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We introduce a pure--stress formulation of the elasticity eigenvalue problemwith mixed boundary conditions. We propose an H(div)-based discontinuousGalerkin method that imposes strongly the symmetry of the stress for thediscretization of the eigenproblem. Under appropriate assumptions on the meshand the degree of polynomial approximation, we demonstrate the spectralcorrectness of the discrete scheme and derive optimal rates of convergence foreigenvalues and eigenfunctions. Finally, we provide numerical examples in twoand three dimensions.

A DG method for a stress formulation of the elasticity eigenproblem with strongly imposed symmetry