多自由度Maxwell阻尼器减震结构随机优化分析

发布时间：2018-10-05 19:23

【摘要】：本文通过随机平均法将设置粘弹性或粘滞阻尼器减震结构转化为近似等效系统,并给出了结构地震作用取值的计算方法,对于多自由度Maxwell阻尼减震结构进行了随机优化分析。其主要内容如下:1、随机平均法是一类预测结构随机响应特性的有效近似方法,其基本假设是小阻尼和宽带弱激励,具有较为严密的理论依据,易于得出一般意义的解。本文将两自由度及任意多自由度带支撑的Maxwell阻尼器耗能减震结构在随机平均意义上等效为非耗能的常规结构,使此类耗能结构的抗震计算及进一步的优化抗震设计等更为简便。获得了耗能减震结构各振型等效阻尼比的表达式。2、在实际工程中,基于地震引起最大动态效应受结构的最大层间位移响应影响最大,且结构的安全可靠度也取决于最大层间位移。又考虑到实际工程中,首层最容易被破坏。本文提出了三个的目标函数:结构的顶层位移标准差、结构各层位移标准差之和以及各层位移标准差权重和。对两自由度及24个自由度的Maxwell型阻尼器减震结构的算例,对比分析了上述三个目标函数由内点法、序列二次规划法及遗传算法的优化结果。数值算例表明,应用遗传算法进行优化,得到的结果最好;所有情况下,阻尼器布置在第9层最优;三种目标函数可以得到完全相同的优化结果,但各层位移标准差权重和这个目标函数最容易搜索到最优解;随着阻尼器个数的线性增加,目标函数值均减少,且目标函数减小幅度越来越小。
[Abstract]:In this paper, the structure with viscoelastic or viscous dampers is transformed into an approximate equivalent system by means of the stochastic averaging method, and the calculation method of the seismic action of the structure is given, and the stochastic optimization analysis of the multi-degree-of-freedom Maxwell damping structure is carried out. The main contents are as follows: (1) the stochastic averaging method is an effective approximation method for predicting the random response characteristics of structures. Its basic assumptions are small damping and wideband weak excitation. It has a more strict theoretical basis and is easy to obtain a general meaning solution. In this paper, the two-degree-of-freedom and arbitrary multi-degree-of-freedom Maxwell dampers are equivalent to conventional structures with no energy dissipation in the sense of random average, which makes the seismic calculation and further optimization of seismic design of this kind of energy-dissipation structures more convenient. The expression of equivalent damping ratio of different vibration modes is obtained. In practical engineering, the maximum dynamic effect caused by earthquake is most affected by the maximum interstory displacement response of the structure. The safety reliability of the structure also depends on the maximum interstory displacement. Also considering the actual project, the first floor is the most vulnerable to destruction. In this paper, three objective functions are proposed: the standard deviation of the top floor of the structure, the sum of the standard deviation of the displacement of each layer of the structure and the weight of the standard deviation of the displacement of each floor. In this paper, the optimization results of the three objective functions are compared and analyzed by the interior point method, the sequential quadratic programming method and the genetic algorithm for the Maxwell dampers with two degrees of freedom and 24 degrees of freedom. Numerical examples show that the optimal results are obtained by using genetic algorithm; in all cases, the dampers are arranged at the 9th level; the three objective functions can obtain the same optimization results. However, the weight of displacement standard deviation of each layer and the objective function can easily find the optimal solution. With the linear increase of the number of dampers, the value of the objective function decreases, and the decrease of the objective function becomes smaller and smaller.
【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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