考虑几何非线性的串联隔震体系随机响应研究

发布时间：2019-07-08 11:19

【摘要】：自二十世纪九十年代至今,隔震技术在我国得到了广泛的应用。在现有已经开发的结构控制技术中,基础隔震被认为是概念简单、性能稳定、造价相对低廉的一种结构被动减震控制手段。随着建筑功能和立面效果的日益提高,一种叠层橡胶支座与悬臂柱串联的隔震结构设计方案油然而生,其主要优点是能够充分利用空间、便于隔震支座维修。伴随而来的关键问题就是悬臂柱尺寸的确定,以及串联隔震体系的安全性和稳定性问题,隔震结构设计遇到了新的挑战。目前我国建筑抗震设计规范2010版仅从宏观上界定了串联隔震体系属于层间隔震范畴,提出了隔震层以下地面以上结构罕遇地震作用下层间弹塑性位移角限制,但串联隔震体系是一种变刚度强非线性的构件,动力学特性复杂,尚需进一步研究。因此,本文以隔震工程中常见的叠层橡胶支座与悬臂柱串联的隔震体系为研究对象,建立了该体系的几何非线性动力学方程,应用微分求积单元法,分析了串联隔震体系的固有振动特性和地震响应行为,探讨了串联隔震体系的随机响应,进行了多个缩尺比例模型的振动台试验,主要内容如下： (1)建立叠层橡胶支座与悬臂柱串联的隔震体系几何非线性动力响应偏微分方程。基于匀质柱假定,考虑串联隔震体系的几何非线性,分别应用Hamilton变分原理和微元体分析方法,推导了叠层橡胶支座几何非线性动力响应运动方程；结合有限单元法,将该动力学模型扩展得到了叠层橡胶支座与悬臂柱串联的隔震体系几何非线性控制方程和边界条件 (2)分析串联隔震体系固有振动特性。应用微分求积原理离散串联隔震体系的非线性控制方程和边界条件,选择替换法处理边界条件,采用微分求积与有限元相结合的方法——微分求积单元法,编制matlab程序求解分析了叠层橡胶支座与悬臂柱串联隔震体系的固有振动特性,并研究了支座刚度、竖向荷载和悬臂柱长细比等因素对串联隔震体系频率的影响,探讨了三类因素和两种因素联合作用下对体系频率的不利情况。 (3)研究叠层橡胶支座与悬臂柱串联隔震体系的几何非线性时域响应行为。针对串联隔震体系几何非线性控制方程,提出了联合使用微分求积单元法、时域微分求积逐步积分法求解串联隔震体系非线性动力响应的有效方法。首先将其在各单元空间域上进行微分求积离散,然后采用时域微分求积逐步积分法将其在时间域内离散,应用方程替换法处理边界方程,最后编制迭代程序求解分析串联隔震体系在远场罕遇水平地震动作用下的地震响应,综合4种支座类型、3种竖向荷载值、36种长细比等因素,通过计算结果讨论悬臂柱长细比对串联隔震体系稳定性的影响。 (4)探讨考虑几何非线性串联隔震体系的随机响应。在串联隔震体系数学模型的基础上,针对三自由度耦合的几何非线性偏微分方程,提出了串联隔震体系随机响应数学模型。以双过滤白噪声地震动功率谱模型为基础,构造串联隔震体系随机响应输入激励,联合应用微分求积单元法、时域微分求积逐步积分法求解串联隔震体系随机响应控制方程,研究了不同支座类型、不同竖向荷载值、不同悬臂柱长细比等因素对串联隔震体系“大震”下随机响应行为的影响。 (5)针对串联隔震体系的地震响应,进行了模拟地震动振动台试验研究。结合实际隔震工程,设计并制作了九种串联隔震体系缩尺模型,其中隔震垫类型三种,悬臂柱类型九种,最终进行了4组共60个工况的振动台试验,得到了串联隔震体系模型四个测点的加速度响应值(测点分别为台面、悬臂柱高度1/2处、悬臂柱顶部、隔震垫顶部)。对比分析了不同支座不同悬臂柱组成的串联隔震体系的地震响应,并且将模型按照相似比换算回原型中,与理论计算的结果进行对比研究,为足尺串联隔震体系模型振动台试验提供一定的参考依据。
[Abstract]:Since the 1990 's, the isolation technology has been widely used in China. In the existing structure control technology, the base isolation is considered to be a kind of passive shock-absorbing control method with simple concept, stable performance and relatively low cost. With the improvement of the building function and the elevation effect, the design scheme of the vibration isolation structure in series with the cantilever column of the laminated rubber bearing is born, and the main advantages of the invention are that the space can be fully utilized to facilitate the maintenance of the vibration isolation support. The key problem is the determination of the size of the cantilever column and the safety and stability of the series isolation system. At present, the seismic design code for buildings in China has only defined the seismic category of the series shock isolation system from the macro level, and the elastic-plastic displacement angle limitation between the lower layer and the lower layer under the above ground is proposed, but the series isolation system is a member with strong stiffness and non-linearity. The dynamic characteristics are complex and need to be further studied. In this paper, the nonlinear dynamic equation of the system is established, and the inherent vibration characteristics and the seismic response behavior of the series isolation system are analyzed by using the differential quadrature method. The random response of the series isolation system is discussed, and the vibration table test of a plurality of scale scale models is carried out. The main contents are as follows: (1) establishing a geometric non-linear dynamic response partial differential square of a vibration isolation system in series with a cantilever column of a laminated rubber support and a cantilever column; Based on the assumption of the homogeneous column, the geometric non-linearity of the series isolation system is considered, the Hamilton variational principle and the micro-element analysis method are applied respectively, and the geometric nonlinear dynamic response motion equation of the laminated rubber bearing is derived; and the finite element is combined. The dynamic model is extended to obtain the geometric nonlinear control equation and boundary of the isolation system in series between the laminated rubber bearing and the cantilever column. Analysis of the inherent vibration of the series isolation system based on the condition (2) In this paper, the nonlinear control equations and boundary