In this paper we analyze a virtual element method for the two dimensional elasticity spectral problem allowing small edges. Under this approach, and with the aid of the theory of compact operators, we prove convergence of the proposed VEM and error estimates, where the influence of the Lam\'e constants is presented. We present a series of numerical tests to assess the performance of the method where we analyze the effects of the Poisson ratio on the computation of the order of convergence, together with the effects of the stabilization term on the arising of spurious eigenvalues.

翻译：本文分析了一种允许微小边的二维弹性谱问题的虚拟单元法。在该方法下，借助紧算子理论，我们证明了所提出的虚拟单元法的收敛性及误差估计，其中展示了拉梅常数的影响。我们进行了一系列数值测试以评估该方法的性能，分析了泊松比对收敛阶计算的影响，以及稳定项对伪特征值产生的影响。