Manconi Elisabetta, Mace Brian R
Dipartimento di Ingegneria Industriale, Universita degli Studi di Parma, Parma, Italy.
J Acoust Soc Am. 2009 Jan;125(1):154-63. doi: 10.1121/1.3021418.
This paper describes a wave finite element method for the numerical prediction of wave characteristics of cylindrical and curved panels. The method combines conventional finite elements and the theory of wave propagation in periodic structures. The mass and stiffness matrices of a small segment of the structure, which is typically modeled using either a single shell element or, especially for laminated structures, a stack of solid elements meshed through the cross-section, are postprocessed using periodicity conditions. The matrices are typically found using a commercial FE package. The solutions of the resulting eigenproblem provide the frequency evolution of the wavenumber and the wave modes. For cylindrical geometries, the circumferential order of the wave can be specified in order to define the phase change that a wave experiences as it propagates across the element in the circumferential direction. The method is described and illustrated by application to cylinders and curved panels of different constructions. These include isotropic, orthotropic, and laminated sandwich constructions. The application of the method is seen to be straightforward even in the complicated case of laminated sandwich panels. Accurate predictions of the dispersion curves are found at negligible computational cost.
本文描述了一种用于数值预测圆柱面板和曲面面板波动特性的波动有限元方法。该方法将传统有限元与周期结构中的波传播理论相结合。结构一小段的质量矩阵和刚度矩阵通常使用单个壳单元进行建模，特别是对于层合结构，使用沿横截面划分网格的一组实体单元，然后利用周期性条件对其进行后处理。这些矩阵通常使用商业有限元软件包来求解。所得特征值问题的解给出了波数和波模式的频率演化。对于圆柱几何形状，可以指定波的周向阶数，以定义波在圆周方向上传播通过单元时所经历的相位变化。通过应用于不同结构的圆柱体和曲面面板来描述和说明该方法。这些结构包括各向同性、正交各向异性和层合夹层结构。即使在层合夹层板这种复杂情况下，该方法的应用也很简单。以可忽略不计的计算成本得到了色散曲线的准确预测。
