中文摘要：

在波动数值模拟中,瑞利阻尼可近似描述介质耗散特性,且可用于抑制人工边界引发的高频和零频失稳,但瑞利阻尼对波动的影响尚未清晰认识。针对集中质量有限元模拟的一维波动,利用傅里叶模态分析了有阻尼离散网格中波动的性质。理论分析表明alpha阻尼必然使得波数为零及邻近的波动对应为非行进波,其使行波衰减一致,而beta阻尼不会导致波数为零及邻近的非行进波,其使行波衰减随着波数增大而增大。数值实验验证了上述结论。本文研究结果为进一步推进瑞利阻尼在波动数值模拟中的应用提供一定的理论依据。

英文摘要：

Rayleigh damping can be used to describe energy dissipation of medium approximately and suppress high or zero frequency instability caused by artificial boundary in wave simulation, but the Rayleigh damping effects on wave motion are not known clearly. Focusing on 1 D wave simulation by lumped mass finite element method, the property of wave motion in discrete grid with Rayleigh damping is investigated by Fourier mode. Theoretical analysis shows that non-traveling wave motion whose wave number is zero or near zero exists and traveling wave attenuation is all the same for different wave number caused by alpha damping, while for beta damping, such non-traveling wave dose not exists and traveling wave attenuation increases with the increasing of wave number. These conclu- sions are verified by numerical experiments. The research results can provide certain theoretical basis for further promoting the application of Rayleigh damping in wave simulation.