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

on solving wave equations on fixed bounded intervals involving robin boundary conditions with time dependent coefficients abstract in this paper it is shown how characteristic coordinates or equivalently how the well known formula of d alembert can be used to solve initial boundary value problems for wave equations on fixed bounded intervals involving robin type of boundary conditions with time dependent coefficients a robin boundary condition is a condition that specifies a linear combination of the dependent variable and its first order space derivative on a boundary of the interval analytical methods such as the method of separation of variables sov or the laplace transform method are not applicable to those types of problems the obtained analytical results by applying the proposed method are in complete agreement with those obtained by using the numerical finite difference method for problems with time independent coefficients in the robin boundary condition s the results of the proposed method also completely agree with those as for instance obtained by the method of separation of variables or by the finite difference method

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

on variable length induced vibrations of a vertical string abstract the purpose of this paper is to study the free lateral responses of vertically translating media with variable length velocity and tension subject to general initial conditions the translating media are modeled as taut strings with fixed boundaries the problem can be used as a simple model to describe the lateral vibrations of an elevator cable for which the length changes linearly in time or for which the length changes harmonically about a constant mean length in this paper an initial boundary value problem for a linear axially moving string equation is formulated in the given model a rigid body is attached to the lower end of the string and the suspension of this rigid body against the guide rails is assumed to be rigid for linearly length variations it is assumed that the axial velocity of the string is small compared to nominal wave velocity and the string mass is small compared to car mass and for the harmonically length variations small oscillation amplitudes are assumed and it is also assumed that the string mass is small compared to the total mass of the string and the car a multiple timescales perturbation method is used to construct formal asymptotic approximations of the solutions to show the complicated dynamical behavior of the string for the linearly varying length analytic approximations of the exact solution are compared with numerical solution for the harmonically varying length it will be shown that galerkin s truncation method cannot be applied in all cases to obtain approximations valid on long timescales

natural frequencies modeshapes and modal interactions for strings vibrating against an obstacle relevance to sitar and veena we study the vibration characteristics of a string with a smooth unilateral obstacle placed at one of the ends similar to the strings in musical instruments like sitar and veena in particular we explore the correlation between the string vibrations and some unique sound characteristics of these instruments like less inharmonicity in the frequencies a large number of overtones and the presence of both frequency and amplitude modulations at the obstacle we have a moving boundary due to the wrapping of the string and an appropriate scaling of the spatial variable leads to a fixed boundary at the cost of introducing nonlinearity in the governing equation reduced order system of equations has been obtained by assuming a functional form for the string displacement which satisfies all the boundary conditions and gives the free length of the string in terms of the modal coordinates to study the natural frequencies and mode shapes the nonlinear governing equation is linearized about the static configuration the natural frequencies have been found to be harmonic and they depend on the shape of the obstacle through the effective free length of the string expressions have been obtained for the time varying mode shapes as well as the variation of the nodal points modal interactions due to coupling have been studied which show the appearance of higher overtones as well as amplitude modulations in our theoretical model akin to the experimental observations all the obtained results have been verified with an alternate formulation based on the assumed mode method with polynomial shape functions

the discrete lot sizing and scheduling problem with sequence dependent setup costs abstract we consider the problem of scheduling several products on a single machine so as to meet the known dynamic demand and to minimize the sum of inventory costs and sequence dependent setup costs the planning interval is subdivided into many short periods e g shifts or days and any lot must last one or several full periods we formulate this problem as a travelling salesman problem with time windows and present a new procedure for determining lower bounds using lagrangean relaxation as well as a heuristic computational results for problems with up to 10 products and 150 periods are reported

simultaneous lotsizing and scheduling by combining local search with dual reoptimization abstract the contribution of this paper is twofold on the one hand the particular problem of integrating lotsizing and scheduling of several products on a single capacitated production line is modelled and solved taking into account sequence dependent setup times thereby continuous lotsizes meeting deterministic dynamic demands are to be determined and scheduled with the objective of minimizing inventory holding costs and sequence dependent setup costs on the other hand a new general algorithmic approach is presented a dual reoptimization algorithm is combined with a local search heuristic for solving a mixed integer programming problem this idea is applied to the above lotsizing and scheduling problem by embedding a dual network flow algorithm into threshold accepting and simulated annealing respectively computational tests show the effectiveness of the new solution method

