Abstract
Under the action of Rayleigh damping, when the shear stress exerts at the boundary of the crack and causes one tip of the crack to rupture with varying velocity, by the singular perturbation method[1], we reduce the governing nonlinear partial differential equations to a system of linear ones and solve them by using generalized Fourier series.
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References
Chien Wei-zang, Theory of Singular Perturbation (in Chinese), (to be published).
Kim, K. S.,Dynamic propagation of a finite crack, Int. J. Solids and Structure, Vol. 15, No. 9 (1979).
Lu Yuan-zhong et al.,A study of the earthquake faulting process, Acta Geophysica Sinica, Vol. 23, No. 2, (1980), (in Chinese).
Kostrov, B. V.,Unsteady propagation of longitudinal shear-cracks, Appl. Math. Mech. (PMM) (1964).
Eshelby, J. D.,The elastic field of a crack extending nonuniformly under general anti-plane loading, J. Mech. Phys. Solids, Vol. 17, No. 3, (1969), 177.
Tu Yu-yang,Foundations of Fracture Mechanics, Science Press, (1979). (in Chinese)
Wang Zy-xie et al.,Introductions to Particular Functions, Science Press, (1965), 692, 711–712. (in Chinese)
Arscott, F. M.,Periodic Differential Equations, Pergamon Press, (1964), 139.
Kamke, E.,Differentialgleichungen Losungsmethoden und Losungen, I. Gewohnliche Differentialgleichungen, eighth edition, (1967).
Gradshteyn, I. S. and Ryzhik, I. M., Table of Integrals, Series and Products, Academic Press, (1980), 372–373, 478–479.
Li Hao, Fracture Theory (in Chinese), (to be published).
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Communicated by Chien Wei-zang.
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Ja-shen, F., Ping, X. Analytic solutions for a finite crack rupturing with type-II at one tip with exciting and decaying processes. Appl Math Mech 3, 749–764 (1982). https://doi.org/10.1007/BF01875739
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DOI: https://doi.org/10.1007/BF01875739