Smooth orthogonal decomposition-based vibration mode identification

A new multivariate data analysis method called smooth orthogonal decomposition (SOD) is proposed to extract linear normal modes and natural frequencies of multi-degree-of-freedom and distributed-parameter vibration systems. It is demonstrated that for an undamped free vibration of a multi-degree-of-freedom system, the computed smooth orthogonal modes are in direct correspondence with the actual normal vibration modes and the smooth orthogonal values are related to the corresponding natural frequencies. The same is also shown to be true for lightly damped free vibrations of both lumped- and distributed-parameter systems. In contrast to the intrinsic limitations of the proper orthogonal decomposition (POD) analysis, which requires the knowledge of system's mass matrix to extract normal modes and cannot uniquely identify modal subspaces that have similar proper orthogonal values, the SOD is shown to overcome both of these deficiencies. Numerical examples are provided to compare the performances of the POD- and SOD-based modal identification in various types of vibration environment.