Dynamic Load Vectors for Localization of Mass and Stiffness Perturbations

Abstract

The well-established Dynamic Damage Locating Vector (DDLV) method offers localization of structural damage through a linear transformation of the null vectors of the transfer matrix change or, in the stochastic case of unknown input, a surrogate hereof. The null vectors are referred to as DDLVs, and it has been previously shown how applying these as loads to the structural domain will result in zero steady-state strain in any subdomain containing stiffness perturbations. The present paper explores the use of DDLVs for localization of mass-related damage and proves that any mass perturbation will, upon application of the DDLVs, be confined to the subdomain exhibiting zero steady-state motion. Since the strain field is realized from a surjective linear transformation of the displacement field, the DDLVs allow for localization of both mass- and stiffness-related damage without adding computational complexity to the existing procedures. The paper outlines the interrogation scheme for both damage types and demonstrates the basic principles through numerical and experimental examples.