Efficient computation of eigenvector sensitivities for structural dynamics

An iterative procedure is presented for computing eigenvector sensitivities due to finite element model parameter variations. The present method is a preconditioned conjugate projected gradient-based technique and is intended to utilize the existing matrix factorizations developed for an iterative eigensolution such as Lanczos or Subspace Iteration. As such, this technique can be integrated into a coupled eigensolver/sensitivity software module and leverage the nonrecurring costs of the solver. The use of projection operators in the algorithm is dictated by the indefinite character of the governing coefficient matrix of the eigenvector derivative. Two model examples are provided to demonstrate both the accuracy of the present technique and its superior efficiency as compared to existing techniques with similar accuracy.