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

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 H2 criterion. The control performance of the TMD_NSD is compared with the classical TMD in terms of maximum dynamic amplification factor (DAFmax). 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 H2 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 DAFmax decreases with the increase in the mass ratio of the classical TMD, while the DAFmax 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 H2 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 H2 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.