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High-order solution of nonlinear acoustic wave equation for isotropic solids using perturbation and finite difference methods

Abstract : Nonlinear acoustic wave equation with Murnaghan parameters in isotropic solids is usually resolved by perturbation method [1-3]. High-order harmonics are obtained by expanding the equation in one linear and a series of nonlinear equations. It is found that errors in harmonics will be accumulated when the order is increased. To estimate these errors at high-order harmonics, numerical method of finite difference in time domain (FDTD) was employed and the solutions were compared to those obtained by perturbation method. Computational parameters from steel were used as an example. Results show that perturbation solutions of fundamental wave and the second-order harmonics are in good agreements with the solutions in FDTD, relative errors are no more than 10%. While for higher order harmonics, relative errors increase heavily, especially for solutions at longer propagation distance or with higher driving amplitude, the difference is up to 50%, or even higher.
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Submitted on : Wednesday, March 2, 2022 - 8:38:48 AM
Last modification on : Wednesday, March 23, 2022 - 3:51:33 PM

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  • HAL Id : hal-03593442, version 1

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Wenhan Lyu, Xianmei Wu, Wei-Jiang Xu, Jiayi Chen. High-order solution of nonlinear acoustic wave equation for isotropic solids using perturbation and finite difference methods. 14th International Conference on Theoretical and Computational Acoustics, ICTCA 2019, Jul 2019, Beijing, China. pp.315-322. ⟨hal-03593442⟩

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