有激发和衰减的有限长裂缝Ⅱ型破裂过程研究
Analytic Solutions for a Finite Crack Rupturing with Type-Ⅱ at One Tip with Exciting and Decaying Processes
-
摘要: 本文考虑在Rayleigh阻尼作用时,沿裂缝长的边界上有剪应力作用,使裂缝一端失稳而产生快速扩展(即Ⅱ型破裂)问题.应用奇异摄动理论[1]及广义富氏级数,给出这个非线性断裂动力学问题的逐次逼近解.较之已有成果,本文考虑了非线性阻尼并给出各级近似解的显式.Abstract: Under the action of Kayleigh damping, when the shear stress exerts at the boundary of the crack and causes one tip of the crack rupturing with varying velocity. By singular perturbation method, we reduce the governing non-linear partial differential equations into a system of linear ones and solve them by using generalized Fourier series.
-
[1] 钱伟长,《奇异摄动理论》,(1980)(即将出版). [2] Kim, K.S.Dynamic Propagation of a Finite Crack, Int. J.S olids and Structure 15, 9 (1979). [3] 陆远忠等,地震破裂过程的研究,地球物理学报,23. 2 (1980). [4] Костров,Б.В.,Неустановишееся распраненис трешины продолъного сдвнга,ПММ,30, (1966). [5] Eshelby, J.D.,The Elastic Field of a Crack Exiending Nonuniformly under General Anti-plane Loading, J.Mech. PhDs, Solids, 17, 3 (1969). [6] 褚武扬,《断裂力学基础》,科学出版社,(1979). [7] 王竹溪等,《特殊函数概论》,科学出版社,(1965), 692, 711-712. [8] Arscott, F, M.,Periodic Differential Equations, Pergamon Press,(1969),139. [9] E.卡姆克,《常微分方程手册》,张鸿林译,科学出版社,(1977), 152-153. [10] Gradshteyn, I.S. et al.,Table of Integrals, Series and Products, Academic Press,(1980). [11] 李颧,《断裂理论》,(1980),(即将出版). [12] В. Б.科斯特罗夫,《构造地震震源力学》,冯德益等译,地震出版社,(1979), 9, 58-59.
点击查看大图
计量
- 文章访问数: 1739
- HTML全文浏览量: 84
- PDF下载量: 538
- 被引次数: 0