Energy Evolution Mechanism of Air Shock Wave Propagation and Attenuation Based on VMD–HT Energy Spectrum

Energy spectrum is an important tool for reflecting time–frequency characteristics of signals. The energy spectra of air shock wave at different explosion distances ware analyzed to investigate the energy evolution mechanism in the propagation and attenuation process. Waveforms of air shock wave were obtained from explosion tests and numerical simulations. Energy propagation and attenuation mechanisms of air shock wave were discussed on the basis of the wave theory of fluid. Instantaneous and marginal energy spectra of air shock wave were calculated using variational modal decomposition (VMD) and Hilbert transform (HT). Energy evolution laws of air shock wave with time, frequency, and explosion distance were analyzed according to the statistical results of the energy spectra. Results showed that the instantaneous energy peak of air shock wave is directly proportional to the square of its pressure peak while inversely proportional to the third power of propagation distance. Nonlinear attenuation of air shock wave will cause frequency dispersion and decelerate the attenuation rate of the total energy of air shock wave. The energy evolution laws of air shock wave with time and frequency reflected by instantaneous and marginal energy spectra were consistent with the theoretical analysis results.