An analytical model is proposed in this paper for predicting time-averaged energies of boundary structures and enclosed sound field. The sound field is directly driven by an acoustic source and the structures are excited through acoustic-structural coupling. The present model is based on the classical modal coupling method but is developed in such a way to improve the computational efficiency in estimating the bandlimited response of acoustic-structural coupled systems particularly in the medium frequency range where a large number of acoustic and/or structural modes is involved. In this frequency range, one often has to deal with manipulation of large complex matrices in order to obtain full mathematical solutions to the system response using the classical modal coupling method. However, this is avoided if the present bandlimited model is used. This paper describes the mathematical development of the model. Numerical examples for a panel-cavity system are presented and the proposed model is compared with the classical modal coupling method in terms of computational efficiency and accuracy in the prediction of the system energies.

Vibration and absorption properties of structures which are used to form an enclosure have significant effects on the acoustical response of the enclosed sound field. Boundary structures such as panels and partitions found in real enclosures like buildings and vehicles are often elastic, thus their perturbational/coupling effect cannot be isolated from the vibrational motion of boundary-induced acoustic modes in the enclosed sound field. The effect of acoustic-structural coupling on the transient and steady-state responses of the sound field has been investigated in both low-and high-frequency ranges. In the medium-frequency range, acoustic-structural coupling problems are not well understood. In this paper, acoustic-structural interactions at medium frequencies are investigated using the modal coupling method and the effect of the coupling on the medium frequency response of the sound field in a panel-cavity system is studied. Features associated with the sound field response are then obtained when modal properties of the boundary structures are varied.

The coupling between rigid-walled modes of a rectangular cavity (RC modes) is used to obtain the shapes and resonance frequencies of rigid-walled modes of a trapezoidal cavity (TC modes) with an inclined rigid wall. A method is established to identify the TC modes, where the modes can be defined to evolve from individual RC modes. The wall inclination generates two coupling mechanisms, namely, the local coupling where the RC modes couple at the inclined wall, and the global coupling where the RC modes couple throughout the trapezoidal volume. The latter arises from the nonorthogonality of the RC modes in the trapezoidal volume. Both couplings are selective that only RC modes with the same number of nodes in the direction perpendicular to the inclination are coupled to each other. For small inclinations, each TC mode possesses the distorted shape of the RC mode that evolves it. When the inclination is increased, the TC-mode shape becomes complicated and unrecognizable, and extrema can also exist in the resonance frequency of the TC mode. These behaviors are determined by the behaviors of the local and global couplings of the RC mode. This paper provides an understanding of how the free vibration characteristics of TC modes change with the inclination and what determines these changes.

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.

Decay times of acoustic modes of a trapezoidal cavity (TC modes) with an inclined wall are studied. Each cavity wall is successively assigned an impedance surface and the other five walls are rigid. The decay times are obtained from the coupling between rigid-walled modes of the rectangular cavity (RC modes) that bounds the trapezoidal cavity. Two coupling mechanisms are identified, namely, the damping coupling and the geometrical coupling. The former is related to the coupling of RC modes at the impedance surface, while the latter is related to the coupling of RC modes at the inclined wall. Both mechanisms include the same volume coupling where RC modes couple throughout the trapezoidal cavity. When the impedance surface is at either of the two trapezoidal walls, the grouping of TC modes with same decay times and the decay time variation with the wall inclination are determined only by the damping coupling. When the surface is at any of the other rectangular walls, both the damping and geometrical couplings are at work. This paper provides an understanding of how the inclined wall and the impedance surface location affect the TC-mode grouping, and what determines the decay time variation with the inclination.