圆柱壳的轴对称平面应变弹性动力学解

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

1.
浙江大学建工学院土木系, 杭州 310027;
2.
浙江大学力学系, 杭州 310027

基金项目: 国家自然科学基金资助项目(10172075)

详细信息

作者简介:
丁皓江(1934- ),男,江苏常州人,教授.

中图分类号: O343.8
计量
- 文章访问数: 2363
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- 被引次数: 0
出版历程
- 收稿日期: 2000-02-08
- 修回日期: 2001-09-18
- 刊出日期: 2002-02-15

A Theoretical Solution of Cylindrical Shells for Axisymmetric Plain Strain Elastodynamic Problems

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

摘要

摘要: 给出一种圆柱壳的轴对称平面应变弹性动力学问题的解析方法。首先通过引入一特定函数将非齐次边界条件化为齐次边界条件,然后利用分离变量法将位移减去特定函数的量展开为关于贝塞尔函数和时间函数乘积的级数,并由贝塞尔函数的正交性,导出时间函数的方程,容易求得此方程的解。将两者叠加可得弹性动力学问题的位移解。运用此方法,可以避免积分变换,并适宜于各种载荷。文中给出了各向同性和柱面各向同性圆柱壳内表面和实心圆柱外表面受冲击荷载作用以及内表面固定的柱面各向同性圆柱壳外表面受冲击荷载作用的数值结果。
- 轴对称平面应变 /
- 特定函数 /
- 积分变换 /
- 柱面各向同性
Abstract: A method is developed for the transient responses of axisymmetric plain strain problems of cylindrical shells subjected to dynamic loads. Firstly, a special function was introduced to transform the inhomogeneous boundary conditions into the homogeneous ones. Secondly, using the method of separation of variables, the quantity that the displacement subtracts the special function was expanded as the multiplication series of Bassel functions and time functions. Then by virtue of the orthogonal properties of Bessel functions, the equation with respect to the time variable was derived, of which the solution is easily obtained. The displacement solution was finally obtained by adding the two parts mentioned above. The present method can avoid the integral transform and is fit for arbitrary loads. Numerical results are presented for internally shocked isotropic and cylindrically isotropic cylindrical shells and externally shocked cylinders, as well as for an externally shocked, cylindrically isotropic cylindrical shell that is fixed at the internal surface.
- axisymmetric plain strain problem /
- special function /
- integral transform /
- cylindrically isotropic

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参考文献(10)

[1]	Huth J H,Cole J D.Elastic-stress waves produced by pressure loads on a spherical shell[J].Journal of Applied Mechanics,1955,22(4):473-478.
[2]	Mcivor I K.The elastic cylindrical shell under radial impulse[J].Journal of Applied Mechanics,1966,33(4):831-837.
[3]	Baker W E,Hu W C L,Jackson T R.Elastic response of thin spherical shells to axisymmetric blast loading[J].Journal of Applied Mechanics,1966,33(4):800-806.
[4]	Chou P C,Koenig H A.A unified approach to cylindrical and spherical elastic waves by method of characters[J].Journal of Applied Mechanics,1966,33(1):159-167.
[5]	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.
[6]	Cinelli G.Dynamic vibrations and stresses in elastic cylinders and spheres[J].Journal of Applied Mechanics,1966,33(4):825-830.
[7]	WANG Xi,GONG Yu-ning.A theoretical solution for axially symmetric problem in elastodynamics[J].Acta Mechanica Sinica,1991,7(3):275-282.
[8]	王熙.各向异性轴对称问题的弹性动力学解[J].力学学报,1997,29(5):606-610.
[9]	王熙.有界圆柱体的动应力和动应力集中现象[J].振动与冲击,1995,14(1):23-29.
[10]	丁皓江,陈伟球,邹道勤,等.横观各向同性弹性力学[M].杭州:浙江大学出版社,1997.