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

Document Type : Regular Article


Nanjing University of Science and Technology, Nanjing, Jiangsu, 210094, China



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.


Allan D. P. (1980). Acoustics: An Introduction to Its Physical Principles and Applications. the Acoustical Society of America.##
Anderson, J. G., G. Katselis and C. Caputo (2000). Analysis of a generic warhead part 1: experimental and computational assessment of free field overpressure. DSTOTR-1313. Australia: Defence Science and Technology Organization.##
Artero-Guerrero, J., J. Pernas-Sánchez and F. Teixeira-Dias (2017). Blast wave dynamics: The influence of the shape of the explosive. Journal of Hazardous Materials 331, 189-199.##
Bowles, T., D. Stevens and M. Stanley (2012). Blast Loads in and Urban Environment: Structures Congress 2012. 201270-79.##
Brode, H. L. (1955). Numerical solutions of spherical blast waves. Journal of Applied Physics 26(6), 766-75.##
Chen, J., H. K. Ching and F. Allahdadi (2007). Shock-induced detonation of high explosives by high velocity impact. Journal of Mechanics of Materials and Structures 2(9), 1701-1721.##
Cooper, G. J. and D. E. M. Taylor (1989). Biophysics of Impact Injury to the Chest and Abdomen. BMJ Military Health. 135, 58-67.##
Dragomiretskiy, K. and D. Zosso (2014). Variational Mode Decomposition. IEEE Transactions on Signal Processing 62(3), 531-544.##
Fouchier, C., D. Laboureur, L. Youinou, E. Lapebie and J. Buchlin (2017). Experimental investigation of blast wave propagation in an urban environment. Journal of Loss Prevention in the Process Industries 49, 248-265.##
Friedlander, F. G. (1946). The diffraction of sound pulses. I. Diffraction by a semi-infinite plate. Proceedings of the Royal Society of London A 186, 322–344.##
Goel, M. D. (2015). Blast: Characteristics, Loading and Computation—An Overview. In: Matsagar V. (eds) Advances in Structural Engineering. Springer, New Delhi.##
He, Z. Y. and Zhao Y. F. (1981). Fundamental of acoustic theory. National Defense Industry Press.##
Held, M. (1983a). Blast waves in free air. Propellants,Explosives, Pyrotechnics 18(1), 1-8.##
Held, M. (1983b). TNT-Equivalent. Propellants, Explosives, Pyrotechnics. 8, 158-167.##
Henrych, J. (1979). The dynamics of explosion and its use. Elsevier, Amsterdam.##
Hong, X., W. Li and W. Li (2020). Energy Spectrum of Explosion Shock Wave Signals of Multi-layer Composite Charge. ACTA ARMAMENTARII 41(11), 2243-2251.##
Huang, N. E. and Wu Z. (2008). A review on Hilbert-Huang transform: Method and its applications to geophysical studies. Reviews of Geophysics. 46(2), G2006.##
Isabelle, S. (2018). Blast Effects: Physical Properties of Shock Waves. Springer Nature.##
Izadifard, R. A. and M. Foroutan (2010). Blast wave parameters assessment at different altitude using numerical simulation. Turkish journal of engineering & environmental sciences 34(1), 25-41.##
Kinney, G. F. and K. J. Grahm (1985). Explosive shocks in air. Springer, Berlin.##
Kong, L., J. Su and Z. Li (2010). Energy Spectrum Analysis of Several Kinds of Explosive Blast. Chinese Journal of Explosives & Propellants. ##
Li, L., F. Wang, F. Shang, Y. Jia, C. Zhao and D. Kong (2017). Energy spectrum analysis of blast waves based on an improved Hilbert–Huang transform. Shock Waves 27(3), 487-494.##
Li, M., J. Jiang and X. Wang (2018). Shock wave propagation characteristics of double layer charge explosion in the air. Explosion and Shock Waves 38 (2), 367-372.##
Li, X., Y. Ma and S. Li (2019). Research on Frenquency Distribution of Peak Area of Blast Shock Wave. Transactions of Beijing Institute of Technology 39(02), 125-130.##
Li, Z., J. Chen, Y. Zi, J. Pan and Y. Wang (2016). Improved VMD for feature visualization to identify wheel set bearing fault of high-speed locomotive. IEEE Instrumentation and Measurement Technology Conference.##
Maiz, L., W. Trzciński, M. Szala, J. Paszula and K. Karczewski (2016). Studies of Confined Explosions of Composite Explosives and Layered Charges. Central European Journal of Energetic Materials 13(4), 957-977.##
Ni, P., J. Li, H. Hao, Y. Xia, X. Wang and J.M. Lee (2018). Time‐varying system identification using variational mode decomposition. Structural Control and Health Monitoring 25(6).##
Silnikov, M. V., M. V. Chernyshov and A. I. Mikhaylin (2015). Blast wave parameters at diminished ambient pressure. Acta Astronautica 109, 235-240.##
Simoens, B. and M. Lefebvre (2015, December). Influence of the Shape of an Explosive Charge: Quantification of the Modification of the Pressure Field. Central European Journal of Energetic Materials.##
Sun, M. and L. Zhi (2020). Modal parametric identification of building structures based on VMD. Journal of Vibration and Shock 39(01), 175-183, 190.##
Thornhill, C. K. (1959). The shape of a spherical blast wave. Armament Research and Development Establishment (ARDE) Memo. (B) 41/59. London: HMSO.##
Vladimir, F. (2018). Intense Shock Waves on Earth and in Space. Moscow Fizmatlit.##
Wang, C., Z. Liu, L. Gao, D. Xu and Z. Zhuang (2017). Analytical and numerical modeling on resonant response of particles in polymer matrix under blast wave. Computational Materials Science 140, 70-81.##
Zhang, E., G. Lu and H. Yang (2020). Band gap features of metaconcrete and shock wave attenuation in it. Explosion and Shock Waves 40(06), 69-77.##