A multistep acoustic method for suppressing the reconstruction instability of instantaneous vibration of an exciting planar structure

Abstract

Abstract A multistep acoustic method is extended to suppress the more serious instability in the inverse process between the time-evolving pressure on the hologram plane and the time-wavenumber acceleration spectrum on the virtual source plane, and further stabilizes the reconstruction of the instantaneous vibration of an exciting planar structure. In the extended method, the solving equation relating the time-evolving pressure to the time-wavenumber acceleration spectrum at each time step is first established. Then, the established equations at several time steps are combined to constitute a new large solving equation. Finally, after one-time solving inverse calculation of the new equation, the time-wavenumber acceleration spectra at these several time steps are solved simultaneously. The multistep calculation in the expanded method not only can reduce the total number of solving the time-wavenumber acceleration spectra for reducing the accumulation errors in the time domain, but also can expand the dimension of the solving inverse matrix to add the number of the nonzero element for improving the filtering effect. A planar plate excited by a steel ball is designed as the numerical simulation to test the ability of the extended method in suppressing the instability of the inverse process of reconstructing the structural surface acceleration. In the simulation, some important parameters, such as the position of the virtual source plane, the sampling number in the wavenumber domain, the noise and the multistep number, are discussed. The simulation results demonstrate that in the reconstruction of the instantaneous vibration, the single-step time domain plane wave superposition method is more sensitive to these parameters and the divergence problem of its solution is more serious, but the extended method has a stronger adaptation ability in the changes of these parameters and can effectively suppress the reconstruction instability of the instantaneous vibration of an exciting structure for providing a more stable solution. An experiment with a steel plate excited by a steel ball is further employed to verify the superiority of the expanded method in suppressing the serious instability of the inverse process of reconstructing the instantaneous vibration.