Cross-Length of Mode Shapes in Structural Dynamics: Concept and Applications

Abstract

Modal mass is one of the modal parameters that are required to define the dynamic behavior of a structure when a modal model is used. In experimental modal analysis (EMA), modal masses are the least reliable modal parameter, while in operational modal analysis (OMA), modal masses cannot be estimated because the exciting forces are not measured. In this paper, the concept of cross-length between mode shapes is formulated for continuous and discrete systems, and important properties are derived from this definition. It is demonstrated that the cross-length is zero for all modes in constant mass density systems. For structures consisting of parts with different mass density, equations that relate the partial cross-lengths over the different volumes and the total masses of the different parts can be formulated for each mode, i.e., there is a relationship between the cross-length and the total mass of the parts with different mass density. The equations proposed in the paper have been validated through numerical simulations and experimental testing on two lab-scaled structures. This methodology can also be applied as a correlation technique, specifically to determine how the mass is distributed in the structure, as well as a technique to construct a proportional FRF in constant mass density systems.