Error estimation and h-adaptive refinement in the analysis of natural frequencies

This paper deals with the estimation of the discretization error and the definition of an optimum h-adaptive process in the finite element analysis of natural frequencies and modes. Consistent and lumped mass matrices are considered. In the first case, the discretization error essentially proceeds from the stiffness modelization, so it is possible to apply the same error estimators than those considered in static problems. On the other hand, the error associated with the modelization of the inertial properties must be taken into account if lumped mass matrices are used. As far as h-adaptivity is concerned, it is usually interesting to obtain meshes with a specified error for each mode. However, traditional criteria for static problems consider only one load case. Defining the optimum mesh as the one that gets the desired error with the minimum number of elements, a method is proposed for the h-adaptive process taking into account a set of natural modes simultaneously. The proposed methods have been validated by applying them to bi-dimensional test problems.