Analyzing excitation forces acting on a plate based on measured acoustic pressure

This paper presents a theoretical study on "seeing" through an elastic structure to uncover the root cause of sound and vibration by using nearfield acoustical holography (NAH) and normal modes expansion. This approach is of generality because vibro-acoustic responses on the surface of a vibrating structure can always be reconstructed, exactly or approximately. With these vibro-acoustic responses, excitation forces acting on the structure can always be determined, analytically or numerically, given any set of boundary conditions. As an example, the explicit formulations for reconstructing time-harmonic excitation forces, including point, line and surface forces, and their arbitrary combinations acting on a rectangular thin plate in vacuum mounted on an infinite baffle are presented. The reason for choosing this example is that the analytic solutions to vibro-acoustic responses are available, and in-depth analyses of results are possible. Results demonstrate that this approach allows one to identify excitation forces based on measured acoustic pressures and reveal their characteristics such as locations, types and amplitudes, as if one could "see" excitation forces acting behind the plate based on acoustic pressure measured on the opposite side. This approach is extendable to general elastic structures, except that in such circumstance numerical results must be sought.