Analytical modeling of sound transmission through clamped triple-panel partition separated by enclosed air cavities

An analytical model for sound transmission through a clamped triple-panel partition of finite extent and separated by two impervious air cavities is formulated. The solution derived from the model takes the form of that for a clamp supported rectangular plate. A set of modal functions (or more strictly speaking, the basic functions) are employed to account for the clamped boundary conditions, and the application of the virtual work principle leads to a set of simultaneous algebraic equations for determining the unknown modal coefficients. The sound transmission loss (STL) of the triple-panel partition as a function of excitation frequency is calculated and compared with that of a double-panel partition. The model predictions are then used to explore the physical mechanisms associated with the various dips on the STL versus frequency curve, including the equivalent 'mass-spring' resonance, the standing-wave resonance and the panel modal resonance. The asymptotic variation of the solution from a finite-sized partition to an infinitely large partition is illustrated in such a way as to demonstrate the influence of the boundary conditions on the soundproofing capability of the partition. In general, a triple-panel partition outperforms a double-panel partition in insulating the incident sound, and the relatively large number of system parameters pertinent to the triple-panel partition in comparison with that of the double-panel partition offers more design space for the former to tailor its noise reduction performance.