Laplace变换法研究SHPB实验中试件的黏弹性波传播问题

郑宇轩; 陈亮; 周风华; 王礼立

doi:10.6052/0459-1879-14-002

Laplace变换法研究SHPB实验中试件的黏弹性波传播问题

doi: 10.6052/0459-1879-14-002

宁波大学省部共建教育部冲击与安全工程重点实验室, 宁波 315211

基金项目: 国家自然科学基金资助项目(11272163,11390361).

详细信息

作者简介:
周风华,研究员,主要研究方向:冲击动力学研究和断裂力学.

中图分类号: O347.4
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- 文章访问数: 1098
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- 被引次数: 0
出版历程
- 收稿日期: 2013-12-31
- 修回日期: 2014-02-28
- 刊出日期: 2014-11-18

USING LAPLACE TRANSFORM TO SOLVE THE VISCOELASTIC WAVE PROBLEMS IN THE SHPB EXPERIMENTS

MOE Key Laboratory of Impact and Safety Engineering, Ningbo University, Ningbo 315211, China

Funds: The project was supported by the National Natural Science Foundation of China (11272163, 11390361).

摘要

摘要: 对分离式霍普金森压杆(split Hopkinson pressure bar, SHPB) 实验中试件的黏弹性波传播的控制方程组进行Laplace 变换,并结合恰当的初始-边界条件求解,得到变换域的应力、速度、应变等变量的像函数的精确表达式. 采用该方法处理SHPB 实验中涉及黏弹性试件内部应力非均匀性问题,并给出数值反变换解. 作为特例,对于弹性试件分别采用级数展开法和留数定理进行反Laplace 变换,从而给出弹性夹层介质中应力波传播问题的解析解.
- 黏弹性波 /
- 分离式霍普金森压杆 /
- 解析解 /
- 拉普拉斯变换 /
- 数值反变换
Abstract: In relation to the dynamic tests of materials, the approach to solve the viscoelastic wave propagations in split Hopkinson pressure bar (SHPB) tests was summarized. By conducting Laplace transform, the governing partial differential equations were transformed to ordinary differential equations for the image functions, which were solved analytically with suitable boundary equations. Inversely transforming these image functions gives the results of the stress, velocity, and strain in the bar. A wave problem are analyzed to evaluate the internal stress distributions in a viscoelastic specimen occurred in SHPB tests. The problem was solved numerically by way of numerical inverse Laplace transform. A special case when the specimen is pure elastic was solved analytically, giving the exact solution to the problem of elastic wave propagation in a sandwich elastic media.
- viscoelasticity wave /
- SHPB /
- analytical solution /
- Laplace transform /
- numerical inverse transform

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参考文献(17)

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