embedding of linear programming in a simulated annealing algorithm for solving a mixed integer production planning problem the present paper is concerned with the grouping of book covers on offset plates in order to minimize the total production cost the mathematical formulation of the problem involves both binary and continuous variables as exact methods are unable to provide solutions in reasonable time a heuristic algorithm of the simulated annealing type is proposed at each iteration the values of the current solution binary variables are altered in order to yield a neighboring solution to compute the corresponding values of the continuous variables and the value of the objective function a linear programming routine is called at each iteration this constitutes the main originality of the present approach and is in principle applicable in mixed integer programming problems the procedure is tested on several examples

on resonances and the applicability of galerkin s truncation method for an axially moving string with time varying velocity abstract in this paper an initial boundary value problem for a linear homogeneous equation describing an axially moving string is investigated the time dependent velocity is assumed to vary harmonically about a constant mean velocity with a small fluctuation amplitude the two timescales perturbation method and the laplace transform method have been employed to the equation of motion in search of infinite mode approximate solutions all resonance cases are investigated in detail it will be shown that galerkin s truncation method cannot be applied to this problem in all cases to obtain approximations valid on long timescales

the discrete lot sizing and scheduling problem abstract the discrete lot sizing and scheduling problem consists in scheduling several products on a single machine so as to meet the known dynamic demand and to minimize the sum of inventory and setup cost the planning interval is phased into many short periods e g shifts or days and setups may occur only at the beginning of a period a branch and bound procedure is presented using lagrangean relaxation for determining both lower bounds and feasible solutions the relaxed problems are solved by dynamic programming computational results on a personal computer are reported for various examples from the literature with up to 12 products and 122 periods or 3 products and 250 periods the procedure yields optimal solutions or at least feasible solutions with tight lower bounds in a few minutes the results are compared with those obtained by solving the usual capacitated lot sizing problem

scattering by obstacles of finite capacity abstract for very general generators of diffusion semigroups we show that the essential and absolutely continuous spectra do not change when one adds an extra dirichlet boundary condition on a small set this is done by proving that the corresponding semigroup differences are hilbert schmidt or trace class respectively our method consists in a factorization argument which is based on calculating the semigroup difference via the feynman kac formula we also derive trace class estimates for differences of resolvent powers provided the underlying semigroup has finite local dimension

studying the effects of production loss due to setup in dynamic production scheduling abstract we study the effects of production loss during setup in dynamic production scheduling for process industries producing several products on non identical flexible processors the production scheduling problem is formulated as a mixed integer programming model and solved using primal and dual lagrangean based procedures real data from a tile company and randomly generated data were used to test the model our computational results show the solution procedure to be fast robust and stable even for cases with large setup costs and production losses and for cases with demands of up to 52 periods

the passage through resonance in a catenary vertical cable hoisting system with slowly varying length abstract a passage through resonance in a catenary vertical cable system with periodic external excitation is analyzed due to the time varying length of the vertical cable the natural frequencies of the system vary slowly and a transient resonance may occur when one of the frequencies coincides with the frequency of an external excitation at some critical time a simplified model of the system with proportional damping is proposed this model is analyzed by using a combined perturbation and numerical technique the method of multiple scales is used to formulate a uniformly valid perturbation expansion for the response near the resonance and a system of first order ordinary differential equations for the slowly varying amplitude and phase of the response results this system is integrated numerically on a slow time scale a model example is discussed and the behavior of the essential dynamic properties of the system during the transition through resonance is examined

