摘要
分布阻尼振子可拓宽结构减振频带,因此可将振子分布于板中以形成复合板(简称“分布振子复合板”),进而实现较宽的减振频带.对于多点支撑处受到宽频非一致激励(例如在不同激励点处的激励频率、幅值与相位有差异)的分布振子复合板,目前还缺乏有效简便的优化控制指标.在作者之前的研究中,针对含分布振子的梁推导了基于模态应变能的模态阻尼计算理论,讨论了模态阻尼与单点激励下梁的减振效果的相关性,并应用于宽频减振设计优化.本文进一步将模态阻尼计算理论推广到分布振子复合板,并将研究从梁的单点激励扩展到板的多点非一致激励下的阻尼减振相关性.首先,在利用模态应变能法推导得到分布振子复合板的模态阻尼计算公式后,从理论上讨论了不同边界条件与模态阶次对计算结果的影响,以及计算理论的适用性.而后,进一步通过有限元参数分析了边界条件、频率比、模态阶次与质量比的影响.最后,通过算例分析了无振子板或分布振子复合板在四个激励点具有多种幅值与相位组合情况下的稳态响应.结果表明,推导的模态阻尼计算公式可正确预测不同边界条件下的模态阻尼,且理论预测的模态阻尼与基板的稳态平均加速度减小率、稳态峰值应变能减小率均有较高的相关性.
Distributed damping oscillators can broaden the vibration reduction frequency band of the structure,so they can be distributed in the plate to form a composite plate to achieve a wide vibration reduction frequency band.At present,there is a lack of effective and simple optimization control indicators for the composite plate distributed with oscillators subjected to broadband nonuniform(such as different excitation frequency,different amplitude,and different phase at different excitation points)multi-point excitation.In our previous research,the modal damping calculation theory based on modal strain energy is derived for the beam distributed with oscillators,and the correlation between the modal damping and the vibration mitigation performance under singlepoint excitation,which is used for the optimization of broadband vibration mitigation.This paper further extends the modal damping theory to the plate case.For this sake,the single-point excitation of the beam is extended to the multi-point non-uniform excitation of the plate.After the derivation of the modal damping calculation formula based on the modal strain energy method,the influences of the boundary conditions and the modal order on the calculation results,and the applicability of the calculation scheme are theoretically discussed.Then,the influences of the boundary condition,the frequency ratio,the modal order,and the mass ratio are further discussed by finite element parametric analysis.Finally,The steady-state response of a plate with or without distributed oscillators under different combinations of excitation amplitudes and phases at four support points is analyzed by finite element method.The results show that the derived modal damping formula can correctly predict the modal damping under different boundary conditions.The theoretically predicted modal damping is highly correlated to the steady-state reduction rates of the average acceleration and the peak strain energy of the base plate.
作者
尹文汉
孙飞飞
刘静涵
张刚
钱忱
YIN Wenhan;SUN Feifei;LIU Jinghan;ZHANG Gang;QIAN Chen(Collegeof Civil Engineering,TongjiUniversity,Shanghai 200092,China;Tongwu(Shanghai)Building Technology Co.,Ltd.,Shanghai 200092,China;PowerChina Huadong Engineering Co.,Ltd.,Hangzhou 311122,Zhejiang,China)
出处
《力学季刊》
CAS
CSCD
北大核心
2022年第3期512-525,共14页
Chinese Quarterly of Mechanics
关键词
振动控制
分布振子
模态应变能法
板
分布式多调谐质量阻尼器
vibration control
distributed dissipative oscillators
modal strain energy method
plate
distributed multiple tuned mass damper(DMTMD)
