运动皮带受带轮跳动激励的横向振动分析

Analysis of Transverse Vibrations of Moving Belt caused by Fulcrum Motion

轴向运动连续体是多种工程系统力学理论研究中的重要模型,其横向振动稳态响应的理论解法尚未成熟。利用Hamilton原理,建立带轮跳动激励下轴向运动皮带横向振动的拉格朗日动力学偏微分方程,将系统运动微分方程表达为复数形式,利用复数的性质和简谐激励稳态响应的规律,直接求得运动皮带受迫振动稳态响应的解析解,从而分析横向振动响应的幅频、相频特性与共振特性,得到系统共振频率。通过工程应用实例,试验验证该方法的合理性和有效性。闭合形式的解析解可进一步分析轴向运动系统振动特性,并且可方便地作为考核数值方法有效性和可靠性的算例。

Axially moving continuous body is an important model in mechanics research of multi-engineering systems.The theoretical solution of steady-state response of the transverse vibration is not yet mature.In this work,a partial differential equation for transverse vibration analysis of the axially moving belts is established by virtue of the Hamilton principle.This system differential equation is expressed in a complex variable form.Analytical solution of steady-state response of the axially moving belts under harmonic excitation of the fulcrum is obtained through the nature of complex variable and the law of steady-state response.Amplitude-frequency,phase-frequency and resonance characteristics of the transverse vibration response are analyzed.Besides,the natural frequency of the system is gained indirectly.According to the engineering application example,a test is designed to verify the rationality and validity of the calculation method.The analytical solution of closed form can further be used to analyze the vibration characteristics of the axially moving system and can be used as a standard to exam the validity and reliability of some other numerical methods.