Extraction of fundamental mode shapes from superposition resonance of a plate

Abstract

This work proposes a method that can extract a set of individual fundamental mode shapes from a set of measured superposition mode shapes, when a structure possesses two or more mode shapes with the same natural frequency. It is revealed that the number of nonzero singular values of a set of measured mode shapes indicates the geometric multiplicity resolved in measured mode shapes. Utilizing the sensitivity of singular values resolved in measured mode shapes, an updating algorithm is developed to extracta set of individual fundamental mode shapes. The performance of the proposed method is demonstrated using a numerical simulation for a selected class of structures.