Modal parameter identification of MDOF structures based on vibration test

The modal mass is defined by mass matrix and mode vector in the process of transferring a multi-degree-of-freedom ∥MDOF∥ system into a single-degree-of-freedom ∥SDOF∥ system in mode space. The modal mass has a relative value depending on the normalization of mode vector and mode vector is often normalized such that the value of modal mass is unit value for the convenience of analysis [Craig, 1981]. This modal mass is used as a representative value for the mass of structure corresponding to a specific mode in the design of mass type dampers [McNamara, 1977, Fujino and Abe, 1992]. Further, it is used to determine the magnitude of modal participation factor and to estimate how the ground acceleration is distributed to each mode in the seismic analysis [Paz and Leigh, 2004]. The modal mass of an idealized analytical model, however, is different to the actual one due to modeling and construction error. Therefore, it is required to estimate the accurate modal mass through experiments. Even though the modal mass is one of the most important coefficients that which constitute a governing equation of motion of a SDOF system like natural frequency and damping ratio, it has not gained many interests compared to natural frequency and damping ratio in dynamic property identification based on vibration test.