基于随机平均法的Maxwell阻尼器耗能结构随机响应分析

发布时间：2018-03-25 23:14

本文选题：随机平均法　切入点：粘弹性阻尼　出处：《广西科技大学》2015年硕士论文

【摘要】：本文利用随机平均法将Maxwell粘弹阻尼耗能隔震结构转变为二阶近似等效定常系统,并获得了结构地震作用取值的解析法,其主要内容为:1.运用随机平均法将Maxwell粘弹阻尼隔震结构的频域运动方程转变为近似等效定常系统二阶运动方程,二阶近似等效定常系统考虑了原结构的耦连性。2.分别运用扩阶复模态法,模态应变能法以及随机平均法将Maxwell粘弹阻尼高层隔震结构转化为三种等效系统;然后通过结构等效系统与模态变换方程,进一步求解得结构的随机地震位移响应解析解;最后通过算例,在结构的阻尼耦合和非耦合情况下,参照基于扩阶复模态法获得的精确等效系统,对比分析了分别基于随机平均法和模态应变能法获得的两种近似等效系统求得的结构位移响应的误差值;由此可知:在非耦合阻尼隔震结构中,基于随机平均法的近似等效系统的计算精度与基于模态应变能法的近似等效系统的计算精度基本一致;在耦合Maxwell粘弹阻尼隔震结构中,基于随机平均法的近似等效系统的计算精度比基于模态应变能法的近似等效系统的计算精度有较大提高。3.将基于随机平均法的Maxwell粘弹阻尼隔震结构二阶近似等效定常系统的位移响应表示为系列独立单自由度二阶标准振子的位移和速度响应的线性组合式,获得了主体结构各层间位移及隔震层相对于地面的相对位移响应统一表达式,获得了高层Maxwell粘弹阻尼耗能隔震结构位移响应方差按标准振子位移、速度响应方差分解及其相关组合系数的解析式;根据系列二阶标准振子位移和速度最大响应值与抗震规范加速度反应谱的对应关系,获得了结构最大地震层间位移;最终,建立了一套完备的基于随机平均法的Maxwell粘弹阻尼隔震结构的地震作用取值的解析分析法。
[Abstract]:In this paper, the stochastic averaging method is used to transform the Maxwell viscoelastic damped energy dissipation isolated structure into a second order approximate equivalent steady system, and an analytical method for determining the seismic action of the structure is obtained. The main content is: 1. The frequency domain motion equation of the Maxwell viscoelastic damping isolation structure is transformed into the second order motion equation of the approximate equivalent steady system by using the stochastic averaging method. The coupling property of the original structure is considered in the second order approximate equivalent constant system. The extended complex mode method, the modal strain energy method and the stochastic average method are used to transform the Maxwell viscoelastic damping high-rise isolated structure into three equivalent systems. Then through the structural equivalent system and modal transformation equation, the analytical solution of random seismic displacement response of the structure is further solved. Finally, through an example, under the case of damping coupling and non-coupling of the structure, Referring to the exact equivalent system based on the extended complex mode method, the errors of the structural displacement responses obtained by the two approximate equivalent systems obtained by the stochastic averaging method and the modal strain energy method are compared and analyzed. It can be seen that the accuracy of the approximate equivalent system based on the stochastic averaging method is basically the same as that of the approximate equivalent system based on the modal strain energy method in the uncoupled damping isolation structure, and in the coupled Maxwell viscoelastic damping isolation structure, the accuracy of the approximate equivalent system is basically the same as that of the approximate equivalent system based on the modal strain energy method. The accuracy of the approximate equivalent system based on the stochastic averaging method is greatly improved than that of the approximate equivalent system based on the modal strain energy method .3.The second order approximate equivalence of the Maxwell viscoelastic damping isolation structure based on the stochastic averaging method is presented. The displacement response of the stationary system is expressed as a linear combination of the displacement and velocity responses of a series of independent single-degree-of-freedom second-order standard oscillators. The unified expressions of the displacement between each floor of the main structure and the relative displacement response of the isolation layer relative to the ground are obtained. The displacement response variance of the high Maxwell viscoelastic damping isolated structure is obtained according to the standard vibrator displacement. According to the relationship between the displacement and the maximum velocity response of a series of second-order standard oscillators and the response spectrum of the seismic code acceleration, the maximum seismic interstory displacement of the structure is obtained. A complete analytical analysis method for seismic action of Maxwell viscoelastic damping isolated structures based on stochastic averaging method is established.
【学位授予单位】：广西科技大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TU352.1

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