt with a low and time varying velocity part ii the beam like case in this paper initial boundary value problems for a linear wave string equation are considered these problems can be used as simple models to describe the vertical vibrations of a conveyor belt for which the velocity is small with respect to the wave speed and is assumed to move with a time varying speed formal asymptotic approximations of the solutions are constructed to show the complicated dynamical behavior of the conveyor belt it will also be shown that the truncation method cannot be applied to this problem in order to obtain approximations valid on long time scales

analysis of the coupled thermoelastic vibration for axially moving beam the coupled thermoelstic vibration characteristics of the axially moving beam are investigated the differential equation of motion of the axially moving beam under the thermoelastic coupling is established based to the equilibrium equation and the thermal conduction equation involving deformation term the eigenequation is deduced and the dimensionless complex frequencies of the axially moving beam with different boundary conditions under the coupled thermoelastic case are calculated by the differential quadrature method the curves of the real parts and imaginary parts of the first three order dimensionless complex frequencies versus the dimensionless axially moving speed are obtained the effects of the dimensionless coupled thermoelastic factor the ratio of length to height the dimensionless moving speed on the stability of the beam are analyzed

constants and finite unary relations in qualitative constraint reasoning extending qualitative csps with the ability of restricting selected variables to finite sets of possible values has been proposed as an interesting research direction with important applications c

temporal constraint networks abstract this paper extends network based methods of constraint satisfaction to include continuous variables thus providing a framework for processing temporal constraints in this framework called temporal constraint satisfaction problem tcsp variables represent time points and temporal information is represented by a set of unary and binary constraints each specifying a set of permitted intervals the unique feature of this framework lies in permitting the processing of metric information namely assessments of time differences between events we present algorithms for performing the following reasoning tasks finding all feasible times that a given event can occur finding all possible relationships between two given events and generating one or more scenarios consistent with the information provided we distinguish between simple temporal problems stps and general temporal problems the former admitting at most one interval constraint on any pair of time points we show that the stp which subsumes the major part of vilain and kautz s point algebra can be solved in polynomial time for general tcsps we present a decomposition scheme that performs the three reasoning tasks considered and introduce a variety of techniques for improving its efficiency we also study the applicability of path consistency algorithms as preprocessing of temporal problems demonstrate their termination and bound their complexities

asymmetric non linear forced vibrations of free edge circular plates part 1 theory in this article a detailed study of the forced asymmetric non linear vibrations of circular plates with a free edge is presented the dynamic analogue of the von karman equations is used to establish the governing equations the plate displacement at a given point is expanded on the linear natural modes the forcing is harmonic with a frequency close to the natural frequency omega n of one asymmetric mode of the plate thus the vibration is governed by the two degenerated modes corresponding to omega n which are one to one internally resonant an approximate analytical solution using the method of multiple scales is presented attention is focused on the case where one configuration which is not directly excited by the load gets energy through non linear coupling with the other configuration slight imperfections of the plate are taken into account experimental validations are presented in the second part of this paper

behavior of derivatives of eigenvalues and eigenvectors in curve veering and mode localization and their relation to close eigenvalues the problem to measure the phenomena of eigenvalue curve veering and mode localization is addressed in this paper the second derivative of an eigenvalue and the first derivative of an eigenvector are taken as the measures numerically showing curve veering and mode localization based on the measurement close eigenvalues as a key factor for the occurrence of the phenomena are defined two eigenvalues are considered to be close if their difference is small enough to cause the occurrence of the phenomena the curve veering and mode localization can be noted by comparison of the derivatives with a critical value and hence the associated eigenvalues are close weakly coupled springs are given as an example

nonlinear model identification and spectral submanifolds for multi degree of freedom mechanical vibrations in a nonlinear oscillatory system spectral submanifolds ssms are the smoothest invariant manifolds tangent to linear modal subspaces of an equilibrium amplitude frequency plots of the dynamics on ssms provide the classic backbone curves sought in experimental nonlinear model identification we develop here a methodology to compute analytically both the shape of ssms and their corresponding backbone curves from a data assimilating model fitted to experimental vibration signals this model identification utilizes taken s delay embedding theorem as well as a least square fit to the taylor expansion of the sampling map associated with that embedding the ssms are then constructed for the sampling map using the parametrization method for invariant manifolds which assumes that the manifold is an embedding of rather than a graph over a spectral subspace using examples of both synthetic and real experimental data we demonstrate that this approach reproduces backbone curves with high accuracy

