Simulations of Rayleigh’s Wave on Curved Surface
Affiliation(s)
Institute of Applied Mathematics, National Cheng-Kung University, Taiwan. Department of Mechanical Engineering, Cheng Shiu University, Taiwan.
Institute of Applied Mathematics, National Cheng-Kung University, Taiwan. Department of Mechanical Engineering, Cheng Shiu University, Taiwan.
ABSTRACT
Impulsive line load in a half-space (Lamb’s problem) can be solved with a closed form solution. This solution is helpful for understanding the phenomenon of Rayleigh’s waves. In this article, we use a boundary element method to simulate the solution of an elastic solid with a curved free surface under impact loading. This problem is considered difficult for numerical methods. Lamb’s problem is calculated first to verify the method. Then the method is applied on the problems with different surface curvatures. The method simulates the phenomenon of Rayleigh’s wave propagating on a curved surface very well. The results are shown in figures.
Impulsive line load in a half-space (Lamb’s problem) can be solved with a closed form solution. This solution is helpful for understanding the phenomenon of Rayleigh’s waves. In this article, we use a boundary element method to simulate the solution of an elastic solid with a curved free surface under impact loading. This problem is considered difficult for numerical methods. Lamb’s problem is calculated first to verify the method. Then the method is applied on the problems with different surface curvatures. The method simulates the phenomenon of Rayleigh’s wave propagating on a curved surface very well. The results are shown in figures.
Cite this paper
S. Shen and C. Wang, "Simulations of Rayleigh’s Wave on Curved Surface," Applied Mathematics, Vol. 4 No. 6, 2013, pp. 963-967. doi: 10.4236/am.2013.46132.
S. Shen and C. Wang, "Simulations of Rayleigh’s Wave on Curved Surface," Applied Mathematics, Vol. 4 No. 6, 2013, pp. 963-967. doi: 10.4236/am.2013.46132.
References
[1] A. C. Eringen and E. S. Suhubi. “Elastodynamics, Volume II,” Academic Press, New York, 1975. [2] D. E. Beskos, “Boundary Element Method in Dynamic Analysis,” Applied Mechanics Review, Vol. 40, No. 1, 1987, pp. 1-23. doi:10.1115/1.3149529 [3] D. E. Beskos, “Boundary Element Method in Dynamic Analysis: Part II (1986-1996),” Applied Mechanics Review, Vol. 50, No. 3, 1997, pp. 149-197. doi:10.1115/1.3101695 [4] S. Y. Shen, “An Indirect Elastodynamics Boundary Element Method with Analytic Bases,” International Journal for Numerical Methods in Engineering, Vol. 57, No. 6, 2003, pp. 767-794. doi:10.1002/nme.702 [5] J. D. Achenbach, “Wave Propagation in Elastic Solid,” Noth-Holland, Amsterdam, 1976.
[1] A. C. Eringen and E. S. Suhubi. “Elastodynamics, Volume II,” Academic Press, New York, 1975. [2] D. E. Beskos, “Boundary Element Method in Dynamic Analysis,” Applied Mechanics Review, Vol. 40, No. 1, 1987, pp. 1-23. doi:10.1115/1.3149529 [3] D. E. Beskos, “Boundary Element Method in Dynamic Analysis: Part II (1986-1996),” Applied Mechanics Review, Vol. 50, No. 3, 1997, pp. 149-197. doi:10.1115/1.3101695 [4] S. Y. Shen, “An Indirect Elastodynamics Boundary Element Method with Analytic Bases,” International Journal for Numerical Methods in Engineering, Vol. 57, No. 6, 2003, pp. 767-794. doi:10.1002/nme.702 [5] J. D. Achenbach, “Wave Propagation in Elastic Solid,” Noth-Holland, Amsterdam, 1976.