conditions of the discrete series isolation system with differential quadrature are applied, and the boundary conditions are treated by the alternative method. The method of the combination of the differential quadrature and the finite element is used to obtain the differential quadrature. In this paper, the natural vibration characteristics of the series isolation system of the laminated rubber bearing and the cantilever column are analyzed by means of the unit method, and the frequency of the series isolation system is studied by the factors such as the stiffness of the bearing, the vertical load and the length of the cantilever. The effect of three factors and two factors on the frequency of the system under the combination of two factors is discussed. (3) When studying the geometrical non-linearity of the laminated rubber bearing and the cantilever column series isolation system, In this paper, the nonlinear dynamic response of the series isolation system is solved by using the differential quadrature method, the time domain differential quadrature method and the step-by-step integration method for the geometric nonlinear control equation of the series isolation system. The method comprises the following steps of: firstly, performing differential quadrature-domain integration on the space domain of each unit, and then using a time-domain differential quadrature integration integration method to discretize the differential quadrature products in a time domain, and applying an equation replacement method In this paper, the seismic response of the series isolation system in the far field is analyzed by the iterative procedure, and the seismic response of the series isolation system under the shock of the far field is analyzed. The four kinds of support types, the three vertical load values, the 36 long thin ratio and other factors are integrated. The result of the calculation is to discuss the stability of the length of the cantilever column and the series isolation system. Qualitative influence. (4) Discussion of geometrical non-linear series isolation On the basis of the mathematical model of the series isolation system, a series of nonlinear partial differential equations with three-degree-of-freedom coupling are proposed. The stochastic response control equation of the series isolation system is solved by using the double filter white noise floor vibration power spectrum model as the basis, constructing the random response input excitation of the series isolation system, and solving the random response control equation of the series isolation system by the time domain differential quadrature method and the time domain differential quadrature integration method. In this paper, different bearing types, different vertical load values, different cantilever column lengths and other factors are used to randomize the "large earthquake" of the series isolation system. In response to the response behavior, (5) the seismic response of the series isolation system is simulated. In this paper, a vibration table test is designed and made. Nine kinds of scale models of series isolation system are designed and fabricated, in which three types of seismic isolation pads and nine types of cantilever columns are designed, and the four groups of vibration isolation systems are finally carried out. The vibration table test of the working conditions results in the acceleration response values of the four measuring points of the series isolation system model (the measuring point is the table top, the height of the cantilever column is 1/2, the cantilever column In this paper, the seismic response of the series isolation system composed of different cantilever columns of different supports is compared and analyzed, and the model is converted back to the prototype according to the similarity ratio, and compared with the results of the theoretical calculation, the vibration table test for the model of the foot-scale series isolation system is given.
【学位授予单位】：兰州理工大学
【学位级别】：博士
【学位授予年份】：2013
【分类号】：TU352.12

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