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Simulations of transverse vibrations of an axially moving string: a modified difference approach. (English) Zbl 1329.74301
Summary: A modified finite difference approach to simulate transverse vibrations of an axially moving string is presented. The stress is treated as a new unknown in discretization of the spatial variable. A set of differential-algebraic equations is established based on the discreted governing equation and the constitutive relation. For linear vibrations, a conserved functional is employed to test the algorithm, and the 1, 2, 3, 4-term truncated modal analytical solutions are compared with the numerical solution. For the free nonlinear vibration, a new conserved functional is used to check the algorithm. Effects of the transport speed on the free and forced nonlinear vibrations are numerically investigated.

74S20 Finite difference methods applied to problems in solid mechanics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
74H45 Vibrations in dynamical problems in solid mechanics
74K05 Strings
Full Text: DOI
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