non linear vibrations of a beam with cantilever hertzian contact boundary conditions abstract the non linear vibrations of a linear beam with cantilever hertizian contact boundary conditions are investigated the method of multiple scales is used to analyze this problem in which it is assumed that the beam remains in contact with the moving surface at all times one primary result from this analysis is the amplitude frequency relation for the various flexural modes the amplitude frequency curves exhibit softening behavior as expected the amount of softening is shown to depend on the linear contact stiffness as well as the specific mode in addition the associated non linear normal modes of this system are derived the modes include a non linear modification to the linear harmonic component as well as a static offset term and second and third harmonic components

querying temporal and spatial constraint networks in ptime we start with the assumption that temporal and spatial knowledge usually captured by constraint networks can be represented and queried more effectively by using the scheme of indefinite constraint databases because query evaluation in this scheme is in general a hard computational problem we seek tractable instances of query evaluation we assume that we have a class of constraints c with some reasonable computational and closure properties the computational properties of interest are that the satisfiability problem and an appropriate version of the variable elimination problem for c should be solvable in ptime under this assumption we exhibit general classes of indefinite constraint databases and first order modal queries for which query evaluation can be done with ptime data complexity we then search for tractable instances of c among the subclasses of horn disjunctive linear constraints over the rationals from previous research we know that the satisfiability problem for horn disjunctive linear constraints is solvable in ptime but not the variable elimination problem thus we try to discover subclasses of horn disjunctive linear constraints with tractable variable elimination problems the class of utvpi constraints is the largest class that we show to have this property finally we restate our general tractability results with c ranging over the newly discovered tractable classes interesting tractable query answering problems for indefinite temporal and spatial constraint databases are identified in this way we close our complexity analysis by precisely outlining the frontier between tractable and possibly intractable query answering problems

normal modes and near resonance response of beams with non linear effects non linear normal modes and the associated frequencies of a uniform beam with simply supported or clamped conditions at both ends have been derived some restricted orthogonality conditions have been pointed out the effects of the longitudinal inertia on the non linear transverse motion are shown to be extremely small the efficacy of using the non linear normal modes towards computation of near resonance response has been clearly brought out

jump conditions for strings and sheets from an action principle abstract i present conditions for compatibility of velocities conservation of mass and balance of momentum and energy across moving discontinuities in inextensible strings and sheets of uniform mass density the balances are derived from an action with a time dependent non material boundary and reduce to matching of material boundary conditions if the discontinuity is stationary with respect to the body i first consider a point discontinuity in a string and a line discontinuity in a sheet in the context of classical inertial motion in three euclidean dimensions i briefly comment on line discontinuities terminating in point discontinuities in a sheet discontinuous line discontinuities in a sheet and an approach to dynamic fracture that treats a crack tip in a sheet as a time dependent boundary point i provide two examples of general solutions for conservative sheet motions near a line discontinuity the approach also enables treatment of actions depending on higher derivatives of position i thus derive balances for an elastica which are applicable to moving contact problems

code loops in dimension at most 8 abstract code loops are certain moufang 2 loops constructed from doubly even binary codes that play an important role in the construction of local subgroups of sporadic groups more precisely code loops are central extensions of the group of order 2 by an elementary abelian 2 group v in the variety of loops such that their squaring map commutator map and associator map are related by combinatorial polarization and the associator map is a trilinear alternating form using existing classifications of trilinear alternating forms over the field of 2 elements we enumerate code loops of dimension d dim v 8 equivalently of order 2 d 1 512 up to isomorphism there are 767 code loops of order 128 and 80826 of order 256 and 937791557 of order 512

