考虑前2阶模态组合的拉索非线性参数共振研究

发布时间：2018-03-16 13:31

本文选题：斜拉桥拉索　切入点：索-桥耦合系统　出处：《防灾减灾工程学报》2015年02期 　论文类型：期刊论文

【摘要】：针对水平拉索的非线性参数共振问题,首先将桥面简化为集中质量块,建立拉索在桥面谐波位移激励下的非线性微分方程,并考虑拉索前2阶模态组合的影响,进而推导索-桥耦合的无量纲非线性运动方程组,最后以实际斜拉桥工程的拉索为例,对拉索发生参数共振的响应进行数值模拟分析。研究表明:当桥面质量块无量纲固有频率Ω3与拉索1阶无量纲固有频率Ω1M之比为2∶1时,拉索的前2阶模态位移和质量块均出现"拍"振现象,且以第1阶模态为主振动模态;而当桥面质量块无量纲固有频率Ω3与拉索2阶无量纲固有频率Ω2M之比为2∶1时,仅有第2阶模态位移和质量块出现"拍"振现象,拉索以第2阶模态为主模态振动,此时第1阶模态位移未出现"拍"振现象;考虑前2阶模态组合时,当质量块的激励频率与系统的固有频率满足参数共振频比关系2∶1时,系统将发生大幅"拍"振现象,且第1阶主模态的位移响应要远大于第2阶主模态的位移响应。
[Abstract]:Aiming at the problem of nonlinear parametric resonance of horizontal cables, the bridge deck is simplified as a lumped mass block, and the nonlinear differential equation of cable subjected to harmonic displacement is established, and the influence of the first two order modal combinations of cables is considered. Furthermore, the equations of dimensionless nonlinear motion of cable-bridge coupling are deduced. Finally, the cable of the actual cable-stayed bridge is taken as an example. The numerical simulation analysis of parametric resonance response of cable is carried out. The results show that when the ratio of dimensionless natural frequency 惟 3 to dimensionless natural frequency 惟 1m of cable mass block is 2: 1, The first 2 order modal displacements and mass blocks of the cables both appear "beat" vibration, and the first mode is the main vibration mode, but when the ratio of dimensionless natural frequency 惟 3 to the second order dimensionless natural frequency 惟 2m of the bridge deck mass block is 2: 1, Only the second order modal displacement and mass block appear "beat" vibration, while the second mode is the main mode vibration, and the first order modal displacement does not appear "beat" phenomenon. When the excitation frequency of the mass block and the natural frequency of the system satisfy the parametric resonance frequency ratio of 2: 1, the system will have a large "beat" phenomenon, and the displacement response of the first main mode is much larger than the displacement response of the second main mode.
【作者单位】：东华理工大学建筑工程学院;湖南大学土木工程学院;苏州科技学院土木工程学院;
【基金】：国家自然科学青年基金项目(51208088) 江西省青年科学家(井冈之星)培养对象计划项目(2013)资助
【分类号】：U448.27

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