Optimum design of a tuned‐mass damper with negative stiffness device subjected to ground excitation

Abstract

In this study, a negative stiffness device based on the magnetic principle is presented and experimentally tested. Then, a tuned mass damper with a negative stiffness device (denoted as TMD_NSD) subjected to harmonic support excitation is optimized in terms of H ∞ optimization criterion, H2 optimization criterion, and stability maximization criterion (SMC). Closed-form expressions for the optimal tuning parameters are derived in terms of both H ∞ criterion and SMC, while the optimal tuning parameters are numerically determined in terms of H 2 criterion. The control performance of the TMD_NSD is compared with the classical TMD in terms of maximum dynamic amplification factor (DAF max ). It is found that the performance of the TMD_NSD based on these three optimization methods is superior to that of the classical TMD. Besides, the performance based on H ∞ and H 2 optimization is almost similar, while the performance based on SMC is less than the first two methods. Compared with the classical TMD, the TMD_NSD could significantly reduce the primary system's peak value and broaden the efficient frequency range of vibration mitigation. However, surprisingly, the DAF max decreases with the increase in the mass ratio of the classical TMD, while the DAF max for the TMD_NSD increases with the increase in mass ratio. Finally, the effectiveness of optimization methods in seismic response control is examined via time history analyses (THA) under 20 real earthquake excitations. The THA findings suggest that the TMD_NSD is superior to the TMD for seismic response mitigation for the three optimization methods. However, it is noted that the displacement response of TMD_NSD based on H ∞ and H 2 optimization is comparable but slightly better than that of the SMC method. Nevertheless, in terms of absolute acceleration control, it is shown that TMD_NSD performance based on the SMC method is better than that of the H ∞ and H 2 methods. Overall, the three optimization methods are validated to be effective for seismic mitigation of the un-damped single-degree-of-freedom (SDOF) primary structure subjected to real seismic excitations.

Equivalent Linearization and Parameter Optimization of the Negative Stiffness Bistable Damper

“…As for the research on vibration reduction, experiments and analytical models have been carried out to investigate the dynamic response control under harmonic and earthquake excitations, and the results indicated that the vibration-reducing effects of a bistable attachment [29] and a bistable tuned-mass damper (BTMD) [30] were effective for a bistable oscillator and a bridge deck, respectively. In addition, bistable vibration isolation (BVI) [31,32] and quasi-zero stiffness (QZS) [33] isolation devices have been developed, and experiments have shown that these devices can significantly improve the vibration isolation effect through the snap-through effect of the bistable structures.…”

“…Li et al [37] and Ullslam et al [38] proposed an innovative dynamic vibration absorber (DVA) and a vibration isolator using negative stiffness and focused on examining the optimal frequency ratio and negative stiffness ratio using the fixed-point theory. Zhang et al [33] invented a tuned-mass damper with a negative stiffness device (TMD_NSD) and verified its excellent vibration-suppressing effect by experimental tests. Charef et al [39] studied a non-traditional tuned-mass damper (NTTMD) employing negative stiffness to dampen a primary system, achieving better optimal tuning parameters.…”

Parameters optimization of grounded dynamic vibration absorber with pendulum connected via the lever mechanism

“…To overcome the limitations of the common DVAs in vibration reduction of primary structure, researchers have explored other solutions, such as the introduction of negative stiffness devices, [18][19][20] flywheel inertial with lever fixed at ground, 21 and lever mechanism. 22 inspired by.…”