spectral analysis for the transverse vibration of an axially moving timoshenko beam the use of frequency dependent spectral element matrix or exact dynamic stiffness matrix in structural dynamics is known to provide very accurate solutions while reducing the number of degrees of freedom to resolve the computational and cost problems thus in the present paper the spectral element model is formulated for the axially moving timoshenko beam under a uniform axial tension the high accuracy of the present spectral element is then verified by comparing its solutions with the conventional finite element solutions and exact analytical solutions the effects of the axial velocity and axial tension on the vibration characteristics the dispersion relation and the stability of a moving timoshenko beam are analytically and numerically investigated

normal modes of vibration for non linear continuous systems a definition and a constructive methodology for normal nodes of motion are developed for a class of vibratory systems the dynamics of which are governed by non linear partial differential equations the definition for normal modes is given in terms of the dynamics on two dimensional invariant manifolds in the system phase space these manifolds are a continuation of the planes which represent the well known normal modes of the linearized system a local asymptotic approximation of the geometric structure of these manifolds can be obtained by using an approach which follows that used for generating center manifolds the procedure also provides the non linear ordinary differential equations which govern individual modal dynamics and a physical description of the system configuration when it is undergoing a modal motion in this paper the general theory is described for the application of vibrations of continuous media but it can easily be extended to other situations in order to demonstrate the power of the approach and its unique procedural aspects three examples involving beam vibrations are worked out in detail the examples are conservative simply supported beams the first demonstrates the methodology for a linear beam model the second is a beam on a non linear elastic foundation and the third example is a beam with non linear torsional springs attached at each end in these examples the simplicity of the mode shapes of the linearized model yields relatively simple calculations that do not obscure the important features of the procedure

point algebras for temporal reasoning algorithms and complexity we investigate the computational complexity of temporal reasoning in different time models such as totally ordered partially ordered and branching time our main result concerns the satisfiability problem for point algebras and point algebras extended with disjunctions for these problems we identify all tractable subclasses we also provide a number of additional results for instance we present a new time model suitable for reasoning about systems with a bounded number of unsynchronized clocks we investigate connections with spatial reasoning and we present improved algorithms for deciding satisfiability of the tractable point algebras

on wave reflections and energetics for a semi infinite traveling string with a nonclassical boundary support abstract the free linear transverse vibrations of a semi infinite axially moving string are considered in order to study the reflection of an incident wave and the damping properties of different types of boundary conditions such as free fixed spring dashpot and mass spring dashpot to obtain the response to the initial conditions the method of d alembert is applied furthermore analytical expressions for the time rate of change of the total mechanical energy of the system are derived the obtained results give insight into the most efficient way of placing a boundary support depending on the direction of the transport velocity moreover for nonclassical boundary conditions the dynamics of the string is described by the relative values of the system parameters

numerical computation of periodic responses of nonlinear large scale systems by shooting method abstract geometrically nonlinear vibrations of three dimensional elastic structures due to harmonic external excitations are investigated in the frequency domain the material of the structure is assumed to be linearly elastic the equation of motion is derived by the conservation of linear momentum in lagrangian coordinate system and it is discretized into a system of ordinary differential equations by the finite element method the shooting method is used to obtain the periodic solutions a procedure which transforms the initial value problem into a two point boundary value problem for the periodicity condition and then it finds the initial conditions which lead to periodic response is developed and presented for systems of second order ordinary differential equations the elmer software is used for computing the local and global mass and stiffness matrices and the force vector as well for computing the correction of the initial conditions by the shooting method stability of the solutions is studied by the floquet theory sequential continuation method is used to define the prediction for the next point from the frequency response diagram the main goal of the current work is to investigate and present the potential of the proposed numerical methods for the efficient computation of the frequency response functions of large scale nonlinear systems which often result from space discretization of real life engineering applications

normal modes of a non linear clamped clamped beam abstract non linear modal analysis approach based on invariant manifold method proposed earlier by shaw and pierre journal of sound and vibration 164 85 124 is utilized here to obtain the non linear normal modes of a clamped clamped beam for large amplitude displacements the results obtained for the fundamental normal mode are compared with the corresponding reported experimental and theoretical studies the effects of modal coupling are examined in greater detail the limitation of the present method for analyzing non linear behavior is highlighted