infinite mode analysis and truncation to resonant modes of axially accelerated beam vibrations abstract the transverse vibrations of simply supported axially moving euler bernoulli beams are investigated the beam has a time varying axial velocity with viscous damping traveling beam eigenfunctions with infinite number of modes are considered approximate analytical solutions are sought using the method of multiple scales a perturbation technique a detailed analysis of the resonances in which upto four modes of vibration involved are performed stability analysis is treated for each type of resonance approximate stability borders are given for the resonances involving only two modes for higher number of modes involved in a resonance sample numerical examples are presented for stabilities

diffusion on delone sets we consider graphs associated to delone sets in euclidean space such graphs arise in various ways from tilings here we provide a unified framework in this context we study the associated laplace operators and show gaussian heat kernel bounds for their semigroups these results apply to both metric and discrete graphs

threshold accepting a general purpose optimization algorithm appearing superior to simulated annealing abstract a new general purpose algorithm for the solution of combinatorial optimization problems is presented the new threshold accepting method is even simpler structured than the wellknown simulated annealing approach the power of the new algorithm is demonstrated by computational results concerning the traveling salesman problem and the problem of the construction of error correcting codes moreover deterministic versions of the new heuristic turn out to perform nearly equally well consuming only a fraction of the computing time of the stochastic versions as an example the deterministic threshold accepting method yields very near to optimum tours for the famous 442 cities traveling salesman problem of grotschel within 1 to 2 s of cpu time

an asymptotic theory for a class of initial boundary value problems for weakly nonlinear wave equations with an application to a model of the galloping oscillations of overhead transmission the aim of this paper is to contribute to the foundation of the asymptotic methods for initial boundary value problems and initial value problems for weakly nonlinear hyperbolic partial differential equations of order two in this paper an asymptotic theory for a class of initial boundary value problems for weakly nonlinear wave equations is presented the theory implies the well posedness of the problem in the classical sense and the validity of formal approximations on long timescales as an application of the theory an initial boundary value problem for a rayleigh wave equation is studied in detail using a two timescale perturbation method from an aeroelastic analysis it is shown that this initial boundary value problem may be regarded as a model describing the growth of wind induced oscillations of overhead transmission lines

operators with singular continuous spectrum i general operators the baire category theorem implies that the family f of dense sets g in fixed metric space x is a candidate for generic sets since it is closed under countable intersections and if x is perfect has no isolated point then a f has uncountable intersections with any open ball in x

zero measure cantor spectra for continuum one dimensional quasicrystals we study schrodinger operators on r with measures as potentials choosing a suitable subset of measures we can work with a dynamical system consisting of measures we then relate properties of this dynamical system with spectral properties of the associated operators the constant spectrum in the strictly ergodic case coincides with the union of the zeros of the lyapunov exponent and the set of non uniformities of the transfer matrices this result enables us to prove cantor spectra of zero lebesgue measure for a large class of operator families including many operator families generated by aperiodic subshifts

generic singular spectrum for ergodic schrodinger operators we consider schrodinger operators with ergodic potential v n f t n n z where t is a nonperiodic homeomorphism we show that for generic f c the spectrum has no absolutely continuous component the proof is based on approximation by discontinuous potentials which can be treated via kotani theory

correlation dimension wonderland theorems existence of generic sets of self adjoint operators related to correlation dimensions of spectral measures is investigated in separable hilbert spaces typical results say that given an orthonormal basis the set of operators whose corresponding spectral measures are both 0 lower and 1 upper correlation dimensional is generic the proofs rely on details of the relations among fourier transform of spectral measures and hausdorff and packing measures on the real line then such results are naturally combined with the wonderland theorem applications are to classes of discrete one dimensional schrodinger operators and general bounded self adjoint operators as well physical consequences include a proof of exotic dynamical behavior of singular continuous spectrum in some settings

transient vibration phenomena in deep mine hoisting cables part 1 mathematical model abstract the classical moving co ordinate frame approach and hamilton s principle are employed to derive a distributed parameter mathematical model to investigate the dynamic behaviour of deep mine hoisting cables this model describes the coupled lateral longitudinal dynamic response of the cables in terms of non linear partial differential equations that accommodate the non stationary nature of the system subsequently the rayleigh ritz procedure is applied to formulate a discrete mathematical model consequently a system of non linear non stationary coupled second order ordinary differential equations arises to govern the temporal behaviour of the cable system this discrete model with quadratic and cubic non linear terms describes the modal interactions between lateral oscillations of the catenary cable and longitudinal oscillations of the vertical rope it is shown that the response of the catenary vertical rope system may feature a number of resonance phenomena including external parametric and autoparametric resonances the parameters of a typical deep mine winder are used to identify the depth locations of the resonance regions during the ascending cycles with various winding velocities

