An extended modal approach for modal parameter identification of structure under the existence of harmonic excitations

The existing operational modal analysis (OMA) methods for the structure subjected to white noise and harmonic combined excitations have some limitations such as easy misjudgment of true and spurious modes and slow identification speed. Through expressing the system response with the extended modal matrix (EMM) and the extended modal response (EMR) vector, a novel operational modal parameter identification approach called the extended modal approach is proposed to obtain structural true modes under the existence of multiple harmonic excitations. The EMRs consist of the true modal responses and the spurious modal responses, and each of the former is random while each of the latter is harmonic. It is also proved theoretically that the EMM can be identified using the power spectrum density transmissibility (PSDT) method. Therefore, the extended modal approach includes three steps: (1) Using the PSDT to identify the EMM; (2) Utilizing the least squares reconstruction method to obtain the EMRs from the underdetermined extended modal equation; (3) Judging each of the EMRs to be true or spurious according to its empirical density function. Structural true modes can be ultimately obtained by removing all spurious modes from the identified results. The new approach is numerically verified through the OMA of two multiple-degree-of-freedom systems and then experimentally verified through the OMA of a test beam. The results in numerical simulation and experiments all show that the extended modal approach can identify accurately and quickly structural true modes under multiple harmonic excitations. Besides, the approach has good robustness against noise contamination.