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

large amplitude non linear normal modes of piecewise linear systems a numerical method for constructing non linear normal modes nnms for piecewise linear autonomous systems is presented these nnms are based on the concept of invariant manifolds and are obtained using a galerkin based solution of the invariant manifold s non linear partial differential equations the accuracy of the constructed non linear modes is checked by the comparison of the motion on the invariant manifold to the exact solution in both time and frequency domains it is found that this construction approach can accurately capture the nnms over a wide range of amplitudes including those with strong non linear effects several interesting dynamic characteristics of the non linear modal motion are found and compared to those of linear modes a two degree of freedom example is used to illustrate the technique the existence stability and bifurcations of the nnms for this example are investigated

nonlinear vibrations of axially moving timoshenko beams under weak and strong external excitations in this paper nonlinear vibrations under weak and strong external excitations of axially moving beams are analyzed based on the timoshenko model the governing nonlinear partial differential equation of motion is derived from newton s second law accounting for the geometric nonlinearity caused by finite stretching of the beams the complex mode approach is applied to obtain the transverse vibration modes and the natural frequencies of the linear equation the method of multiple scales is employed to investigate primary resonances nonsyntonic excitations superharmonic resonances and subharmonic resonances some numerical examples are presented to demonstrate the effects of a varying parameter such as axial speed external excitation amplitudes and nonlinearity on the response amplitudes for the first and second modes when other parameters are fixed the stability of the response amplitudes is investigated and the boundary of instability is located

an optimal k consistency algorithm abstract this paper generalizes the arc consistency algorithm of mohr and henderson 4 and the path consistency algorithm of han and lee 2 to a k consistency algorithm arc consistency and path consistency being 2 consistency and 3 consistency respectively the algorithm is a development of freuder s synthesis algorithm 1 it simultaneously establishes i consistency for each 1 i k it has worst case time and space complexity which is optimal when k is a constant and almost optimal for all other values of k in the case that all order i constraints exist for all 1 i n this algorithm is a solution to the consistent labeling problem with almost optimal worst case time and space complexity

a reflected wave superposition method for vibration and energy of a travelling string this paper considers the analytical free time domain response and energy in an axially translating and laterally vibrating string the domain of the string is either a constant or variable length dependent upon the general initial conditions the translating tensioned strings possess either fixed fixed or fixed free boundaries an alternative analytical solution using a reflected wave superposition method is presented for a finite translating string firstly the cycles of vibration for both constant and variable length strings are provided which for the latter are dependent upon the variable string length each cycle is divided into three time intervals according to the magnitude and the direction of the translating string velocity applying d alembert s method combined with the reflection properties expressions for the reflected waves at the two boundaries are obtained subsequently superposition of all of the incident and reflected waves provides results for the free vibration of the string over the three time intervals the variation in the total mechanical energy of the string system is also shown the accuracy and efficiency of the proposed method are confirmed numerically by comparison to simulations produced using a newmark beta method solution and an existing state space function representation of the string dynamics

technical communique boundary control of the axially moving kirchhoff string in this note the axially moving kirchhoff string is considered it is proved that this non linear string can be stabilized by the linear boundary control which is the negative feedback of the transversal velocity of the string at one end furthermore it is concluded that the axially moving kirchhoff string is stable without an active control when one of its ends is free to move transversally

complexity classification in qualitative temporal constraint reasoning we study the computational complexity of the qualitative algebra which is a temporal constraint formalism that combines the point algebra the point interval algebra and allen s interval algebra we identify all tractable fragments and show that every other fragment is np complete

wave propagation in and vibration of a travelling beam with and without non linear effects part i free vibration the relation between the wave propagation and the free vibration in a travelling beam with simple supports has been thoroughly investigated the frequency equation of such a beam has been derived using the phase closure principle since the characters of the waves change drastically as the axial speed is increased beyond a certain value the phase closure principle has been applied differently in these two speed regimes the justifications for some approximate methods of obtaining the natural frequencies are also discussed lastly the non linear normal modes are derived again using the phase closure principle the computation of the forced response using the wave propagation approach is discussed in part ii

