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In this paper we analyze a virtual element method for the two dimensionalelasticity spectral problem allowing small edges. Under this approach, and withthe aid of the theory of compact operators, we prove convergence of theproposed VEM and error estimates, where the influence of the Lam\'e constantsis presented. We present a series of numerical tests to assess the performanceof the method where we analyze the effects of the Poisson ratio on thecomputation of the order of convergence, together with the effects of thestabilization term on the arising of spurious eigenvalues.

A virtual element method for the elasticity spectral problem allowing small edges