Accuracy in finite element computation for eigenfrequencies

In this paper we propose an original numerical method to get upper and lower bounds for the eigenfrequencies of an elastic structure. This method is based on a ‘static’ formulation for eigenvalue problems built up from a new quotient R_s which is defined on a load space. From R_s properties, upper and lower bounds for the exact eigenfrequencies are proved. The application of the method requires the solution of an eigenvalue problem of finite dimension and the computation of a constant which is characteristic of the discretization subspace. Results of numerical tests are given for the vibration problem of an elastic clamped membrane.