Abstract
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.
Highlights
In addition to the two seismic force components in the horizontal direction, there is still vertical seismic force components
As the concept of the displacement-based seismic design (DBSD) is addressed to highlight the importance of the proper determination of equivalent damping, in the DBSD, the equivalent stiffness is taken as the secant stiffness at maximum deformation, so the appropriate equivalent damping should be determined based on such a prescription
Twenty-one SDOF systems are designed according to the DBSD procedure and analyzed to indicate that the proposed equivalent damping relationships are suitable for the DBSD
Summary
In addition to the two seismic force components in the horizontal direction, there is still vertical seismic force components. Kitagawa et al [23] have reported the analysis of reinforced concrete elements by considering the effect of strain speed They treated the Maxwell model as a supplementary restoring force on the equation of motion of the system discretized by a central difference method, which is categorized into an explicit integration scheme. The equivalent linearization can solve the problem of nonlinear structure; a nonlinear stochastic optimal control strategy for single degree of freedom viscoelastic system with actuator saturation is proposed based on the stochastic averaging method and stochastic dynamical programing principle. Considering the comprehensive effect of brace, strain history of damper, dynamic characteristics of structure, and excitation, it establishes a complete analytical solution of stochastic response analysis and equivalent damping of a SDOF nonlinear dissipation structure with the brace under biaxial earthquake action. The new approach can be directly applied to damping engineering design with the response spectrum method
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