变截面单元环状周期结构固有频率分裂规律研究

doi:10.3901/JME.2024.07.114

机械工程学报 ›› 2024, Vol. 60 ›› Issue (7): 114-123.doi: 10.3901/JME.2024.07.114

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变截面单元环状周期结构固有频率分裂规律研究

高楠¹, 王世宇^1,2,3, 夏春花¹, 魏振航¹

1. 天津大学机械工程学院天津 300354;
2. 天津大学机构理论与装备设计教育部重点实验室天津 300354;
3. 天津市非线性动力学与控制重点实验室天津 300354

收稿日期:2023-03-20 修回日期:2023-12-10 出版日期:2024-04-05 发布日期:2024-06-07
通讯作者: 王世宇，男，1974年出生，博士，教授，博士研究生导师。主要研究方向为旋转机械系统动力学、振动分析与控制。E-mail：wangshiyu@tju.edu.cn
作者简介:高楠，男，1992年出生，博士研究生。主要研究方向为旋转机械系统动力学。E-mail：nicholasgao@tju.edu.cn；夏春花，女，1995年出生，博士研究生。主要研究方向为旋转机械系统动力学。E-mail：xiaohua1810201@163.com；魏振航，男，2000年出生，博士研究生。主要研究方向为旋转机械系统动力学。E-mail：wzh201057@tju.edu.cn
基金资助:
国家自然科学基金资助项目(52175109)。

Study on Natural Frequency Splitting of a Ring-shaped Periodic Structure with Variable Cross-section Features

GAO Nan¹, WANG Shiyu^1,2,3, XIA Chunhua¹, WEI Zhenhang¹

1. School of Mechanical Engineering, Tianjin University, Tianjin 300354;
2. Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, Tianjin 300354;
3. Tianjin Key Laboratory of Nonlinear Dynamics and Control, Tianjin 300354

Received:2023-03-20 Revised:2023-12-10 Online:2024-04-05 Published:2024-06-07

摘要/Abstract

摘要： 在实际工程应用中，环状周期结构往往存在变截面单元。针对因变截面单元周期特性而导致的固有频率分裂现象，基于力矩平衡关系，采用Hamilton原理建立一般性动力学模型。以贯穿孔为例，基于经典振动理论得到固有频率及其分裂规律。考虑分组模式拓扑构型，推导具体消除频率分裂的规则，深入分析贯穿孔的孔径、数量和位置等参数对频率及其分裂行为的影响。设计试件并搭建实验台验证理论模型的正确性和消除规则的有效性。研究结果表明：由于贯穿孔使局部质量和弯曲刚度同时减小，进而导致固有频率改变，增大孔径和数量使重频频率减小，使分裂频率的分裂程度增大；保持孔径的一致性和位置的对称性可有效消除分裂。该研究方法和结论可用于工程领域类似周期结构动力学问题的研究并指导结构的设计。

关键词: 环状周期结构, 变截面单元, 固有频率分裂, 分组模式, 消除规则

Abstract: The ring-shaped periodic structure (RSPS) with variable cross-section features is widely used in engineering practice. Due to the asymmetric variable cross-section features, the natural frequencies can split. Based on the static equilibrium relation, a general dynamic model of an RSPS with variable cross-section features is established by using Hamilton’s principle. Taking the through holes as an example, a dynamic model of the RSPS with cyclically symmetric through holes is derived, and the closed-form expressions of natural frequencies are obtained according to the classical vibration theory. The specific rules for eliminating frequency splitting are proposed based on a grouping pattern. The effects of the parameters of the through hole such as diameter, count, and angular position on natural frequencies and splitting behaviors are investigated. Splitting or non-splitting of natural frequencies is verified by the experiment with a test rig. The results show that the through holes can reduce the mass and stiffness, and then change the natural frequency; larger diameter and count of through holes decrease the repeated frequencies but increase the differences between the split frequencies. Remaining identical and symmetric through holes can eliminate the split. The research method and conclusion can be employed to study the dynamics of similar periodic structures and guide structural design.

Key words: ring-shaped periodic structure, variable cross-section feature, natural frequency splitting behavior, grouping pattern, elimination rule

中图分类号:

TH113
TH122

高楠, 王世宇, 夏春花, 魏振航. 变截面单元环状周期结构固有频率分裂规律研究[J]. 机械工程学报, 2024, 60(7): 114-123.

GAO Nan, WANG Shiyu, XIA Chunhua, WEI Zhenhang. Study on Natural Frequency Splitting of a Ring-shaped Periodic Structure with Variable Cross-section Features[J]. Journal of Mechanical Engineering, 2024, 60(7): 114-123.

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变截面单元环状周期结构固有频率分裂规律研究

Study on Natural Frequency Splitting of a Ring-shaped Periodic Structure with Variable Cross-section Features

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