Modified Adaptive Negative Stiffness Device with Variable Negative Stiffness and Geometrically Nonlinear Damping for Seismic Protection of Structures

Adaptive negative stiffness device is one of the promising seismic protection devices since it can generate seismic isolation effect through negative stiffness when it is mostly needed and achieve similar vibration mitigation as a semi-active control device. However, the adaptive negative stiffness device generally combined with linear viscous damping underpins the drawback of degrading the vibration isolation effect during the high-frequency region. In this paper, a modified adaptive negative stiffness device (MANSD) with the ability to provide both lateral negative stiffness and nonlinear damping by configuring linear springs and linear viscous dampers is proposed to address the above issue. The negative stiffness and nonlinear damping are realised through a linkage mechanism. The fundamentals and dynamic characteristics of a SDOF system with such a device are analyzed and formulated using the Harmonic Balance Method, with a special focus on the amplitude–frequency response and transmissibility of the system. The system with damping nonlinearity as a function of displacement and velocity has been proven to have attractive advantages over linear damping in reducing the transmissibility in the resonance region without increasing that in the high-frequency region. The effect of nonlinear damping on suppressing displacement and acceleration responses is numerically verified under different sinusoidal excitations and earthquakes with different intensities. Compared with linear damping, the MANSD with nonlinear damping could achieve additional reductions on displacement and acceleration under scaled earthquakes, especially intensive earthquakes.

H∞ Optimization of Tuned Inerter Damper with Negative Stiffness Device Subjected to Support Excitation

In this study, H∞ optimization is conducted for a tuned inerter damper (TID) with negative stiffness device (denoted as TID_NSD) subjected to harmonic support excitation. The study shows that there are still two nonzero-frequency fixed points independent of the damping of the TID_NSD; therefore, the optimum tuning frequency and damping ratio for the TID_NSD are, respectively, derived based on the well-known fixed points theory. By imposing the zero-frequency fixed point having the same amplitude as the other two nonzero-frequency fixed points, the optimum negative stiffness ratio, which makes the primary system with a TID_NSD remain stable, is obtained. Moreover, the role of a negative stiffness device of a TID_NSD system in response control of a single degree-of-freedom (SDOF) structure is evaluated through parametric study. Also, a numerical analysis is conducted on both a SDOF and multiple DOFs structure to validate the feasibility of the derived formulas by simulations with real earthquake records. Numerical results demonstrate that the maximum displacement and the maximum absolute acceleration of the structure equipped with TID_NSD system are reduced by increasing the absolute value of negative stiffness ratio. The results also show that the optimally designed TID_NSD system outperforms the optimally designed TID system in terms of the displacement and absolute acceleration mitigation control. The closed-form solutions proposed in this study can be useful for the optimal design of the structure equipped with TID_NSD.

A Novel Negative Stiffness Amplification System Based Isolation Method for the Vibration Control of Underground Structures

Underground structures can be vulnerable during strong earthquakes, and seismic mitigation systems designed for these structures are instrumental in improving multiple aspects of seismic performance. To deal with this problem, a novel isolation system is proposed for underground structures, employing the incorporation of a negative-stiffness amplification system (NSAS) and an isolator. The proposed NSAS consists of the subconfiguration of a spring with positive stiffness in parallel with a dashpot, which is then in series with a negative-stiffness device. The mechanical model and physical realization of the NSAS are presented, based on which the energy-dissipation-enhancement mechanism of NSAS is detailed. On this basis, comprehensive parameter analyses were conducted between the NSAS isolation system and a conventional isolation system. Analysis results showed that the NSAS exhibited a significant energy-dissipation-enhancement effect, in which the series connection of the negative and positive stiffnesses amplified the dashpot’s deformation for enhanced energy-dissipation capacity and efficiency. Compared with a conventional isolator, the NSAS isolation system provided the underground structure with a multiperformance and multilevel mitigation effect, particularly yielding lower responses of displacement and shear forces at the same time. More vibration energy could be dissipated by NSAS, thereby alleviating the energy-dissipation burden of underground structures.

Seismic Assessment of a Benchmark Highway Bridge Equipped with Optimized Shape Memory Alloy Wire-Based Isolators

In this paper, an evolutionary multi-objective optimization algorithm named NSGA-II was used to determine the optimum radius for shape memory alloy (SMA) wires employed in conjunction with the lead rubber bearing (LRB), referred to as an SMA-LRB isolator. This algorithm simultaneously minimizes the mid-span displacement and the base shear force. Then, the optimized SMA-LRBs were implemented in a benchmark bridge to reduce excessive displacements. The results obtained from the nonlinear dynamic analysis show that the implemented approach could effectively optimize the SMA-LRBs. These improved smart isolators can noticeably reduce the maximum displacements and residual deformations of the structure; meanwhile, the base shear and deck acceleration remain less than those of the non-isolated benchmark bridge. This isolator can reduce the maximum mid-span displacement of the bridge by up to 61%, and the mid-span residual deformations by up to 100%, compared to an uncontrolled isolated bridge under different ground motions. This optimized passive system was compared with nonlinear dampers, passive SMA dampers, and a negative stiffness device. The results indicate that the optimized SMA-LRB isolators are generally more successful in reducing and recovering displacements than the other controllers.