spectral and topological properties of a family of generalised thue morse sequences the classic middle thirds cantor set leads to a singular continuous measure via a distribution function that is known as the devil s staircase the support of the cantor measure is a set of zero lebesgue measure here we discuss a class of singular continuous measures that emerge in mathematical diffraction theory and lead to somewhat similar distribution functions yet with significant differences various properties of these measures are derived in particular these measures have supports of full lebesgue measure and possess strictly increasing distribution functions in this sense they mark the opposite end of what is possible for singular continuous measures for each member of the family the underlying dynamical system possesses a topological factor with maximal pure point spectrum and a close relation to a solenoid which is the kronecker factor of the system the inflation action on the continuous hull is sufficiently explicit to permit the calculation of the corresponding dynamical zeta functions this is achieved as a corollary of analysing the anderson putnam complex for the determination of the cohomological invariants of the corresponding tiling spaces

on the transversal vibrations of an axially moving continuum with a time varying velocity transient from string to beam behavior in this paper an initial boundary value problem for a linear equation describing an axially moving stretched beam will be considered the velocity of the beam is assumed to be time varying since the order of magnitude of the bending stiffness terms depends on the vibration modes and the frequencies involved a combination of two simplified models that is a string equation for the lower frequencies and a beam with string effect equation for the higher frequencies will be used to describe the transversal vibrations of the system accurately based on the calculations of the natural frequencies the regions of applicability of these sub models will be determined a two time scales perturbation method will be used to construct formal asymptotic approximations of the solutions non resonant and some resonant cases will be studied for four different values of the relative errors an important implication of the earlier results in the literature is that for these types of axially moving continua problems the use of only string like models is not appropriate to describe the dynamics of these types of axially moving continua problems correctly one has to include small bending stiffness in the model in this paper it is explicitly shown how to work with a combined model that is a string model at the low frequencies and a tensioned beam model at the higher frequencies

generic sets in spaces of measures and generic singular continuous spectrum for delone hamiltonians we show that geometric disorder leads to some purely singular continuous spectrum generically the main input is a result of simon known as the wonderland theorem in 17 section 2 here we provide an alternative approach and actually a slight strengtheningbyshowingthatvarioussetsofmeasuresdefinedbyregularityproperties aregenericinthesetofallmeasuresonalocallycompactmetricspace asabyproduct we obtain the fact that a generic measure on euclidean space is singular continuous

two parameter spectral averaging and localization for non monotonic random schrodinger operators we prove exponential localization at all energies for two types of one dimensional random schr6dinger operators the poisson model and the random displacement model as opposed to anderson type models these operators are not monotonic in the random parameters therefore the classical one parameter version of spectral averaging as used in localization proofs for anderson models breaks down we use the new method of two parameter spectral averaging and apply it to the poisson as well as the displacement case in addition we apply results from inverse spectral theory which show that two parameter spectral averaging works for sufficiently many energies all but a discrete set to conclude localization at all energies

on transversal oscillations of a vertically translating string with small time harmonic length variations abstract in this paper the free transverse vibrations of a vertically moving string with a harmonically time varying length are studied the string length variations are assumed to be small by using the multiple timescales perturbation method in conjunction with a fourier series approach we determine the resonance frequencies and derive the non secularity conditions in the form of an infinite dimensional system of coupled ordinary differential equations this system describes the long time behavior of the amplitudes of the oscillations then the eigenvalues of the obtained system are studied by the galerkin truncation method and applicability of this method is discussed apart from this the dynamic stability of the solution is investigated by an energy analysis additionally resonance detuning is considered