The Stochastic Optimization Of The Multi-DOF Dissipation Structure With Maxwell Damper

In this paper, using the stochastic averaging method the dampers structure with viscoelastic or viscous is converted to an approximate equivalent system, and the computing method of the value for seismic action is given. Stochastic optimization is studied for multiple degrees of freedom damping structure with Maxwell damping. Main content of the article is as follows:1. Stochastic averaging method is a kind of effective method to predict the approximate stochastic response characteristics, and the basic assumption is the small damping and broadband weak incentives. It has a more rigorous theoretical basis, and its solution is easy to draw a general sense. In this article, two and arbitrary degrees of freedom for the structure with supported Maxwell dampers energy dissipation on average sense are equivalent to conventional structure without energy dissipation, so that the calculation of such seismic energy dissipation structures and further optimization of seismic design become easier. Every the equivalent modal damping ratios of expression for energy dissipation structure is achieved.2. In actual project, consider the maximum dynamic effects caused by the earthquake are affected mainly by the largest displacement response of the layer structure, and safety also depends on the the largest displacement of layers. Also consider the most likely to be destroyed is the first floor in actual project. This article, so, proposed three object functions, namely, the displacement standard deviation of top layer, the sum of the displacement standard deviation for every layers and the weighted sum of the displacement standard deviation for every layers. In this article, the two examples of 2 and24 degrees of freedom of the structure with Maxwell dampers are analyzed, using the three object functions and optimized by the interior point method, sequential quadratic programming method and genetic algorithm. The numerical results show that the optimization results of genetic algorithm optimization are best, and all cases, the optimal layout is dampers layout in 9th layer; The results of three object functions optimization results are agree well, but the object function of the weighted sum of every layers displacement standard deviation is the most easy to search the optimal solution; With the linear increase of number of dampers, the object function values are reduced, reducing rate tends to small.