SummaryThe active disturbance rejection control of a delayed 2-degree-of-freedom structure against earthquake motion force is investigated. A shaking table that resembles the acceleration profiles of most known earthquakes is used to generate the horizontal force. To compensate the motions caused by the earthquake simulator, an active tuned mass and damper system is attached to the structure. Due to the strong effects of the motion forces as a disturbance input, an active disturbance rejection controller including an extended state observer is designed and implemented. The controller designed is modified with including a state predictor to address the control input delays induced by the remote networked control or actuator delays. The stability of the whole system is verified via Lyapunov analysis and tested on the structure sample including shaking table. The results show the effectiveness of the proposed approach to regulate the structure motions in different earthquake scenarios.

In this paper, one of the most efficient passive absorbers, called nonlinear energy sink (NES), is analytically studied. A two-degree-of-freedom system is considered which consists of a linear oscillator (LO) with a base excitation and an NES, called grounded NES (GNES), which is connected to the ground with a nonlinear spring. In this study, we proposed a new arrangement of potential elements in GNES and studied invariant manifolds of the system, as well as the energy absorption performance of the NES. The system is considered in the vicinity of 1:1 resonance to investigate the strongly modulated response (SMR). To this end, after obtaining the equations of motion, the Manevitch complex variable and multiple scale method are applied to solve the equations, analytically. Then, the slow invariant manifold (SIM) is obtained. Also, the energy dissipation ratio of the NES and the percentage of the instantaneous total energy stored in the NES are calculated via the time-amplitude diagram. The results show that when the nonlinear effect decreases, the occurrence of energy pumping is less probable. Also, when the excitation amplitude decreases, the percentage of the instantaneous total energy stored in the NES increases as well as the amount of energy dissipation.