Shape sensitivity analysis of natural frequencies of structures using boundary elements

The boundary element approach to shape sensitivity analysis of eigenvalues of free vibrating elastic structures is presented. The eigenvalue problem is described in terms of the boundary integral equation method. Using the variational approach for variable regions, first-order sensitivities of simple frequencies are derived. Dependence of eigenvalues with respect to the stochastic shape of the boundary is considered. The numerical procedure of discretization of the problem is characterized. Numerical examples for two-dimensional problems are presented.