黏弹性阻尼隔振系统动力分析与优化设计
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摘要
旨在研究具有频率依赖性的黏弹性阻尼隔振系统的动力特性及优化设计。引入分数阶导数开尔文模型建立能够考虑黏弹性阻尼材料频率依赖性的隔振系统数学模型;提出无量纲黏弹性影响系数,基于泰勒级数求解特征方程,得到激励频率影响下的隔振系统自振频率和等效阻尼比;最后,优化弹性单元与黏弹性单元的刚度比,实现隔振系统在宽频带和峰值频率下的较优隔振效果。研究结果表明:相比于具有同等静态刚度的线性隔振系统,黏弹性阻尼隔振系统具有更高的阻尼比,较宽的隔振曲线放大区,相对较高的自振频率;可通过优化弹性单元与黏弹性单元的刚度比获得较优的系统隔振效率,最优数值取决于隔振目标。
Dynamic characteristics and parametric optimization of a vibration isolation system with viscoelastic( VE) damping were studied. Firstly,a single-DOF dynamic model for the system was established,and the fractional derivative Kelvin model was introduced to consider the effect of frequency-dependence on dynamic characteristics of the system. Then,the VE influence coefficient was proposed. Based on Taylor series,the system's characteristic equation was solved to obtain the vibration isolation system's natural frequency and equivalent damping ratio under the influence of the excitation frequency. At last,the stiffness ratio between the elastic element and the VE one was optimized to realize the optimal vibration isolation effect of the system under wide frequency band and the peak value response frequency. The results showed that compared to a linear vibration isolation system with the same static state stiffness,the vibration isolation system with VE damping has a higher damping ratio,a wider amplification region of vibration isolation curve and a larger natural frequency; the optimal system vibration isolation efficiency is obtained through optimizing the stiffness ratio between the elastic element and the VE one,and the optimal value depends on the vibration isolation target.
Dynamic characteristics and parametric optimization of a vibration isolation system with viscoelastic( VE) damping were studied. Firstly,a single-DOF dynamic model for the system was established,and the fractional derivative Kelvin model was introduced to consider the effect of frequency-dependence on dynamic characteristics of the system. Then,the VE influence coefficient was proposed. Based on Taylor series,the system's characteristic equation was solved to obtain the vibration isolation system's natural frequency and equivalent damping ratio under the influence of the excitation frequency. At last,the stiffness ratio between the elastic element and the VE one was optimized to realize the optimal vibration isolation effect of the system under wide frequency band and the peak value response frequency. The results showed that compared to a linear vibration isolation system with the same static state stiffness,the vibration isolation system with VE damping has a higher damping ratio,a wider amplification region of vibration isolation curve and a larger natural frequency; the optimal system vibration isolation efficiency is obtained through optimizing the stiffness ratio between the elastic element and the VE one,and the optimal value depends on the vibration isolation target.
引文
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[2]申跃奎.地铁激励下振动的传播规律及建筑物隔振减振研究[D].上海:同济大学,2007.
[3]凌育洪,吴景壮,马宏伟.地铁引起的振动对框架结构的影响及隔振研究-以某教学楼为例[J].振动与冲击,2015,34(4):184-189.LING Yuhong,WU Jingzhuang,MA Hongwei.Effects of subway vibration on a frame structure and its vibration isolation.[J].Journal of Vibration and Shock,2015,34(4):184-189.
[4]IBRAHIM R A.Recent advances in nonlinear passive vibration isolators[J].Journal of Sound and Vibration,2008,314(3):371-452.
[5]贾俊峰,欧进萍,刘明,等.新型三维隔震装置力学性能试验研究[J].土木建筑与环境工程,2012,34(1):29-34.JIA Junfeng,OU Jinping,LIU Ming,et al.Mechanical performance tests of a novel three-dimensional isolation bearing[J].Journal of Civil Architectural&Environmental Engineering,2012,34(1):29-34.
[6]赵亚敏,苏经宇,陆鸣.组合式三维隔震支座力学性能试验研究[J].工程抗震与加固改造,2010,32(1):57-62.ZHAO Yamin,SU Jingyu,LU Ming.Mechanical performance test of combined 3-dimensional isolation bearing for 3-dimensional base-isolated buildings[J].Earthquake Resistant Engineering and Retrofitting,2010,32(1):57-62.
[7]XU Zhaodong,GAI Panpan,ZHAO Huiyi,et al.Experimental and theoretical study on a building structure controlled by multi-dimensional earthquake isolation and mitigation devices[J].Nonlinear Dynamics,2017,89(1):723-740.
[8]朱俊涛.磁流变弹性体对宽频激励平台隔减振研究[D].南京:东南大学,2013.
[9]FUJITA S,MINAGAWA K,KODAIRA T.Required properties of seismic isolation system for nuclear power plants[C]∥ASME 2010 Pressure Vessels and Piping Division/K-PVP Conference.American Society of Mechanical Engineers,2010.
[10]CHAE H D,CHOI S B.A new vibration isolation bed stage with magnetorheological dampers for ambulance vehicles[J].Smart Materials and Structures,2014,24(1):1-14.
[11]PARK S W.Analytical modeling of viscoelastic dampers for structural and vibration control[J].International Journal of Solids and Structures,2001,38(44):8065-8092.
[12]XU Zhaodong,XU Chao,HU Jian.Equivalent fractional Kelvin model and experimental study on viscoelastic damper[J].Journal of Vibration and Control,2015,21(13):2536-2552.