纵向荷载作用下简支梁参数振动的理论与试验研究  

Theoretical and experimental study on parametric vibration of simply supported beam under longitudinal load

作　　者：陈舟 陈泽鸿 陈思远 温嘉豪 罗冬梅 卢汉文 CHEN Zhou;CHEN Ze-hong;CHEN Si-yuan;WEN Jia-hao;LUO Dong-mei;LU Han-wen(School of Transportation,Civil Engineering&Architecture,Foshan University,Foshan 528225,China;Guangdong Nanhai Construction Investment Development Co.,Ltd,Foshan 528200,China)

机构地区：[1]佛山科学技术学院交通与土木建筑学院,广东佛山528225 [2]广东南海建设投资发展有限公司,广东佛山528200

出　　处：《佛山科学技术学院学报（自然科学版）》2023年第2期12-21,共10页Journal of Foshan University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(51908146);科技部高端人才引进计划资助项目(G2022030014L);广东省海外名师资助项目。

摘　　要：为了研究简支梁在纵向力作用下参数振动的发生过程及作用机理,推导了梁的Mathieu-Hill方程,运用Bolotin法求解出二阶精度的动力不稳定区域近似解,并结合Runge-Kutta法对其进行验证;开展激振试验得到了不同加速度作用下梁的动力响应,并提出了利用波形分析与功率谱相结合的方法判定梁的振动形态,对简支梁在纵向荷载作用下参数振动的发生进行了详细的阐述。结果表明:Bolotin法求解计算的动力不稳定区域的正确性,简支梁在纵向简谐力作用下会发生参数振动,梁发生参数振动的过程历经暂态振动、参数振动、暂态振动3个阶段,结构几何非线性的存在会抑制梁动力响应的无限增长。In order to study the process and mechanism of parametric vibration of simply supported beam under longitudinal force,the Mathieu Hill equation of beam is derived.The Bolotin method is used to obtain the approximate solution of dynamic instability region with second-order accuracy,and the Runge Kutta method is used to verify it.The dynamic response of the beam under different accelerations is obtained by the excitation experiment.In this paper,a method combining waveform analysis with power spectrum is proposed to determine the vibration shape of the beam,and the occurrence of parametric vibration of the beam is described in detail.The results show that the dynamic instability region calculated by the Bolotin method is correct.The simply supported beam will generate parametric vibration under the action of longitudinal simple harmonic force.The process of the parametric vibration of the beam will go through three stages:transient vibration,parametric vibration and transient vibration.The existence of structural geometric nonlinearity will inhibit the infinite growth of beam dynamic response.

关 键 词：简支梁 参数振动 试验研究 波形分析法 功率谱分析法 

分 类 号：TU375.102[建筑科学—结构工程]