非均质环形谐振子结构性能分析方法  

An analysis method for structures of ring-shaped resonators with heterogeneous materials

作　　者：裴永乐 徐亮[1] 黄伟[1] 高立民[1] 李录贤[2] 原晓斌[1] PEI Yongle;XU Liang;HUANG Wei;GAO Limin;LI Luxian;YUAN Xiaobin(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,复杂服役环境重大装备结构强度与寿命全国重点实验室,飞行器环境与控制陕西省重点实验室,西安710049

出　　处：《中国惯性技术学报》2024年第8期821-827,共7页Journal of Chinese Inertial Technology

基　　金：陕西省自然科学基础研究计划项目(2023JCQN0030);西安市博士后创新基地项目(2023J23122);西安光学精密机械研究所部署项目(2023523013)。

摘　　要：传统环形谐振子结构特性分析方法是基于均质弹性力学理论的,无法准确描述非均质材料力学特性对环形谐振子结构静、动态性能的影响规律。基于圆弧形结构的欧拉梁理论,根据非均质本构关系,运用Hamilton原理,提出一种非均质环形谐振子结构性能分析方法。利用非均质环形谐振子理论和布勃诺夫-伽辽金法,获得非均质环形谐振子静态弯曲问题和动态转动问题的理论解。然后,分析了材料的非均质力学特性对环形谐振子弯曲挠度、二阶弯曲角频率及进动系数的影响规律。典型非均质材料性能分析结果表明,传统方法对于二阶弯曲角频率计算误差达59%以上,而所提方法能够精确预测非均质谐振子结构的静、动态响应,计算出二阶弯曲角频率。Based on the theory of homogeneous elasticity,the traditional method for analyzing the structural characteristics of a ring-shaped resonators cannot accurately describe the influence of the mechanical properties of heterogeneous materials on the static and dynamic performance of resonators.According to the Euler beam theory of circular curved structures,a method for analyzing the structural properties of ring-shaped resonators with heterogeneous materials is established,utilizing the constitutive relationships of heterogeneous materials and Hamilton principle.With the theory above and Bubnov-Galerkin method,theoretical solutions are derived for the static bending and dynamic rotating problems.Then,the influence of heterogeneous mechanical properties is analyzed for the bending deflection,second-order bending angular frequency and precession coefficient.The performance analysis results of typical heterogeneous materials show that the traditional method has an error of over 59% in calculating the second-order bending angular frequency,while the proposed method can accurately predict the static and dynamic responses of structures of heterogeneous resonators and calculate the second-order bending angular frequency.

关 键 词：非均质材料 欧拉梁理论 HAMILTON原理 环形谐振子 转动问题 

分 类 号：U666.1[交通运输工程—船舶及航道工程]