Finitie element synthesis of real eigenvalue problems. Case study of adaptation of vibration eigenpairs.

Abstract

A methodology of the shift synthesis of real eigenvalue problems is presented so that the structure modification can be synthesized for a given set of the change of eigenvalue and eigenvector. The change of the aimed eigenpair due to the design parameters is estimated by the first order perturbation of the finite element solution in the vicinity of the baseline structure. The approximate equation between the objective eigenpair and the estimated one is employed as a subsidiary condition for the functional comprised of the sum of the squared design parameters. The design parameters are determined by the minimization of the functional so that the modification is sought as near the beseline structure as possible. The numerical examples are carried out in regard to the modification of a cantilever beam and a simplified truck chasis by use of the bending stiffness of the beams as design parameters.