Abstract
The dynamic responses of a linear primary structure coupled with a nonlinear energy sink (NES) are investigated under harmonic excitation in the 1 : 1 resonance regime. In civil engineering, initial conditions are usually zero or approximately zero. Therefore, in this study, only these conditions are considered. The strongly modulated response (SMR), whose occurrence is conditional, is the precondition for effective target energy transfer (TET) in this system. Therefore, this study aims to determine the parameter range in which the SMR can occur. The platform phenomenon and other related phenomena are observed while analyzing slow-varying equations. An excitation amplitude interval during which the SMR can occur is obtained, and an approximate analytical solution of the optimal nonlinear stiffness is found. The numerical results show that the NES based on the optimal stiffness performs better in terms of control performance.
Highlights
Natural disasters and man-made damages are considered in civil engineering
Vibration control can be divided into active control, semiactive control, and passive control. e main differences between the three categories are the external energy requirement and the energy input method
Passive control devices have the simplest structure and lowest cost, as they do not require any external energy. They have been widely investigated and applied for several years. e tuned mass damper (TMD) is the most representative type of passive control device that has been installed in several prominent buildings globally, e.g., the John Hancock Tower in Boston, Citicorp Center office building in New York, and Chiba Port Tower in Japan [1]
Summary
Natural disasters and man-made damages are considered in civil engineering. structural vibration control has become a research hotspot in recent years. Liu et al studied the cubic stiffness nonlinear energy sink system under ground harmonic excitation, and the necessary condition and sufficient condition of strongly modulated response (SMR) are obtained [20]. E platform phenomenon caused by the modulation response is proposed and analyzed for the first time in this study Based on this phenomenon, the range of modulation response of the nonlinear system is derived, through which the optimal stiffness of the NES independent of initial conditions can be obtained. A two-degree-of-freedom (2-DOF) system under harmonic excitation composed of a linear primary structure and cubic stiffness NES is investigated in this study. Jumping is a rapidly varying behavior whose response path may not be adequately simulated. is Displacement of the primary structure
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