sound synthesis of a nonlinear string using volterra series this paper proposes to solve and simulate various kirchhoff models of nonlinear strings using volterra series two nonlinearities are studied the string tension is supposed to depend either on the global elongation of the string first model or on the local strain located at x second and more precise model the boundary conditions are simple dirichlet homogeneous ones or general dynamic conditions allowing the string to be connected to any system typically a bridge for each model a volterra series is used to represent the displacement as a functional of excitation forces the volterra kernels are solved using a modal decomposition the first kernel of the series yields the standard modes of the linearized problem while the next kernels introduce the nonlinear dynamics as a last step systematic identification of the kernels lead to a structure composed of linear filters sums and products which are well suited to the sound synthesis using standard signal processing techniques the nonlinear dynamic introduced through this simulation is significant and perceptible in sound results for sufficiently large excitations

analysis of non linear mode shapes and natural frequencies of continuous damped systems in this paper the aim is to find the non linear mode shapes and natural frequencies for a class of one dimensional continuous damped systems with weak cubic inertia damping and stiffness non linearities this paper presents general formulations for natural frequencies and mode shapes with all non linearity effects initially the non linear system with general boundary conditions is discretized and using a two dimensional manifold the model of cubic non linearities is constructed and the general equation of motion which governs non linear system is derived the method of multiple scales is then used to extend the non linear mode shapes and natural frequencies during this analysis it is realized that when the natural frequencies of the linear system become equal to the natural frequencies of the non linear system a one to one internal resonance will appear also there is a three to one internal resonance which is not dependent on the damping of the system finally general formulations of amplitude for vibrations natural frequencies and mode shapes of the non linear system are obtained in parametric forms thus a non linear problem with some simple integration can be solved the formulations are capable of handling any non linearities in inertia damping stiffness or any combination of them under any arbitrary boundary conditions

non linear free periodic vibrations of open cylindrical shallow shells this paper is concerned with the non linear free periodic vibrations of thin open cylindrical and shallow shells vibrating in the geometrically non linear regime a multi degree of freedom model with hierarchical basis functions is adopted and the principle of the virtual work is used to define the time domain equations of motion these equations are transformed into the frequency domain by the harmonic balance method and are finally solved by an arc length continuation method shells of different thicknesses and of different curvature radius are analysed and the variation of the non linear natural frequencies of these shells with the vibration amplitude are investigated in some detail the variation of the mode shapes with the vibration amplitude is demonstrated it is found that both softening and hardening spring effects occur and that the number of couplings between vibration modes is rather large in undamped shells

nonlinear normal modes of structural systems via asymptotic approach abstract an asymptotic approach based on the method of multiple scales is employed to construct the nonlinear normal modes nnm s of self adjoint structural systems with arbitrary linear inertia and elastic stiffness operators general cubic inertia and geometric nonlinearities the methodology employed for constructing the approximate invariant manifolds of individual nnm s away from internal resonances and of the resonant modes near three to one internal resonances attempts to generalize previous studies based on asymptotic techniques the theory is applied to a hinged hinged uniform elastic beam carrying a lumped mass and undergoing axis stretching depending on the lumped mass relative to the beam mass and on its position along the span different classes of nonlinear normal modes and their stability are investigated

tractable disjunctions of linear constraints basic results and applications to temporal reasoning we study the problems of deciding consistency and performing variable elimination for disjunctions of linear inequalities and disequations with at most one inequality per disjunction this new class of constraints extends the class of generalized linear constraints originally studied by lassez and mcaloon we show that deciding consistency of a set of constraints in this class can be done in polynomial time we also present a variable elimination algorithm which is similar to fourier s algorithm for linear inequalities finally we use these results to provide new temporal reasoning algorithms for the ord horn subclass of allen s interval formalism we also show that there is no low level of local consistency that can guarantee global consistency for the ord horn subclass this property distinguishes the ord horn subclass from the pointizable subclass for which strong 5 consistency is sufficient to guarantee global consistency and the continuous endpoint subclass for which strong 3 consistency is sufficient to guarantee global consistency copyright 2001 elsevier science b v

