Reconstruction of the Force Applied to a Plate in the Time Domain From Sound Pressure Measurements

Abstract

This paper provides a non-contact approach to reconstruct the distributed or concentrated force applied to a plate in the time domain. This approach is based on sound pressure measurements and is realized by coupling the techniques of real-time near-field acoustic holography (RT-NAH) and force reconstruction. A microphone array is used to measure the sound pressures in the near field of the plate. The measured sound pressures are taken as the inputs of the RT-NAH to reconstruct the vibration responses, including the normal acceleration, velocity, and displacement, on the surface of the plate. With the reconstructed vibration responses, the equation of motion governing the forced vibration can be further processed to reconstruct the force applied to the plate in the time domain. In the process of reconstructing the vibration responses, a displacement–pressure impulse response function is derived for the first time and is used in the RT-NAH. Results of numerical simulations as well as experiments demonstrate that the proposed approach can identify the location of the force accurately and reconstruct the time history of the force effectively, thereby helping to diagnose the mechanical cause of the radiated noise.