多频共振发生的条件及性质
Occurrence conditions and properties of multi-frequency resonance
姚彻 1魏晓军1
作者信息
- 1. 中南大学土木工程学院,湖南长沙,410075
- 折叠
摘要
对结构能否发生多频共振及发生多频共振的种数进行理论分析,并给出分析步骤.在非线性情况下通过作图对多频共振发生区域的几何性质进行分析,并从力学角度对其物理意义进行阐述,最后通过实例对多频共振发生的条件及性质理论进行验证.研究结果表明:在线性情况下,可精确判断出所选频率间是"不存在多频共振"、"存在一种多频共振"还是"存在无穷多种多频共振";在非线性情况下,发现在大的共振区域越能形成大的非共振区域;在结构含有3个频率(其中包括固有频率及外荷载频率)时,以2组频率比为横、纵坐标绘图,发现当图中点的2个坐标分量的最简公分母很小时,该点附近以及此类点连线附近会存在较大的多频共振区域;在结构含有2个频率且当截断数为n时,增大非线性耦合强度K,最晚发生多频共振的频率比为截断数为n+1时最早发生多频共振的频率比,因此,在非线性动力学研究中,需谨慎考虑内共振可能出现的情形.
Abstract
The conditions for the occurrence and the number of kinds of multi frequency resonance along with the analysis procedure were theoretically discussed.In the nonlinear case,the geometric properties of the region where multi frequency resonance occured were analyzed through drawing,and its physical significance was explained from a mechanical perspective.Finally,the theory was verified through examples.The results show that for a linear structure,it can be accurately predicted whether there is no multi-frequency resonance,one multi-frequency resonance or infinite multi frequency resonance between the selected frequencies.A larger nonresonant region can be formed near a larger resonant region.When three frequencies and two ratios were selected as the coordinate axes were considered,there are large areas of multi-frequency resonance occurred near the points whose two coordinates have a small common denominator.In the case of two frequencies,when the truncation number is n,in the process of increasing the nonlinear coupling strength K,the frequency ratio of the latest occurrence of multi frequency resonance is actually the frequency ratio of the earliest occurrence of multi frequency resonance when the truncation number is n+1.Therefore,caution should be exercised in selecting possible scenarios of internal resonance in nonlinear dynamics research.
关键词
多频共振/非线性/区域Key words
multi-frequency resonance/nonlinearity/region引用本文复制引用
基金项目
国家自然科学基金资助项目(52178181)
出版年
2024
国家科技期刊平台
NSTL
万方数据