The first paper by authors presented an optimal design method for vibration reduction using additional scalar spring elements. As an advanced work of the previous one, this paper deals with a coupled acoustic-structural system using additional beam elements. First, an analytical sensitivity of the sound pressure level is formulated transforming the dynamic mass matrix of the coupled system into the symmetric matrix. A new-coupled reduction method is also presented based on frequency response functions. Then, an analytical sensitivity with respect to a cross-sectional property of an additional beam element is formulated without using an inverse matrix of the dynamic mass matrix. And, an optimization problem, where the sound pressure level at a target frequency domain as an objective function is formulated and then the methods for sensitivity analysis and optimization are shown with respect to, additional beam elements, is formulated. Finally, we demonstrate the effectiveness of the proposed method through the simple numerical example.
