带Maxwell阻尼器耗能结构的平稳与非平稳随机地震响应分析

发布时间：2018-02-12 23:15

本文关键词： 随机平均法 Maxwell 扩阶复模态法模态应变能法　出处：《广西科技大学》2015年硕士论文　论文类型：学位论文

【摘要】：在现今的计算结构地震响应的各种方法中,模态应变能法和以第一频率为基本固有频率的振型分解法是应用的最普遍的方法,对于Maxwell型粘弹性阻尼器耗能结构,由上述两种方法建立的等效系统,它的假设条件较多,对结构位移响应和响应方差误差较大。故而,获得便于工程设计人员使用且计算精度高的等效系统,是一项有意义的研究课题。通过随机平均法,对带Maxwell型粘弹性阻尼器单自由度和多自由度耗能结构的随机地震响应进行了分析,然后基于随机平均法对Maxwell阻尼器耗能结构进行了等效自振和等效强振分析,并且还对带Maxwell型阻尼器耗能结构在平稳随机地震激励下的结构响应进行了分析。应用扩阶复模态法,对于在建筑结构中安装了Maxwell阻尼器的耗能减震结构,将阻尼器的本构方程引入到结构的运动方程中,然后再利用结构的原方程与阻尼器的本构方程建立一个状态矢量,对方程进行扩阶处理,把结构的运动方程变为时不变的一阶微分方程,进而解出单自由度和多自由度带Maxwell阻尼器耗能减震结构随机地震响应的精确解析解,并分别对它在平稳和非平稳的随机地震激励下的结构响应进行了分析。对单自由度和多自由度带Maxwell型阻尼器耗能减震结构,分别采用了近似法和精确法进行了对比分析,其中近似法为随机平均法和模态应变能法,精确法为扩阶复模态法。通过这三种方法,分别对安装了Maxwell型阻尼器的耗能结构进行了随机地震响应分析,并且通过工程实例,还对其在平稳白噪声地震激励下的随机地震响应进行了精度分析。
[Abstract]:The modal strain energy method and the mode decomposition method with the first frequency as the basic natural frequency are the most popular methods for calculating the seismic response of structures. For the viscoelastic dampers of Maxwell type, the mode strain energy method and the mode decomposition method with the first frequency as the basic natural frequency are the most popular methods. The equivalent system established by the above two methods has many hypothetical conditions and large variance error to the displacement response and response of the structure. Therefore, an equivalent system which is convenient for engineering designers and has high calculation accuracy is obtained. By means of stochastic averaging method, the random seismic responses of single-degree-of-freedom and multi-degree-of-freedom structures with Maxwell viscoelastic dampers are analyzed. Then, the equivalent natural vibration and the equivalent strong vibration of the Maxwell dampers are analyzed based on the stochastic averaging method, and the structural responses of the dampers with Maxwell dampers under stationary random earthquake excitation are also analyzed. For the energy dissipation structure with Maxwell damper installed in the building structure, the constitutive equation of the damper is introduced into the motion equation of the structure, and then a state vector is established by using the original equation of the structure and the constitutive equation of the damper. By extending the order of the equation, the equation of motion of the structure is transformed into a time-invariant first order differential equation, and then the exact analytical solution of the random seismic response of the structure with single and multiple degrees of freedom with Maxwell dampers is obtained. The structural responses under stationary and non-stationary random earthquake excitation are analyzed respectively. The approximate method and the exact method are used to compare and analyze the energy dissipation structures with single degree of freedom and multiple degrees of freedom with Maxwell dampers, respectively. The approximate method is the stochastic average method and the modal strain energy method, and the exact method is the extended complex mode method. Through these three methods, the random seismic response analysis of the energy dissipation structures with Maxwell dampers is carried out, and the engineering examples are given. The accuracy of random seismic response under stationary white noise excitation is also analyzed.
【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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