• 论文 •

### 复杂边界条件下的多跨梁的振动模型

1. 南京航空航天大学 机械结构力学及控制国家重点实验室, 南京 210016
• 收稿日期:2014-06-03 修回日期:2014-09-05 出版日期:2015-05-20 发布日期:2015-06-02
• 通讯作者: 聂宏(1960—),男,安徽芜湖人,教授,博士生导师,hnie@nuaa.edu.cn,主要研究方向飞行器起落装置设计. E-mail:hnie@nuaa.edu.cn
• 作者简介:刘向尧(1984—),男,辽宁沈阳人,博士研究生,liuxiangyao@nuaa.edu.cn
• 基金资助:

国家自然科学基金(51105197,51075203);江苏高校优势学科建设工程

### Vibration model for multi-span beam with arbitrary complex boundary conditions

LIU Xiangyao, NIE Hong, WEI Xiaohui

1. State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
• Received:2014-06-03 Revised:2014-09-05 Online:2015-05-20 Published:2015-06-02

Abstract:

The transverse free vibration equations for Timoshenko beam were derived. Based on these equations, the vibration model for a multi-span beam with arbitrary complex boundary conditions was given by the transfer matrix method. Without considering the shear deformation and moment of inertia of the neutral axis, the model was simplified as the analogous model for Bernoulli-Euler beam. Three simplified models of some engineering significance were given. They are the free vibration model for a two-span beam, a cantilever with a lumped mass, and a beam with arbitrary lumped masses and translational springs. A comparison between the frequency equations derived by the three simplified models and those by the previous studies shows good consistency of the two, and it is thus concluded that the model developed in this paper is reasonable and feasible.