reasoning about temporal relations the tractable subalgebras of allen s interval algebra allen s interval algebra is one of the best established formalisms for temporal reasoning this article provides the final step in the classification of complexity for satisfiability problems over constraints expressed in this algebra when the constraints are chosen from the full allen s algebra this form of satisfiability problem is known to be np complete however eighteen tractable subalgebras have previously been identified we show here that these subalgebras include all possible tractable subsets of allen s algebra in other words we show that this algebra contains exactly eighteen maximal tractable subalgebras and reasoning in any fragment not entirely contained in one of these subalgebras is np complete we obtain this dichotomy result by giving a new uniform description of the known maximal tractable subalgebras and then systematically using a general algebraic technique for identifying maximal subalgebras with a given property

moufang loops with a unique nonidentity commutator associator square in 9 griess considers a class of loops called code loops which have applicability to a construction of the monster and its nonassociative algebra see 7 these loops turn out to be moufang loops which have a unique nonidentity commutator a unique nonidentity associator and a unique nonidentity square moufang loops with one or more of these properties also play an important role in the authors work on loops which have alternative loop rings 2 5 81 for example a nonassociative loop which has an alternative loop ring over a ring of characteristic different from two must be a moufang loop with a unique nonidentity commutator and associator which coincide in this paper we study moufang loops with the properties in question in section 3 we concentrate on loops which have unique nonidentity commutators and or associators and investigate some of their properties in section 4 we consider moufang loops with a unique nonidentity square and show that these are exactly the code loops of griess

a generalized treatment of the energetics of translating continua part i strings and second order tensioned pipes the energetics of translating one dimensional uniform strings and highly tensioned pipes with vanishing bending stiffness and flowing fluid are analyzed for fixed free and damped boundary conditions the interaction between the translating continua and the boundary supports causes energy transfer at a fixed boundary the transverse component of tension does work and the coriolis forces at a free end cause energy flux into the second order continuum under a symmetric boundary configuration the total energy of free oscillation varies periodically at the fundamental natural frequency asymmetric boundary supports in the pipe fluid system lead to damped or self excited motions at a viscously damped boundary the condition for maximal energy dissipation the destabilizing effect of dissipation and the stabilizing effect of negative damping are examined analytically using travelling wave solutions the energies transferred at the different boundary supports are quantified by energy reflection coefficients which are determined completely by the boundary conditions numerical simulations verify the analytically predicted energy variations

temporal reasoning about fuzzy intervals traditional approaches to temporal reasoning assume that time periods and time spans of events can be accurately represented as intervals real world time periods and events on the other hand are often characterized by vague temporal boundaries requiring appropriate generalizations of existing formalisms this paper presents a framework for reasoning about qualitative and metric temporal relations between vague time periods in particular we show how several interesting problems like consistency and entailment checking can be reduced to reasoning tasks in existing temporal reasoning frameworks we furthermore demonstrate that all reasoning tasks of interest are np complete which reveals that adding vagueness to temporal reasoning does not increase its computational complexity to support efficient reasoning a large tractable subfragment is identified among others generalizing the well known ord horn subfragment of the interval algebra extended with metric constraints

hardening softening behaviour in non linear oscillations of structural systems using non linear normal modes the definition of a non linear normal mode nnm as an invariant manifold in phase space is used in conservative cases it is shown that normal form theory allows one to compute all nnms as well as the attendant dynamics onto the manifolds in a single operation then a single mode motion is studied the aim of the present work is to show that too severe truncature using a single linear mode can lead to erroneous results using single non linear mode motion predicts the correct behaviour hence the nonlinear change of co ordinates allowing one to pass from the linear modal variables to the normal ones linked to the nnms defines a framework to properly truncate non linear vibration pdes two examples are studied a discrete system a mass connected to two springs and a continuous one a linear euler bernoulli beam resting on a non linear elastic foundation for the latter a comparison is given between the developed method and previously published results

on binary constraint problems the concepts of binary constraint satisfaction problems can be naturally generalized to the relation algebras of tarski the concept of path consistency plays a central role algorithms for path consistency can be implemented on matrices of relations and on matrices of elements from a relation algebra we give an example of a 4 by 4 matrix of infinite relations on which on iterative local path consistency algorithm terminates we give a class of examples over a fixed finite algebra on which all iterative local algorithms whether parallel or sequential must take quadratic time specific relation algebras arising from interval constraint problems are also studied the interval algebra the point algebra and the containment algebra

