Stochastic Optimization of Dissipation Structures Based on Lyapunov Differential Equations and the Full Stress Design Method

Abstract

This article presents a Lyapunov precise integral-based analysis method for seismic structures with added viscous fluid dampers. This study uses the full stress algorithm as the optimization method, considering the mean square of interstory drifts as the optimization objective, the position of the damper as the optimization object, and the random vibration analysis method as the calculation method to optimize seismic frame structures with viscous dampers. A precise integral solution is derived for the Lyapunov equation based on the general expression of the Lyapunov differential equation for the damping system under the excitation of a nonstationary stochastic process using two types of modulation functions: g(t)=1 and g(t)=t. Finally, the optimal damping arrangement is achieved using this method with a six-layer non-eccentric planar frame. In addition, the optimization results of this study are verified with those in the literature using time-history analysis, which verifies the feasibility and effectiveness of the proposed method. This study provides a method for the optimal configuration of dampers for seismic response of structures, which is beneficial for engineering applications and the protection of seismic structures.

Study on the Damping Efficiency of a Structure with Additional Viscous Dampers Based on the Shaking Table Test

“…Tubaldi et al [21,22] investigated the probabilistic response assessment and non-stationary stochastic response of structures. Zhang et al [23] proposed a structural analysis method based on Lyapunov differential equations. Su et al [24] explored the optimal design of non-linear viscous dampers for large-scale structures under non-stationary seismic excitation, employing a stochastic approach.…”

Study on the Influence and Optimization Design of Viscous Damper Parameters on the Damping Efficiency of Frame Shear Wall Structure

“…Seismic response is essentially a random vibration, which needs to be understood from a probabilistic perspective. The researchers have also studied the random vibration response of structures with additional viscous dampers under seismic excitation [34], as well as the research on their optimized design [35,36], and conducted probabilistic seismic response assessment studies [37,38]. However, they did not consider the influence of different damper parameters on the optimal seismic response control and optimal damper placement.…”