爆炸下球壳变形空间周期分布的理论计算方法

早期研究提出了对振动叠加应变增长现象的解剖式分析方法，进而发现爆炸加载下带扰动源球壳上的弯曲波和壳体变形呈空间周期分布的规律。参考Timoshenko梁的弯曲理论，基于平截面假定和壳体发生较小的弯曲变形的假设，推导出球壳上弯曲波波速和波长的关系，计算得到最短弯曲波和与膜振动频率相近的弯曲波的波速，还结合早期研究提出的壳体变形分布周期与弯曲波波速的关系，计算得到了壳体变形空间分布的周期。结果表明:（1）理论计算结果与数值仿真结果基本吻合，其中弯曲波波速的计算结果与数值仿真结果相差在15%以内，壳体变形空间分布周期的计算结果与数值仿真结果相差在12%以内；（2）弯曲波波长越短，波速越快，当波长无限短时，波速趋于极限值，约为声速的0.574倍。本计算方法为解剖式分析方法提供了一定的理论依据。

A theoretical method for calculating spatial periodic distribution of deformation of a spherical shell under explosive loading

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.