  This paper studies the family of interior penalty discontinuous Galerkin
methods for solving the Herrmann formulation of the linear elasticity
eigenvalue problem in heterogeneous media. By employing a weighted Lam\'e
coefficient norm within the framework of non-compact operators theory, we prove
convergence of both continuous and discrete eigenvalue problems as the mesh
size approaches zero, independently of the Lam\'e constants. Additionally, we
conduct an a posteriori analysis and propose a reliable and efficient
estimator. The theoretical findings are supported by numerical experiments.
