Relationship between acoustic radiation modes and structural modes and its applications

Both acoustic radiation modes and structural modes play an important role in the field of structure-borne sound, however, little work has been done for inherent relations between these two kinds of modes. This paper is concerned with the relationship between the radiation modes and structural modes. First, a governing equation for relating the radiation mode and structural mode is given based on the characteristics of the modes. Then, using the symmetric or anti-symmetric properties of two kinds of modes, the corresponding relations are presented. And then, numerical examples are given to verify the theoretical investigations, and it has been shown that, for a simply supported rectangular panel vibrating at low frequency, the first radiation mode is mainly due to (odd, odd) structural modes; the following radiation modes are respectively due to (even, odd), (odd, even), and (even, even) structural modes. Finally, such relations are applied to active acoustic structural control and provide a direct help for the arrangement of the secondary forces.