两端具有质量块弹性支撑悬臂梁振动特性研究  

Study on vibration characteristics of elastically supported cantilever beam with two end masses

作　　者：唐礼平[1] 王建国[1] TANG Liping;WANG Jianguo(School of Civil and Hydraulic Engineering, Hefei University of Technology, Hefei 230009, China)

机构地区：[1]合肥工业大学土木与水利工程学院

出　　处：《合肥工业大学学报（自然科学版）》2019年第10期1375-1381,共7页Journal of Hefei University of Technology：Natural Science

基　　金：国家自然科学基金资助项目(11172087)

摘　　要：文章针对两端具有质量块弹性支撑悬臂梁,基于Euler-Bernoulli梁的基本假设,计入质量块的偏心距和转动惯量的影响,利用Hamilton变分原理建立了悬臂梁的运动微分方程和边界条件,获得了计算梁固有频率的特征方程、振型函数及其正交性条件。数值计算结果表明,考虑尖端质量块的偏心距、转动惯量可提高研究结构共振频率和振型的精确度;通过调整竖向平移弹簧刚度系数、转动弹簧刚度系数及尖端质量块质量,可以改变梁的固有频率和振型形状。For elastically supported cantilever beam with two end masses, based on the basic assumption of the Euler-Bernoulli beam and considering the influence of the eccentricity and the moment of inertia of the masses, the differential equations and boundary conditions of the cantilever beam are established by the Hamilton variational principle. The characteristic equation of the natural frequency analysis, the mode shape function and the orthogonality condition of the beam are obtained. The numerical results show that the accuracy of the resonance frequency and mode shape of the beam can be improved with considering the eccentricity and the moment of inertia of the end masses. By adjusting the vertical translational spring stiffness coefficient and the rotational spring stiffness coefficient, and the mass of the end masses, the natural frequency and mode shape of the beam can be changed.

关 键 词：压电层合梁 弹性支撑悬臂梁 固有频率 正则化振型 

分 类 号：TB122[理学—工程力学]