A Dimensionless Quotient for Determining Coupling Strength in Modal Energy Analysis

Modal energy analysis (MODENA) is an energy-based method recently proposed to estimate the dynamic response of a coupled structure/acoustic cavity system. The accuracy of MODENA is affected by the coupling strength between structural and acoustic modes. A dimensionless coupling quotient which is equal to the ratio of the gyroscopic coupling coefficient and the critical coefficient at modal frequencies is defined to determine the coupling strength in MODENA. The coupling strength of the system is classified as weak, moderate, or strong, according to the coupling quotient with a proposed criterion. When computing the modal input power in MODENA, the mobility of the uncoupled mode can be used if the modes are weakly coupled, but the mobility of the coupled mode should be adopted to obtain accurate results if many modes are moderately coupled. The effectiveness of the proposed criterion is validated via a numerical example where a plate is coupled with an acoustic cavity. Results show that many low-order structural and acoustic modes are moderately coupled while almost all high-order modes are weakly coupled. Errors of the energy responses appear in a low-frequency band, but accurate results are acquired in a mid- to high-frequency band when the mobility of uncoupled mode is used.