Identification of impact force on a thick plate based on the elastodynamic and higher-order time-frequency analysis

Abstract

The current paper presents a novel approach to precisely locate and characterize an impact load in thick plates. The approach is based on the analysis of the acoustic waveforms measured by a sensor array located on the plate surface in combination with the theoretical Green's function for the plate. The Green's functions are derived based on either the exact elastodynamic theory or an approximate shear deformation plate theory. For accurate estimation of the location of the impact source, the time differences in the arrival times of the waves at the sensors and their propagation velocities are determined first. This is accomplished through the use of a combined higher-order time-frequency (CHOTF) method, which is capable of detecting signals with lower signal to noise ratio compared with other available methods. Since most of the energy in the wave is carried by the flexural waves ( A0 mode), the group velocity of this mode is extracted using the CHOTF technique for estimating the impact source location. The estimates are shown to be in excellent agreement with the actual locations and time histories of the applied impact loads.

Identification of the Impact Location in a Gas Duct System Based on Acoustic Wave Theory and the Time Frequency

“…Therefore, the group speed of the reflective wave as well is not constant and dependant on the cut-off frequency. It is obtained through equation (11). In this section, the cut-off frequencies f rmn , acoustic modes, the phase speed c p and the group speed c g are calculated by the theoretical method discussed in the previous section.…”

“…4. Using equation (10) and equation (11), the phase speed c p and the group speed c g were also theoretically calculated. The Mach number is not considered in this validation test.…”

“…There are slight differences among these results (calculated results are listed in Table 1). These differences average approximately 3.8% due to the use of the time-frequency resolution of the STFT method [11]. However, the dispersive phenomenon .…”

“…According to these results, the phase speed of the direct waves associated with the (0,0) mode is approximately 343±2 m/s. The group speed and phase speed of the (1,0) mode calculated theoretically using equation (11) are also plotted together with the speed of the direct wave. As the phase speed of the direct waves is identical to the sound speed of air in an anechoic chamber, it is 343 m/s at 20°C.…”

“…The time delay τ depends on the frequency, as the group speed depends on the frequency. The group speed and phase speed of the (1,0) mode were calculated theoretically using equation (11). These results are plotted in Fig.…”