非小量角位移假定下滚动型调谐质量阻尼器的减振分析

Study on the Vibration Reduction Performance of TRMD Under Non-small Angular Displacement Assumption

对滚动式调谐质量阻尼器(TRMD)中球形振子转角位移的小量假定问题进行了深入研究,运用Lagrange运动方程推导了TRMD在球形振子小量假定和非小量假定下的受控体系动力方程,给出了数值解法。结合算例探讨了在简谐激励和地震作用下设置有TRMD的受控体系减振情况,比较和分析了小量假定与非小量假定对受控结构控制性能的影响。结果表明,当外激励较强时小量假定对控制结构的减振分析影响较大,会放大其减振效果,其适用性与激励种类及强度有关,具有一定的局限性,不容忽视。论文同时对小量假定的适用范围进行了探讨。

In order to simplify the calculation,the angular displacement of the oscillator is usually assumed to be small in the process of establishing the dynamic equation of the tuned rolling mass damper(TRMD).When the excitation is not large,the assumption has little influence on the analysis results,but when the excitation is large,its influence cannot be ignored.The problem of small assumption of the angular displacement of the oscillator in the tuned rolling mass damper(TRMD)was studied deeply.The dynamic equation of the controlled system under the small assumption and non-small assumption of the oscillator were derived by using Lagrange equation,and the numerical solution was given.The vibration reduction of controlled system with TRMD under harmonic excitation and earthquake was discussed by the examples,and the influence of small and non-small assumption on the control performance of controlled structure was compared and analyzed.The results show that when the external excitation was strong,the small assumption has great influence on the vibration reduction analysis of the control structure,which will enlarge its vibration reduction effect.Its applicability was related to the type and intensity of excitation,and has certain limitations,which cannot be ignored.The scope of application of small assumption is also discussed in this paper.