Dubuc Brennan, Ebrahimkhanlou Arvin, Salamone Salvatore
Department of Civil, Architectural and Environmental Engineering, University of Texas at Austin, 301 East Dean Keeton Street, Austin, Texas 78712, USA.
J Acoust Soc Am. 2018 Jun;143(6):3220. doi: 10.1121/1.5040140.
This paper presents a numerical approach based on spectral methods for the computation of guided ultrasonic wave modes (i.e., Lamb and shear horizontal) in nonuniformly stressed plates. In particular, anisotropic elastic plates subjected to a normal stress profile, which varies nonuniformly over their thickness, are considered. The proposed approach computes the modeshapes and the full three-dimensional dispersion spectrum (i.e., real frequency, complex wavenumber). It therefore includes both propagating (real wavenumber) and non-propagating (complex wavenumber) modes. Furthermore, an approach for robustly post-processing the dispersion spectra in order to compute the group velocity of propagating modes is presented, which is based on a spectral quadrature method. Numerical results are presented for two case studies: (1) a bending profile in a fiber-reinforced graphite/epoxy plate, and (2) an exponential profile in a silver plate. The results show the computational efficiency (i.e., spectral convergence) of the proposed method compared to other existing approaches such as the sublayering and finite element methods.
本文提出了一种基于谱方法的数值方法，用于计算非均匀应力板中的导波模式（即兰姆波和水平剪切波）。特别地，考虑了在厚度方向上非均匀变化的法向应力分布作用下的各向异性弹性板。所提出的方法计算模态形状和完整的三维频散谱（即实频率、复波数）。因此，它既包括传播模式（实波数），也包括非传播模式（复波数）。此外，还提出了一种基于谱求积法对频散谱进行稳健后处理以计算传播模式群速度的方法。给出了两个案例研究的数值结果：（1）纤维增强石墨/环氧树脂板中的弯曲分布；（2）银板中的指数分布。结果表明，与其他现有方法（如分层法和有限元法）相比，所提方法具有计算效率（即谱收敛性）。
