Complex modal analysis of structural vibration and acoustic radiation of plates

Inhomogeneous damping distribution leads to the occurrence of complex modes of structures. Complex modes' vibration and acoustic radiation characteristics are different from real modes. This paper studies the complex modal characteristics of inhomogeneously damped plates for forced vibration. We used the state space method to obtain the complex eigenvalues and eigenvectors of the vibration system and calculated the relationship between modal coordinates and frequency under unit force. The results show that the absolute values of the modal coordinates of two conjugate complex eigenvectors are different, and the structure's vibration is dominated by the eigenvectors corresponding to eigenvalues with positive imaginary parts near natural frequencies. When investigating the structural sound radiation in the vibration mode space, each mode's acoustic radiation is not independent but coupled with each other. The influence of the coupling between complex modes on the calculation results of the acoustic radiation power of the plate is studied in this paper. The results show that the coupling effect between modes cannot be ignored when calculating the acoustic radiation power based on complex modes. Finally, the error of calculating acoustic power using the decoupling approximation instead of the complex mode method is analyzed.