Large-Amplitude Damped Free Vibration of a Stretched String

Anand, G. V.

doi:10.1121/1.1911578

Cited by 60 publications

(41 citation statements)

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“…It can be argued that physically relevant initial conditions have an almost constant T [12]. For a reference position of a straight stretched string, both Equations (5) and (7) require that be constant for T to be constant.…”

Section: Initial and Boundary Conditionsmentioning

confidence: 99%

Flow‐induced vibrations of non‐linear cables. Part 1: Models and algorithms

Evangelinos

Lucor

et al. 2002

Numerical Meth Engineering

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SUMMARYIn this paper, we develop governing equations for non-linear cables as well as a formulation for the coupled ow-structure problem. The structure is discretized with second-order accuracy while the ow is discretized using spectral=hp elements in the context of the arbitrary Lagrangian-Eulerian formulation (ALE). Several benchmark problems are considered and the computational implementation is detailed. In the second part of this work large-scale simulation examples are presented.

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Section: Initial and Boundary Conditionsmentioning

confidence: 99%

Flow‐induced vibrations of non‐linear cables. Part 1: Models and algorithms

Evangelinos

Lucor

et al. 2002

Numerical Meth Engineering

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“…In [1,2,5], the authors proposed a less natural model, consisting in neglecting the quartic term − x in (120). This can be fully justified (see [7]) when the string is submitted to transverse solicitations only.…”

Section: Approximations Of the Geometrically Exact Modelmentioning

confidence: 99%

Energy preserving schemes for nonlinear Hamiltonian systems of wave equations: Application to the vibrating piano string

Chabassier

Joly

2010

Computer Methods in Applied Mechanics and Engineering

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This paper considers a general class of nonlinear systems, "nonlinear Hamiltonian systems of wave equations". The first part of our work focuses on the mathematical study of these systems, showing central properties (energy preservation, stability, hyperbolicity, finite propagation velocity . . . ). Space discretization is made in a classical way (variational formulation) and time discretization aims at numerical stability using an energy technique. A definition of "preserving schemes" is introduced, and we show that explicit schemes or partially implicit schemes which are preserving according to this definition cannot be built unless the model is trivial. A general energy preserving second order accurate fully implicit scheme is built for any continuous system that fits the nonlinear Hamiltonian systems of wave equations class. The problem of the vibration of a piano string is taken as an example. Nonlinear coupling between longitudinal and transversal modes is modeled in the "geometrically exact model", or approximations of this model. Numerical results are presented.

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“…Position x" (t) is the current one of the slider and is the lefthand side moving boundary of the string in the deformed con"guration. Neglecting the longitudinal elastic motion of the string [1,2] is an appropriate assumption at lower frequencies and small amplitude of lateral motion. To obtain the coupled equations of motion.…”

Section: Formulation Of Equilibrium Equationsmentioning

confidence: 99%