Sensitivities of eigenvalues and eigenvectors from complex perturbations

Abstract

The utility of complex perturbations to estimate the sensitivity of modal parameters in self-adjoint conservative models is examined. In the Complex Step Derivative (CSD) approach the parameter for which the derivative is required is perturbed in the direction of the imaginary axis and the eigenvalue problem for the perturbed matrices is solved; the real part has the solution of the unperturbed eigenvalue problem and the imaginary the sensitivities times the perturbation magnitude. This paper examines the utility of the CSD approach as a method to compute sensitivities in structural dynamics. © The Society for Experimental Mechanics, Inc. 2012.