Abstract
For free and random vibrations of weakly damped systems, a one-to-one relationship between vibration modal shapes of dynamic mechanical systems and linear compound matrix, and a one-to-one relationship between modal responses and principal components are demonstrated using the concept of modal coordinates. Based on this theoretical link, a novel time-domain structural system three-dimensional statistical operational modal analysis technique is proposed then. Numerical simulation processing results show that, the new PCA based method is insensitive to Gauss measurement noise, and enables to identify main contribution modal shapes and eigenfrequencies from the displacement response-only in despite of system boundary, load type, and load position.