| 压电弹性动力学中第二类Volterra积分方程的数值解法 |
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| 引用本文： | 丁皓江,王惠明,陈伟球.压电弹性动力学中第二类Volterra积分方程的数值解法[J].应用数学和力学,2004,25(1):15-21. |
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| 作者姓名： | 丁皓江 王惠明 陈伟球 |
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| 作者单位： | 浙江大学 建工学院 土木系,杭州 310027;2.浙江大学 机械与能源学院 力学系,杭州 310027 |
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| 基金项目： | 国家自然科学基金(10172075) |
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| 摘 要： | 对于径向变形的压电空心圆柱和空心球弹性动力学问题，丁皓江等最近的研究表明，可以将它转变为关于一个时间函数的第二类Volterra积分方程，使求解工作得到极大的简化，又使探索第二类Volterra积分方程的快速而又高精度的数值解法成为一个关键．采用插值逼近方法，成功地导出了两个新型的递推公式，不仅计算速度快，且在较大时间步长时仍具有足够的精度，有着广泛的应用价值．
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| 关 键 词： | 压电 弹性动力学 Volterra积分方程 数值解 递推公式 |
| 文章编号： | 1000-0887(2004)01-0015-07 |
| 收稿时间： | 2002-11-01 |
| 修稿时间： | 2002年11月1日 |
New Numerical Method for Volterra Integral Equation of the Second Kind in Piezoelastic Dynamic Problems |
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| 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,2004,25(1):15-21. |
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| Authors: | DING Hao-jiang WANG Hui-ming CHEN Wei-qiu |
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| Institution: | Department of Civil Engineering, Zhejiang University, Hangzhou 310027, P.R. China; |
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| 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. |
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| Keywords: | piezoelectric elastodynamic problem Volterra integral equation numerical solution recursive formulae |
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