Simulations of transverse vibrations of an axially moving string: a modified difference approach.

*(English)*Zbl 1329.74301Summary: 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.

##### MSC:

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 |

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\textit{L. Chen} et al., Appl. Math. Comput. 166, No. 3, 596--607 (2005; Zbl 1329.74301)

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##### References:

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