Direct Deconvolution Approach Toward Force Reconstruction for a Thin Plate From Pressure Measurements

This paper proposes a direct deconvolution approach toward force reconstruction for a thin plate by taking the acquired pressure as the input. The analytical relationship between the force spectrum on the surface of the plate and the pressure spectrum in the near field of the plate is established in the wavenumber-time domain by means of the equation of motion of the plate and the real-time nearfield acoustic holography, based on which the unknown force spectrum at each wavenumber point is then reconstructed through the pressure measured by a microphone array. The force in spatial and temporal domains is finally obtained by performing an inverse spatial Fourier transform on its force spectrum at each time step. Two numerical simulations demonstrate that the proposed approach is feasible in locating the position of the force accurately and identifying its time-history simultaneously, even the forces with various types in local regions, such as distributed or concentrated shapes or in the case of an environment with a low signal-to-noise ratio. The experimental result of an impact force reconstruction validates the effectiveness of the approach even more. The highlight of this paper lies in using an analytical way instead of the time-consuming experimental way to establish the force-pressure relationship, which makes it possible to reconstruct the external force through a non-contact acoustic measurement and to further understand the root cause of sound radiation of the plate.