a conserved quantity and the stability of axially moving nonlinear beams free nonlinear transverse vibration is investigated for an axially moving beam modeled by an integro partial differential equation based on the equation a conserved quantity is defined and confirmed for axially moving beams with pinned or clamped ends the conserved quantity is applied to demonstrate the lyapunov stability of the straight equilibrium configuration in transverse nonlinear of beam with a low axial speed

a unifying approach to temporal constraint reasoning abstract we present a formalism disjunctive linear relations dlrs for reasoning about temporal constraints dlrs subsume most of the formalisms for temporal constraint reasoning proposed in the literature and is therefore computationally expensive we also present a restricted type of dlrs horn dlrs which have a polynomial time satisfiability problem we prove that most approaches to tractable temporal constraint reasoning can be encoded as horn dlrs including the ord horn algebra by nebel and burckert and the simple temporal constraints by dechter et al thus dlrs is a suitable unifying formalism for reasoning about temporal constraints

nonlinear normal modes for vibratory systems under harmonic excitation this paper considers the use of numerically constructed invariant manifolds to determine the response of nonlinear vibratory systems that are subjected to harmonic excitation the approach is an extension of the nonlinear normal mode nnm formulation previously developed by the authors for free oscillations wherein an auxiliary system that models the excitation is used to augment the equations of motion in this manner the excitation is simply treated as an additional system state yielding a system with an extra degree of freedom dof whose response is known a reduced order model for the forced system is then determined by the usual nnm procedure and an efficient galerkin based solution method is used to numerically construct the attendant invariant manifolds the technique is illustrated by determining the frequency response for a simple 2 dof mass spring system with cubic nonlinearities and for a discretized beam model with 12 dof the results show that this method provides very accurate responses over a range of frequencies near resonances

reasoning about qualitative temporal information abstract representing and reasoning about incomplete and indefinite qualitative temporal information is an essential part of many artificial intelligence tasks an interval based framework and a point based framework have been proposed for representing such temporal information in this paper we address two fundamental reasoning tasks that arise in applications of these frameworks given possibly indefinite and incomplete knowledge of the relationships between some intervals or points i find a scenario that is consistent with the information provided and ii find the feasible relations between all pairs of intervals or points for the point based framework and a restricted version of the interval based framework we give computationally efficient procedures for finding a consistent scenario and for finding the feasible relations our algorithms are marked improvements over the previously known algorithms in particular we develop an o n2 time algorithm for finding one consistent scenario that is an o n improvement over the previously known algorithm where n is the number of intervals or points and we develop an algorithm for finding all the feasible relations that is of far more practical use than the previously known algorithm for the unrestricted version of the interval based framework finding a consistent scenario and finding the feasible relations have been shown to be np complete we show how the results for the point algebra aid in the design of a backtracking algorithm for finding one consistent scenario that is shown to be useful in practice for planning problems

identification of coupled non linear modes from free vibration using time frequency representations abstract a new method based on time frequency representations is presented for identifying the non linear modal parameters of a multi degree of freedom non linear lightly damped mechanical system the coupled non linear modes are first introduced it is shown that by using the coupled non linear modes the free response can be expressed as a linear combination of frequency and amplitude modulated components this suggests the use of time frequency methods to characterize these modulation laws and then identify the coupled non linear modes these modulation laws are extracted by using an extended definition of the so called ridges of the continuous gabor transform which enables a more accurate estimation an identification procedure of the coupled non linear modes is proposed and the validity of the whole process is confirmed by performing computer simulations of different types of non linear elastic dynamic systems

the complexity of query evaluation in indefinite temporal constraint databases abstract in previous work we have developed the scheme of indefinite l constraint databases where l the parameter is a first order constraint language this scheme extends the constraint database proposal of kanellakis et al 1990 1995 to include indefinite or uncertain information in the style of imielinski and lipski 1984 in this paper we study the complexity of query evaluation in an important instance of this abstract scheme indefinite temporal constraint databases our results indicate that the data combined complexity of query evaluation does not change when we move from queries in relational calculus over relational databases to queries in relational calculus with temporal constraints over temporal constraint databases this fact remains true even when we consider query evaluation in relational databases with indefinite information vs query evaluation in indefinite temporal constraint databases in the course of our work we provide precise bounds on the complexity of decision quantifier elimination for a subtheory of presburger arithmetic and a subtheory of real addition with order the bounds for the latter theory are original and of independent interest

