激光激发Lamb波的有限元时域和频域数值分析

Numerical Analysis of Laser-Generated Lamb Waves by Finite Element Method in Time and Frequency Domain

以平面应变理论为基础,从弹性动力学平衡方程出发,推导得到频域动力学平衡方程。忽略材料的粘性特征,分别在时域和频域中建立激光激发兰姆(Lamb)波的有限元数值模型。比较分析两种模型的求解过程,在此基础上,在频域中研究激光作用在粘弹性薄板上激发Lamb波的特征。结果表明,激光激发的Lamb波主要包含低频的弱色散的对称模和色散的反对称模;有限元频域模型能有效地处理粘弹性材料中Lamb波的传播问题;材料的粘性特征会引起Lamb波的振幅衰减,且不同模式波的衰减(因子)不同。

Based on the theory of plane strain and the elastic equations of dynamic equilibrium, the equations of dynamic equilibrium in the frequency domain are derived. The finite element models of laser-generated Lamb waves in the time and frequency domain are established for elastic material. Based on the numerical calculations, the solving process of the two models is compared. Moreover, the characteristics of laser-generated Lamb waves on a thin viscoelastic plate are analyzed in the frequency domain. The results show laser-generated Lamb waves mainly include the lower frequency components of the weak dispersion symmetric mode and the dispersive anti-symmetric mode. The propagation of laser-generated Lamb waves on viscoelastic materials can be calculated effectively by the finite element model in the frequency domain. In addition, the amplitudes of Lamb waves are attenuated in the viscoelastic material, and the attenuation coefficients to different modes of the wave are different.