Mace Brian R, Duhamel Denis, Brennan Michael J, Hinke Lars
ISVR, University of Southampton, Southampton SO17 1BJ, United Kingdom.
J Acoust Soc Am. 2005 May;117(5):2835-43. doi: 10.1121/1.1887126.
A method is presented by which the wavenumbers for a one-dimensional waveguide can be predicted from a finite element (FE) model. The method involves postprocessing a conventional, but low order, FE model, the mass and stiffness matrices of which are typically found using a conventional FE package. This is in contrast to the most popular previous waveguide/FE approach, sometimes termed the spectral finite element approach, which requires new spectral element matrices to be developed. In the approach described here, a section of the waveguide is modeled using conventional FE software and the dynamic stiffness matrix formed. A periodicity condition is applied, the wavenumbers following from the eigensolution of the resulting transfer matrix. The method is described, estimation of wavenumbers, energy, and group velocity discussed, and numerical examples presented. These concern wave propagation in a beam and a simply supported plate strip, for which analytical solutions exist, and the more complex case of a viscoelastic laminate, which involves postprocessing an ANSYS FE model. The method is seen to yield accurate results for the wavenumbers and group velocities of both propagating and evanescent waves.
本文提出了一种方法，通过该方法可以从有限元（FE）模型预测一维波导的波数。该方法涉及对传统的低阶有限元模型进行后处理，其质量矩阵和刚度矩阵通常使用传统的有限元软件包来求解。这与之前最流行的波导/有限元方法（有时称为谱有限元方法）形成对比，后者需要开发新的谱单元矩阵。在这里描述的方法中，使用传统的有限元软件对波导的一部分进行建模并形成动态刚度矩阵。应用周期性条件，从所得传递矩阵的特征解中得出波数。描述了该方法，讨论了波数、能量和群速度的估计，并给出了数值示例。这些示例涉及梁和简支板条中的波传播，对于这些情况存在解析解，以及粘弹性层合板这种更复杂的情况，其中涉及对ANSYS有限元模型进行后处理。该方法对于传播波和消逝波的波数和群速度都能产生准确的结果。
