New Numerical Method for Volterra Integral Equationof the Second Kind in Piezoelastic Dynamic Problems
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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
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 approadmate 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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