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Mathematical Problems in Engineering
Volume 2017 (2017), Article ID 7384940, 10 pages
Research Article

Stochastic Response Characteristic and Equivalent Damping of Weak Nonlinear Energy Dissipation System under Biaxial Earthquake Action

Civil Engineering and Architecture Department, Guangxi University of Science and Technology, Liuzhou 545006, China

Correspondence should be addressed to Yu Xia

Received 24 January 2017; Accepted 12 April 2017; Published 10 May 2017

Academic Editor: Roman Lewandowski

Copyright © 2017 Yu Xia et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The random response characteristic of weak nonlinear structure under biaxial earthquake excitation is investigated. The structure has a SDOF (single degree of freedom) with supporting braces and viscoelastic dampers. First, it adopts integral constitutive relation and establishes a differential and integral equations of motion. Then, according to the principle of energy balance, the equation is linearized. Finally, based on the stochastic averaging method, the general analytical solution of the variance of the displacement and velocity response and the equivalent damping is deduced and derived. At the same time, the joint probability density function of the amplitude and phase and displacement and velocity of the energy dissipation structure are also given. The dynamic characteristics of a structure with viscoelastic dampers are determined as a solution to the variance of displacement response, so the equivalent damping is taken into consideration as a solution to replace the original nonlinear damping. It means it has established a unified analytical solution of stochastic response analysis and equivalent damping of a SDOF nonlinear dissipation structure with the brace under biaxial earthquake action in this paper.