各向同性均匀有限长管本征振动研究  

Eigen Vibrations of an Isotropic Homogeneous Finite Hollow Cylinder

作　　者：吴昭军[1] 汤立国[1] 

机构地区：[1]厦门大学海洋与环境学院,水声通信与海洋信息技术教育部重点实验室,福建厦门361005

出　　处：《厦门大学学报（自然科学版）》2011年第6期980-983,共4页Journal of Xiamen University：Natural Science

基　　金：国家自然科学基金项目(10704064)

摘　　要：研究各向同性均匀有限长管在不同端边界条件下的本征振动是利用本征函数展开法求解各向同性均匀有限长、半无限长及无限长管瞬态响应问题的基础.利用弹性动力学理论对两端为应力自由、刚性及刚性滑移边界条件任意组合的有限长管本征振动进行详细分析.分析结果表明,当管两端皆为刚性滑移边界条件时,可获得扭曲、纵向及弯曲振动的本征函数;当管两端皆为应力自由或刚性边界条件,或一端为应力自由而另一端为刚性边界条件,或一端为刚性滑移而另一端为刚性边界条件时,只能获得扭曲振动的本征函数,而无法获得纵向及弯曲振动的本征函数;当管一端为应力自由而另一端为刚性滑移边界条件时,只能获得平凡解.Studying the eigen vibrations of an isotropic homogeneous finite hollow cylinder under different end boundary conditions is the basis of solving the transient response problems of isotropic homogeneous finite,semi-infinite and infinite hollow cylinders by the method of eigenfunction expansion.The eigen vibrations of the finite hollow cylinder are analyzed in detail when two ends are arbitrary combinations of traction-free,rigid and rigid-smooth boundaries.It is proved that significant eigenfunctions of the torsional,longitudinal and flexural vibrations can be obtained if both two end boundaries of the finite hollow cylinder are rigid-smooth.If both two end boundaries are traction-free or rigid,or one is traction-free and the other is rigid,or one is rigid-smooth and the other is rigid,the eigenfunctions of the torsional vibrations can be derived,but those of the longitudinal and flexural vibrations cannot be obtained.Trivial solution is obtained if one of the end boundaries is traction-free and the other is rigid-smooth.

关 键 词：本征函数 有限长管 刚性 应力自由 刚性滑移 

分 类 号：O326[理学—一般力学与力学基础]