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.

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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)

Abstract

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.

2010 MSC Number:

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

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

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