This paper describes a modal analysis technique to approximate the vibrations of incompressible elastic solids using a stabilized finite element method to approximate the associated eigenvalue problem. It is explained why residual based formulations are not appropriate in this case, and a formulation involving only the pressure gradient is employed. The effect of the stabilization term compared to a Galerkin approach is detailed, both in the derivation of the approximate formulation and in the error estimate provided.

中文翻译：

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使用压力稳定有限元法对不可压缩材料的弹性振动进行模态分析

本文描述了一种模态分析技术，用于使用稳定有限元方法来近似不可压缩弹性固体的振动，以近似相关的特征值问题。解释了为什么基于残差的公式在这种情况下不合适，并且采用了仅涉及压力梯度的公式。与 Galerkin 方法相比，稳定项的影响在近似公式的推导和提供的误差估计中都有详细说明。