LIU Wenxiang, ZHANG Dezhi, ZHONG Fangping, CHENG Shuai, ZHANG Qingming. A theoretical method for calculating spatial periodic distribution of deformation of a spherical shell under explosive loading[J]. Explosion And Shock Waves, 2020, 40(6): 064201. doi: 10.11883/bzycj-2019-0340
Citation:
LIU Wenxiang, ZHANG Dezhi, ZHONG Fangping, CHENG Shuai, ZHANG Qingming. A theoretical method for calculating spatial periodic distribution of deformation of a spherical shell under explosive loading[J]. Explosion And Shock Waves, 2020, 40(6): 064201. doi: 10.11883/bzycj-2019-0340
LIU Wenxiang, ZHANG Dezhi, ZHONG Fangping, CHENG Shuai, ZHANG Qingming. A theoretical method for calculating spatial periodic distribution of deformation of a spherical shell under explosive loading[J]. Explosion And Shock Waves, 2020, 40(6): 064201. doi: 10.11883/bzycj-2019-0340
Citation:
LIU Wenxiang, ZHANG Dezhi, ZHONG Fangping, CHENG Shuai, ZHANG Qingming. A theoretical method for calculating spatial periodic distribution of deformation of a spherical shell under explosive loading[J]. Explosion And Shock Waves, 2020, 40(6): 064201. doi: 10.11883/bzycj-2019-0340
The strain growth, caused by vibration superposition, has been anatomized by the membrane strain and the bending strain in existing studies, and the bending wave and deformation spatial periodic distribution of a spherical shell under explosive loading have been found. By referring to the theoretical method for Timoshenko beam bending, based on a plane-section assumption and a small-deformation limit, the relation between the velocity and the wavelength of bending wave was deduced, and the velocities of the shortest bending wave and the bending wave with a frequency similar to that of the membrane vibration were calculated. By combining the relation between the deformation spatial distribution period and the bending wave velocity presented in existing studies, the deformation spatial distribution period was calculated. The main conclusions are as follows: (1) The theoretical results are in good agreement with the numerical results, in which the difference between the numerical and theoretical results of bending wave velocity is within 15%, and the difference between the numerical and theoretical results of the deformation spatial distribution period is within 12%. (2) The shorter the wavelength, the higher the wave velocity, when the wavelength is infinite short, the bending wave velocity tends to the limit value, about 0.574 times the speed of sound. The theoretical method presented in this paper provides a certain theoretical support for anatomizing strain growth.
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