on the boundary conditions for axially moving beams axially moving beam typed structures are of technical importance and present in a wide class of engineering problem as the axial speed of a beam may significantly affect the dynamic characteristics of the structure even at a low velocity it is important to accurately predict the dynamic characteristics and stability of such structures in most previous studies the net energy flux through the left end and right end boundaries of the finite beam over two simple supports has been implicitly assumed to be zero by completely ignoring the effects of its left incoming and right outgoing semi infinite beam parts or by applying fixed boundary conditions for its longitudinal vibration which seems to be very non realistic from the physical point of view thus this paper investigates the effects of the continuously incoming and outgoing semi infinite beam parts on the dynamic characteristics and stability of an axially moving beam by using the spectral element method the spectral element model is formulated from the equations of motion derived by using the hamilton s principle extended for the systems of changing mass it is numerically shown that the effects of the continuously incoming and outgoing semi infinite beam parts should be taken into account for further accurate prediction of the dynamic characteristics and stability for such axially moving beams

reasoning about temporal relations a maximal tractable subclass of allen s interval algebra we introduce a new subclass of allen s interval algebra we call ord horn subclass which is a strict superset of the pointisable subclass we prove that reasoning in the ord horn subclass is a polynomial time problem and show that the path consistency method is sufficient for deciding satisfiability further using an extensive machine generated case analysis we show that the ord horn subclass is a maximal tractable subclass of the full algebra assuming p np in fact it is the unique greatest tractable subclass amongst the subclasses that contain all basic relations

from local to global consistency abstract in reasoning tasks involving the maintenance of consistent databases so called qqconstraint networks q q it is customary to enforce local consistency conditions in order to simplify the subsequent construction of a globally coherent model of the data in this paper we present a relationship between the sizes of the variables domains the constraints arity and the level of local consistency sufficient to ensure global consistency based on these parameters a new tractability classification of constraint networks is presented we also show based on this relationship that any relation on bi valued variables which is not representable by a network of binary constraints cannot be represented by networks with any number of hidden variables

modal analysis of mechanical systems with impact non linearities limitations to a modal superposition this paper presents an attempt to generalize the modal superposition formula to mechanical systems with impact type non linearities following the procedure introduced for smooth non linearities the study is restricted to simple one and two degree of freedom systems with a unilateral constraint on one of the degrees of freedom for which the response can be analytically determined generalized frequencies modes and masses are built in the procedure the results obtained for various sets of parameters point out some limitations to the validity of a general modal superposition formula

the energetics and the stability of axially moving kirchhoff strings l the energetics and the stability of free transverse vibration of an axially moving string are investigated based on the kirchhoff nonlinear model the model is derived in a physically meaningful manner the time rate of the total mechanical energy associated with the vibration is calculated to show that the energy is not conserved it is proved that there exists a conserved quantity that remains a constant during the nonlinear vibration the conserved quantity is applied to verify the lyapunov stability of the axially moving kirchhoff string

bifurcation analysis of coupled lateral torsional vibrations of rotor systems abstract this paper presents a numerical method to analyze the bifurcation of coupled lateral torsional vibrations of rotor systems based on a hamiltonian approach a three degree of freedom dynamic model of a rotor is derived nonlinear ordinary differential equations are derived from the dynamic model the stability of the equilibrium and linear normal modes lnms are analyzed using a linearized matrix of the system equation for bifurcation analysis of the periodic orbits a nonlinear normal modes nnms computation algorithm is performed using multiple shooting methods and pseudo arclength continuation multiple shooting points are continued from lnms near equilibrium bifurcation points of the nnms are detected from the stability change of the periodic orbits during the continuation the proposed stability analysis an nnms computation of coupled lateral torsional vibration is demonstrated using two different rotor models a system with strong eccentricity and a system with weak eccentricity