NEW NUMERICAL METHOD FOR VOLTERRA INTEGRAL EQUATION OF THE SECOND KIND IN PIEZOELASTIC DYNAMIC PROBLEMS

Applied Mathematics and Mechanics (English Edition) ›› 2004, Vol. 25 ›› Issue (1): 16-23.

NEW NUMERICAL METHOD FOR VOLTERRA INTEGRAL EQUATION OF THE SECOND KIND IN PIEZOELASTIC DYNAMIC PROBLEMS

丁皓江¹, 王惠明², 陈伟球¹

1. Department of Civil Engineering, Zhejiang University, Hangzhou 310027, P. R. China;
2. Department of Mechanics, Zhejiang University, Hangzhou 310027, P. R. China

收稿日期:2002-11-01 修回日期:2003-08-03 出版日期:2004-01-18 发布日期:2004-01-18
基金资助:
the National Natural Science Foundation of China(10172075)

NEW NUMERICAL METHOD FOR VOLTERRA INTEGRAL EQUATION OF THE SECOND KIND IN PIEZOELASTIC DYNAMIC PROBLEMS

DING Hao-jiang¹, WANG Hui-ming², CHEN Wei-qiu¹

1. Department of Civil Engineering, Zhejiang University, Hangzhou 310027, P. R. China;
2. Department of Mechanics, Zhejiang University, Hangzhou 310027, P. R. China

Received:2002-11-01 Revised:2003-08-03 Online:2004-01-18 Published:2004-01-18
Supported by:
the National Natural Science Foundation of China(10172075)

摘要/Abstract

摘要： The elastodynamic problems of piezoelectric hollow cylinders and spheres under radial deformation can be transformed into a second kind Volterra integral equation about a function with respect to time, which greatly simplifies the solving procedure for such elastodynamic problems. Meanwhile, it becomes very important to find a way to solve the second kind Volterra integral equation effectively and quickly. By using an interpolation function to approximate the unknown function, two new recursive formulae were derived, based on which numerical solution can be obtained step by step. The present method can provide accurate numerical results efficiently. It is also very stable for long time calculating.

Abstract: The elastodynamic problems of piezoelectric hollow cylinders and spheres under radial deformation can be transformed into a second kind Volterra integral equation about a function with respect to time, which greatly simplifies the solving procedure for such elastodynamic problems. Meanwhile, it becomes very important to find a way to solve the second kind Volterra integral equation effectively and quickly. By using an interpolation function to approximate the unknown function, two new recursive formulae were derived, based on which numerical solution can be obtained step by step. The present method can provide accurate numerical results efficiently. It is also very stable for long time calculating.

中图分类号:

丁皓江;王惠明;陈伟球. NEW NUMERICAL METHOD FOR VOLTERRA INTEGRAL EQUATION OF THE SECOND KIND IN PIEZOELASTIC DYNAMIC PROBLEMS[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(1): 16-23.

DING Hao-jiang;WANG Hui-ming;CHEN Wei-qiu. NEW NUMERICAL METHOD FOR VOLTERRA INTEGRAL EQUATION OF THE SECOND KIND IN PIEZOELASTIC DYNAMIC PROBLEMS[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(1): 16-23.

参考文献

[1] Kress R. Linear Integral Equation[M]. Berlin: Springer-Verlag, 1989.
[2] Delves L M, Mohamed J L. Computational Method for Integral Equations[M]. Cambridge: Cambridge University Press, 1985.
[3] Christopher T H, Baker M A. The Numerical Treatment of Integral Equation [M]. Oxford: Oxford University Press, 1977.
[4] Hamming R W. Numerical Methods for Scientists and Engineers (2nd Edition)[M]. New York:McGraw-Hill, 1973.
[5] SHEN Yi-dan Integral Equation[M]. Beijing:Peking University of Science and Technology Press,1992. (in Chinese)
[6] YAN Yu-bin,CUI Ming-gen. The exact solution of the second kind Volterra integral equation[J].Numerical Mathematics-A Jounal of Chinese University., 1993,15(4): 291-296. (in Chinese)
[7] LI Hong-xiang, WANG Guo-jin, WANG Cun-zheng. Exact solutions of several classes of integral equations of Volterra type and ordinary differential equations [J]. Journal of Shanghai Institute of Railway Technology, 1995, 16(1): 72-85. (in Chinese)
[8] Souchet R. An analysis of three-dimensional rigid body collisions with friction by means of a linear integral equation of Volterra[J]. International Journal of Engineering Science, 1999, 37(3): 365-378.
[9] Rose J L, Chou S C, Chou P C. Vibration analysis of thick-walled spheres and cylinders[J].Journal of the Acoustical Society of America, 1973,53(3): 771-776.
[10] Pao Y H, Ceranoglu A N. Determination of transient responses of a thick-walled spherical shell by the ray theory[J]. ASME Journal of Applied Mechanics, 1978, 45(1):114-122.
[11] WANG Xi, Gong Yu-ming. A theoretical solution for axially symmetric problem in elastodynamics [J]. Acta Mechanica Sinica, 1991,7(3): 275-282.
[12] DING Hao-jiang, WANG Hui-ming, CHEN Wei-qiu. A theoretical solution of cylindrical shells for axisymmetric plain strain elastodynamic problems[J]. Applied Mathematics and Mechanics (English Edition) ,2002, 23(2): 138-145.
[13] DING Hao-jiang, WANG Hui-ming, HOU Peng-fei. The transient responses of piezoelectric hol low cylinders for axisymmetric plane strain problems[J]. International Journal of Solids and Structures, 2003,40 (1): 105-1 23.
[14] DING Hao-jiang, WANG Hui-ming, LING Dao-sheng. Analytical solution of a pyroelectric hollow cylinder for piezothermoelastic axisymmetric dynamic problems [J] . Journal of Thermal Stresses,2003,26(3):261-276.
[15] DING Hao-jiang, WANG Hui-ming, CHEN Wei-qiu. Transient responses in a piezoelectric spherically isotropic hollow sphere for symmetric problems [J]. ASME Journal of Applied Mechanics,2003,70(3):436-445.

NEW NUMERICAL METHOD FOR VOLTERRA INTEGRAL EQUATION OF THE SECOND KIND IN PIEZOELASTIC DYNAMIC PROBLEMS

NEW NUMERICAL METHOD FOR VOLTERRA INTEGRAL EQUATION OF THE SECOND KIND IN PIEZOELASTIC DYNAMIC PROBLEMS

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