Design method of tuned mass damper by LMI based robust control theory for seismic excitation

This paper presents a new design method based on a robust-control strategy in the form of a linear matrix inequality (LMI) approach for a passive tuned mass damper (TMD), which is one of the common passive-control devices for structural vibration control. To apply the robust control theory, we first present an equivalent expression that describes a passive TMD as an active TMD. Then, some LMI-based condition is derived that not only guarantees robust stability but also allows us to adjust the robust H¥ performance. In particular, this paper considers the transfer function from a seismic-wave input to structural responses. Unlike other methods, this method formulates the problem to be a convex optimization problem that ensures a global optimal solution and considers uncertainties of mass, damping, and stiffness of a structure for designing a TMD. Numerical example uses both a single-degree-of-freedom (SDOF) and 10DOF models, and seismic waves. The simulation results demonstrated that the TMD that is designed by the presented method has good control performance even if the structural model includes uncertainties, which are the modeling errors.

Hybrid mass damper: theoretical and experimental power flow analysis

In this paper, a hybrid mass damper (HMD) and its hyperstability thanks to a power flow approach are studied. The HMD proposed combines an active control system with an optimal passive device. The initial passive system is an electromagnetic Tuned Mass Damper (TMD) and the control law is a modified velocity feedback with a phase compensator. The resulting hybrid controller system is theoretically hyperstable and ensures fail-safe behavior. Experiments are performed to validate the numerical simulation and provide good results in terms of vibration attenuations. Both excitation from the bottom in the frequency domain and shock response in the time domain are tested and analyzed. The different power flows in terms of active and reactive powers are estimated numerically and experimentally on the inertial damper (passive and active) and on the HMD. More over, through a mechanical analogy of the proposed system, it is shown that this hybrid device can be seen as an active realization of an inerter based tuned-mass-damper associated with a sky-hook damper. Observations and analysis provide insight into the hyperstable behavior imposed by the specific control law.

An improved multi-mode seismic vibration control method using multiple tuned mass dampers

Multiple vibration modes of an engineering structure might be excited by earthquake ground motions. Multiple tuned mass dampers (MTMDs) are widely used to control these multi-mode vibrations. However, in the commonly used MTMD system, the mass element in each tuned mass damper (TMD) is normally assumed to be the same. To improve the performance of MTMDs for seismic-induced vibration control, non-uniform MTMD masses are adopted in the present study to improve the mass utilization of TMD, and a location factor is proposed to determine the best location of each TMD in the MTMD system. The effectiveness of the proposed method is validated through numerical study. The results show that the proposed method effectively reduces the seismic responses of the structure induced by multiple vibration modes.

A Hybrid Tuned Mass Damper for Response Mitigation of Offshore Platforms

A new hybrid type of the Tuned Mass Damper (HTMD), which consists of a Tuned Liquid Column Damper (TLCD) fixed on the top of a traditional Tuned Mass Damper (TMD), is developed for vibration control of an offshore platform. The results obtained from the parametric investigation show that the mass ratio between TLCD and TMD significantly affects the HTMD's performance. To assess the effectiveness and robustness of HTMD, extensive comparisons are made between an optimized HTMD and an optimum TMD with the same weight as the HTMD. The numerical computations indicate that the proposed HTMD offers a higher level of effectiveness in suppressing structural vibrations compared with a traditional TMD. However, the optimum HTMD is not robust in resisting the variation of the structural stiffness.

Experimental study and numerical simulation of inerter-based systems

Based on a single degree of freedom system, the inerter principles of an inertial mass damper and clutch inerter damper are introduced. The motion equations of the systems are derived, and the rotational speed and damping are considered. In addition, a reducer is innovatively combined with clutch inerter damper to significantly improve the inertance. Accordingly, an innovative reducer clutch inerter damper is proposed. Shaking table experiments are carried out on the uncontrolled inertial mass damper, clutch inerter damper, and reducer clutch inerter damper structures under the inputs of harmonic and seismic waves. Simulation models of the four types of structures are developed, and the validity of the theoretical models is verified by a comparison between the simulation and experiment. Moreover, the nonlinear models of clutch inerter damper and reducer clutch inerter damper are discussed. Finally, according to the test results, the vibration reduction effects of the three inerters are analyzed, and the reasons why they are different from the ideal clutch inerter damper are also explained. The results show that clutch inerter damper, especially reducer clutch inerter damper, has a good vibration damping performance.