A direct algebraic method to calculate the sensitivity of element modal strain energy

Abstract

The sensitivity study of modal strain energy (MSE) is of primary importance for its extensive applications in structural damage detection and health monitoring fields. In this paper, the first-order sensitivity formulae of the element MSE for a real symmetric undamped system are derived based on the algebraic eigensensitivity method. The formulae are simple and compact having the desirable properties of preserving the band and symmetry structures of the stiffness and mass matrices. Three types of analysis have been investigated on the first-order sensitivity of element MSE via a numerical parametric studies: the sensitivity to structural geometric and physical parameters, the sensitivity to structural parameter variation due to damage, and the effect of noise on the element MSE sensitivities. It is demonstrated that the element MSE is more sensitive to the geometrical parameters than the physical parameters. The fact that the element MSE change in a damaged element is larger than that of any other undamaged element is not always true for the higher modes. The sensitivity of element MSE for the lower modes is less affected by noise than that for the higher modes and therefore it will be the most likely to indicate the structural damage. © 2009 John Wiley & Sons, Ltd.