计及横向剪切效应的环形谐振子理论研究  

Research on Ring-Shaped Resonators with Transverse Shear Effect Considered

作　　者：裴永乐 高立民[1] 徐亮[1] 李华[1] 李晓辉[1] 李录贤[2] PEI Yong-le;GAO Li-min;XU Liang;LI Hua;LI Xiao-hui;LI Lu-xian(Xi'an Institute of Optics and Precision Mechanics, CAS, Xi'an 710119, China;State Key Laboratory for Strength and Vibration of Mechanical Structures, Shaanxi Key Laboratory of Environment and Control for Flight Vehicle, School of Aerospace Engineering, Xi'an Jiaotong University, Xi'an 710049, China)

机构地区：[1]中国科学院西安光学精密机械研究所,西安710119 [2]西安交通大学航天航空学院,机械结构强度与振动国家重点实验室,飞行器环境与控制陕西省重点实验室,西安710049

出　　处：《导航定位与授时》2022年第4期142-148,共7页Navigation Positioning and Timing

摘　　要：经典环形谐振子理论是一种基于忽略横向剪切变形假设建立的环理论,因而无法准确求解高径比较大的环问题。为了克服上述不足,基于Timoshenko理论和哈密顿原理,建立考虑横向剪切效应的环形谐振子新理论,包括广义本构关系、平衡方程和周期性条件等。利用经典的布勃诺夫-伽辽金法,并结合有限元法,获得谐振子在缓慢、匀速转动过程中二阶弯曲角频率和进动系数的理论解。研究表明,横向剪切变形会在一定程度上影响环形结构二阶弯曲角频率和进动系数的计算结果;环形谐振子的进动系数不是恒定的,它会随着高径比h/r的增大而缓慢地减小。The classical theory for the ring-shaped harmonic oscillator is a kind of theory for thin ring with transverse shear deformation ignored,therefore it cannot be used to solve problems of medium-thick ring accurately with large stiffness.In order to overcome the defect above,this paper is presented to establish a new theory with the transverse shear effect considered,including generalized constitutive relations,equilibrium equations and periodic conditions,based on the Timoshenko theory and Hamilton's principle.Using the Bubnov-Galerkin and finite element methods,solutions of the second-order bending angular frequency and precession coefficient are obtained for resonators during the slow and uniform rotation process.This paper indicates that the transverse shear deformation can affect results of the second-order bending angular frequency and precession coefficient to some extent while the value of precession coefficient is not constant,which decreases gradually with the increase of height-to-radius ratio h/r.

关 键 词：环形结构 Timoshenko理论 二阶弯曲角频率 进动系数 简化理论解 

分 类 号：V241.5[航空宇航科学与技术—飞行器设计]