压电弹性动力学中第二类Volterra积分方程的数值解法

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

1.
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

基金项目: 国家自然科学基金(10172075)

详细信息

作者简介:
丁皓江(1934- ),男,江苏常州人,教授,博导(联系人.Tel:86-571-7993057;E-mail:hjding@mail.hz.zj.cn).

中图分类号: O347.1；O241.8
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出版历程
- 收稿日期: 2002-11-01
- 修回日期: 2003-08-03
- 刊出日期: 2004-01-15

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

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

摘要

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．
- 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.
- piezoelectric /
- elastodynamic problem /
- Volterra integral equation /
- numerical solution /
- recursive formulae

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参考文献(15)

[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]	沈以淡. 积分方程[M].北京: 北京理工大学出版社, 1992.
[6]	阎玉斌, 崔明根. 第二类Volterra积分方程的准确解[J]. 高等学校计算数学学报, 1993,15(4): 291—296.
[7]	李鸿祥, 王国金, 王存政. 几类积分方程和常微分方程的精确解[J]. 上海铁道学院学报, 1995, 16(1):72—85.
[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. doi: 10.1016/S0020-7225(98)00065-2
[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. doi: 10.1121/1.1913390
[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. doi: 10.1115/1.3424212
[11]	WANG Xi, Gong Yu-ming. A theoretical solution for axially symmetric problem in elastodynamics[J].Acta Mechanica Sinica,1991,7(3): 275—282. doi: 10.1007/BF02487596
[12]	丁皓江，王惠明，陈伟球.圆柱壳的轴对称平面应变弹性动力学解[J].应用数学和力学， 2002, 23(2): 138—145.
[13]	DING Hao-jing, WANG Hui-ming, HOU Peng-fei. The transient responses of piezoelectric hollow cylinders for axisymmetric plane strain problems[J].International Journal of Solids and Structures,2003,40(1):105—123. doi: 10.1016/S0020-7683(02)00525-5
[14]	DING Hao-jing, 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. doi: 10.1080/713855893
[15]	DING Hao-jing, WANG Hui-ming, CHEN Wei-qiu. Transient responses in a piezoelectric spherically isotropic hollow sphere for symmetric problems[J].ASME Journal of Applied Mechanics2003，70(3)：436—445.

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压电弹性动力学中第二类Volterra积分方程的数值解法

作者简介:
丁皓江(1934- ),男,江苏常州人,教授,博导(联系人.Tel:86-571-7993057;E-mail:hjding@mail.hz.zj.cn).

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

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压电弹性动力学中第二类Volterra积分方程的数值解法

作者简介: 丁皓江(1934- ),男,江苏常州人,教授,博导(联系人.Tel:86-571-7993057;E-mail:hjding@mail.hz.zj.cn).

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出版历程

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

计量

出版历程

目录

作者简介:
丁皓江(1934- ),男,江苏常州人,教授,博导(联系人.Tel:86-571-7993057;E-mail:hjding@mail.hz.zj.cn).