多项式拟合振型函数法求解多跨传动轴的弯曲振动响应  

Bending vibration responses of a multi-span shaft by using the polynomial fitting mode function method

作　　者：彭勃 朱如鹏[1] 李苗苗[1] 李峙岳 

机构地区：[1]南京航空航天大学机电学院,南京210016

出　　处：《振动与冲击》2017年第18期118-124,共7页Journal of Vibration and Shock

基　　金：国家自然科学基金资助项目(51375226;51505215);南京航空航天大学研究生创新基地(实验室)开放基金资助项目(kfjj20150506)

摘　　要：为求解边界条件为弹支的多跨传动轴弯曲振动响应,基于第二类拉格朗日方程,建立了瑞利连续轴动力学模型,并使用伽辽金法将偏微分方程转化为常微分方程;提出了多跨传动轴振型函数的多项式拟合方法,通过传递矩阵法计算得到了传动轴有限截面的振型值,据此用多项式分别拟合振型函数及其高阶导数。以直升机尾传动轴为算例,将拟合得到的前三阶振型函数及相应的高阶导数代入到动力学方程组中,通过振型叠加法计算得到了尾传动轴在偏心激励下的弯曲振动响应。算例结果表明,该方法具有较好的收敛性和可靠性。In order to solve the bending vibration response of a multi-span shaft under elastic support boundary conditions,a dynamic model of the Rayleigh continuous shaft was established based on the second Lagrange equation,and the partial differential equations were transformed into the ordinary differential ones by using Galerkin ＇s method. A polynomial fitting method for the mode shape functions of the multi-span shaft was proposed,the mode shape values at finite sections of the shaft were calculated by means of the transfer matrix method,and the mode shape functions and their higher order derivatives were fitted by using polynomials. A helicopter tail driving shaft was taken as an example,the fitted mode shape functions of three orders and their higher-order derivatives were substituted into the dynamic equations,and the bending vibration responses of the tail driving shaft under eccentric excitation were calculated by the mode superposition method. The study results reveal that the method has good convergence and reliability.

关 键 词：多跨传动轴 弹性支承 弯曲振动 振型 多项式拟合 

分 类 号：TH113.1[机械工程—机械设计及理论] O32[理学—一般力学与力学基础]