爆炸下球壳变形空间周期分布的理论计算方法

刘文祥; 张德志; 钟方平; 程帅; 张庆明

doi:10.11883/bzycj-2019-0340

爆炸下球壳变形空间周期分布的理论计算方法

doi: 10.11883/bzycj-2019-0340

刘文祥^{1, 2,},
张德志¹,
钟方平¹,
程帅¹,
张庆明^2, ,

1.
西北核技术研究院强动载与效应实验室，陕西西安 710024
2.
北京理工大学爆炸科学与技术国家重点实验室，北京 100081

详细信息

作者简介:
刘文祥（1982－　），男，博士，副研究员，liuwenxiang@nint.ac.cn

通讯作者:
张庆明（1963－　），男，博士，教授，qmzhang@bit.edu.cn

中图分类号: O383
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出版历程
- 收稿日期: 2019-09-03
- 修回日期: 2020-05-22
- 刊出日期: 2020-06-01

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

1.
Laboratory of Intense Dynamic Loading and Effect, Northwest Institute of Nuclear Technology, Xi’an 710024, Shaanxi, China
2.
State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100000, China

摘要

摘要: 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。
- 爆炸容器 /
- 应变增长 /
- 弯曲波 /
- 空间周期分布
Abstract: 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.
- explosive vessel /
- strain growth /
- bending wave /
- spatial periodic distribution

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图 1 球壳数值模型

Figure 1. The numerical model for the spherical shell

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图 2 扰动源半径为10 mm时球壳上扰动源正对位置的应变曲线

Figure 2. Total strain-time curves of spherical shell at the pole opposite to the site of perturbation when the disturbance source radius is 10 mm

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图 3 薄壳变形机理

Figure 3. Deformation mechanism of thin shell

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图 4 壳体上不同位置的弯曲应变曲线和不同时刻的壳体上弯曲波

Figure 4. Bending strain-time curves at different positions on spherical shell and bend waves at different moments

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图 5 2种扰动源半径下壳体应变峰值的分布

Figure 5. Total strain along spherical shell for two kinds of disturbance source radii

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图 6 壳体弯曲变形示意图

Figure 6. Schematic diagram of spherical shell bending deformation

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图 7 球壳上弯曲波波速与波长的关系

Figure 7. Relation between length and velocity of bending wave

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图 8 弯曲波A的波长与波速

Figure 8. Length and velocity of bending wave A

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表 1 弯曲波的速度

Table 1. Velocities of bending waves propagating along shell.

α/(°)	与膜振动频率相近的弯曲波A		最短弯曲波
α/(°)	到达时间/μs	平均波速/(m·s⁻¹)	到达时间/μs	平均波速/(m·s⁻¹)
44.2	436.3	427.1	63.4	2 964.8
88.0	909.7	427.1	131.6	3 069.1
136.0	1 436.6	443.4	203.8	3 188.7
180.0	1 894.7		267.5

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参考文献(12)

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