Iterative computation of modal sensitivities

The computation of frequency and mode shape sensitivities with respect to design parameters is essential to many, structural optimization and finite element updating algorithms. Approximating the gradients may lead to poor estimates and loss of convergence, but on the other hand the cost of exact methods, such as Nelson's (Nelson, R.,, "Simplified Calculations of Eigenvector Derivatives," A1AA Journal, Vol. 14, No. 9,1976, pp. 1201-1205), is often not acceptable for industrial-size models. The present study thus analyses existing approximation methods, suggests a first-order improvement of Fox and Kapoor's modal basis (Fox, R., and Kapoor, M., "Rate of Change of Eigenvalues and Eigenvectors"' A1AA Journal, Vol. 6, No. 12, 1968, pp. 2426-242, 9) and proposes a residual iteration technique allowing accurate computations of modeshape sensitivities. An engine cover model and a model of the Ariane 5 main cryogenic stage are used to analyze, for models of realistic sizes, the accuracy and computational costs of the proposed methods.