Numerical Analysis on the Dispersion Effect of the Longitudinal Wave in Elastic Bar

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Journal of Vibration and Shock ›› 2011, Vol. 30 ›› Issue (6) : 83-85.

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Numerical Analysis on the Dispersion Effect of the Longitudinal Wave in Elastic Bar

Qin Hu1 ; Aihong Han2

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Abstract

In Hamiltonian space, the dispersion effect of the longitudinal wave in elastic bar
is investigated by multi-symplectic method. The multi-symplectic formulations and several local
conservation laws (including the multi-symplectic conservation law, the local energy conservation
law and the local momentum conservation law) of the longitudinal wave equation that describes
the dispersion effect in elastic bar are presented firstly. Then the multi-symplectic midpoint
scheme is constructed to solve the multi-symplectic partial differential equations that are derived
from the longitudinal wave equation. The numerical experiments are also reported finally, the
results of which show that the multi-symplectic scheme can simulate the dispersion effect of the
longitudinal wave in elastic bar well. In addition, the multi-symplectic scheme can satisfy the local
conservation laws exactly, which implies that the multi-symplectic method is an efficient
algorithm with excellent long-time numerical behaviors

Key words

Multi-symplectic / Elastic bar / Dispersion effect

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Qin Hu;Aihong Han. Numerical Analysis on the Dispersion Effect of the Longitudinal Wave in Elastic Bar [J]. Journal of Vibration and Shock, 2011, 30(6): 83-85