On acoustic and structural modal cross-couplings in plate-cavity systems

Modal cross-couplings are sometimes neglected in the prediction of sound field and structural responses of vibroacoustic systems where an enclosed sound field is coupled to a vibrating boundary structure. In such systems, there are two types of modal cross-couplings and they are commonly referred to as acoustic modal cross-coupling (ACC) and structural modal cross-coupling (SCC). The prediction errors generated from neglecting either of these cross-couplings are dependent not only on the modal properties of the vibroacoustic system (e.g., modal densities, dampings, etc.), but also on whether the sound field or the structure is directly driven. However, the physical mechanisms and characteristics of both cross-couplings are not well understood and, consequently, the conditions when ACC or SCC has a significant contribution to the system responses become unknown. This paper presents a mathematical description which allows the two types of modal cross-couplings to be studied independently. This description is then used to obtain the physical mechanisms and features of both cross-couplings. The effects of each type of cross-couplings on the system responses are then investigated and the general conditions under which these modal cross-couplings may be ignored are underlined.