带支撑一般积分型粘弹性阻尼隔震结构的随机地震响应分析

发布时间：2018-11-11 21:54

【摘要】：本文采用带支撑一般积分型粘弹性阻尼器模型,分别用传递矩阵法以及随机平均法对耗能隔震结构在地震激励下的响应以及基于抗震规范的地震作用取值方法进行了研究。首先,采用带支撑的粘弹性积分本构关系,进行耗能隔震结构的微分积分方程组的精确建模。将上部结构的位移按照前N阶振型展开,得到结构用前N阶振型表示的积分微分方程组。利用传递矩阵法,在非扩阶的原始空间上直接获得结构在任意地震激励下的位移、速度和阻尼器受力的瞬态响应解析表达式。针对3种平稳和9种非平稳地震激励模型,获得了带支撑积分型粘弹性阻尼耗能隔震结构的位移、速度和阻尼器受力响应的平稳与非平稳均方响应解析解。其次,运用随机平均法将耗能隔震结构的微分积分方程组转化为二阶等效定常系统的微分方程组,利用传递矩阵法对等效系统进行求解,得到耗能隔震结构的位移和速度响应的近似解析解。并针对平稳与非平稳地震激励模型,获得了带支撑积分型粘弹性耗能隔震结构的随机响应方差的解析表达式。以传递矩阵法的结果为参照,将随机平均法的结果与模态应变能法对比分析,得出了随机平均法具有较高的精度。最后,在白噪声地震激励下,通过恒等变换,将传递矩阵法与随机平均法得到的结构响应方差分解为系列一阶、二阶标准振子响应方差的线性组合;然后,将结构响应极值的平方分解为系列一阶、二阶标准振子极值响应方差的线性组合;根据系列标准振子的极值响应与响应方差之间的对应关系,建立了耗能隔震结构基于规范反应谱的极值效应及等效静态地震作用取值的精确与近似解析分析方法。
[Abstract]:In this paper, the general integral viscoelastic damper model with braces is used to study the response of energy-dissipation isolated structures under earthquake excitation and the seismic action selection method based on seismic code by using transfer matrix method and stochastic average method, respectively. Firstly, the differential integral equations of energy-dissipation isolated structures are modeled accurately by using the viscoelastic integral constitutive relation with support. The displacements of the superstructure are expanded according to the former N-order modes, and the integro-differential equations of the structures expressed by the pre-N-order modes are obtained. By using the transfer matrix method, the analytical expressions of the displacement, velocity and the transient response of the dampers under arbitrary earthquake excitation are obtained directly in the non-extended original space. For three kinds of stationary and nine kinds of non-stationary seismic excitation models, the analytical solutions of displacement, velocity and force response of dampers with integral viscoelastic damping are obtained. Secondly, the differential and integral equations of energy-dissipation isolated structures are transformed into the differential equations of second-order equivalent time-invariant systems by means of stochastic averaging method, and the equivalent systems are solved by the transfer matrix method. An approximate analytical solution of displacement and velocity response of energy-dissipation isolated structures is obtained. For stationary and non-stationary seismic excitation models, an analytical expression of random response variance of an integral viscoelastic energy dissipation isolated structure with support is obtained. By comparing the results of the transfer matrix method with the modal strain energy method, it is concluded that the stochastic average method has a higher accuracy. Finally, under the excitation of white noise earthquake, the structural response variance obtained by the transfer matrix method and the stochastic average method is decomposed into a series of linear combinations of the first order and the second order standard oscillator response variance through the identity transformation. Then, the square of the structural response extremum is decomposed into a series of linear combinations of first-order, second-order standard oscillator extreme response variance. According to the corresponding relationship between extreme response and response variance of a series of standard vibrators, an accurate and approximate analytical method for determining the extreme value effect and equivalent static seismic action of energy-dissipation isolated structures based on the gauge response spectrum 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】：2017
【分类号】：TU352.1

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