A framework for numerical and experimental correlation of mode shapes with low spatial resolution: a catamaran’s case study

Abstract

This work presents a framework for correlating numerical and experimental mode shapes with low spatial resolution using the Local Correspondence of Modes and Modal Coordinates (LCMC). As a case study, an operational modal analysis of a catamaran was performed. Thirteen global natural frequencies and their respective modes were identified in the range between 1 Hz and 50 Hz, using only six sensors placed on its main deck. Thus, due to experimental modes' spatial incompleteness, this required its full numerical model to be assembled and reduced using the System Equivalent Reduction Expansion Process (SEREP) to its main deck. Consequently, the reduced numerical modal matrix was used to fill in the gaps in the sparse set of the experimental modes, creating the mixed modal matrix. Then, this matrix was correlated and expanded using LCMC to the degrees of freedom (DOFs) that have not been measured. As a result, the spatial resolution of the catamaran's experimental mode shapes was successfully increased from 6 to 174 DOFs. In general, the use of LCMC improved the Modal Assurance Criteria (MAC) of the correlated modes matrix compared to the MAC of the mixed modal matrix.