偏心柱壳自由振动的级数变换求解方法  

Series transformation method for the free vibration of eccentric cylindrical shell

作　　者：张冠军 李天匀[3] 朱翔[3] 

机构地区：[1]高性能船舶技术教育部重点实验室(武汉理工大学),湖北武汉430063 [2]武汉理工大学能源与动力工程学院,湖北武汉430063 [3]华中科技大学船舶与海洋工程学院,湖北武汉430074

出　　处：《振动工程学报》2017年第6期947-954,共8页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(51479079);高等学校博士学科点专项科研基金资助项目(20120142110051)

摘　　要：由于制造误差或其他特殊方面需求,在实际工程中经常可以见到偏心柱壳。针对此类柱壳的自由振动,提出了一种新的求解方法。根据偏心柱壳截面的几何特性,将偏心圆柱薄壳转化为周向变厚度柱壳。基于Flügge薄壳理论推导出偏心柱壳的自由振动方程,采用波传播的思想将偏心柱壳位移以双Fourier级数形式展开,周向变厚度表示为周向角度坐标的函数,通过三角函数变换将变系数的偏微分方程组转换为周向模态相互耦合的有限阶线性方程组,通过对耦合方程进行求解得到偏心柱壳的固有频率及振型。通过与有限元结果对比验证了所提方法的准确性,同时分析了壳体主要参数对偏心柱壳对称及反对称模态的影响。Eccentric cylindrical shell often can be seen in the practical engineering due to manufacturing error or other special re-quirements. A new method to study the free vibration characteristics of eccentric cylindrical shell is proposed in this paper. Ac-cording to the geometry characteristics of the cross section of eccentric cylindrical shell, the eccentric problem is converted into a circumferentially varying thickness problem. The displacements are expanded in double Fourier series in the view of wave propagation and the circumferential thickness is represented as a trigonometric function form. Through a series transformation, the partial differential equations with variable coefficients are converted into a set of linear equations which couple with each other about circumferential modal parameters. Natural frequencies and mode shapes of the eccentric cylindrical shell are ob-tained by solving the coupled equations. The influence of main parameters of the shell on the symmetric and anti-symmetric modes of elliptic cylindrical shell is discussed in detail.

关 键 词：偏心柱壳 自由振动 反对称模态 级数变换 偏心率参数 

分 类 号：O327[理学—一般力学与力学基础] U663[理学—力学]