Time-Space Identification of Mechanical Impacts and Distributed Random Excitations on Plates and Membranes

The identification of dynamic loads acting on structures is a key aspect of several engineering domains involving structure-borne sound and vibration problems, stress analysis, or even the study of fatigue-induced structural damages. This work is concerned with the reconstruction of localized transient and distributed random excitations on plates and membranes from their measured vibration response. In previous investigations by the authors, the virtual fields method (VFM), an identification approach based on the principle of virtual work, was employed to identify mechanical and acoustic loadings applied to a bending panel. However, vibration data was obtained using scanning laser Doppler vibrometry (LDV), which provides a frequency-resolved measurement of the response from a combination of measurements at discrete points taken at different times. This limits the application of the VFM to stationary excitations in both space and frequency, and the acquisition time is generally long to obtain dense spatial measurements. In contrast, the deflectometry technique used here directly provides a full-field measurement of slopes so that no scan operation is required (compared to LDV). With the addition of a high-speed camera, the measurements are resolved in both space and time, enabling the study of non-stationary excitations. Moreover, since the acquisition time is independent of the number of measurement points, high spatial density measurements can be performed in seconds. This paper first reviews the principles of the VFM for non-stationary excitations and the method is extended to membranes. The deflectometry technique is then demonstrated and experimental reconstruction results on an aluminum panel are presented for two different transient mechanical loadings: instrumented impact hammer (single deterministic excitation) and impacting metal marbles (multiple unknown excitations). Finally, the identification of random excitations (diffuse acoustic field and turbulent boundary layer) is considered using a plate and a membrane.