Exact Solutions for a Novel H2 Optimal Design of Electromagnetic Tuned Mass Damper

To realize structural vibration control,a two parameters H2 optimization design was proposed to optimize the tuning ratio and damping ratio for electromagnetic tuned mass damper (EMTMD). The control effect of this two parameters optimization design is better than that of classical tuned mass damper (TMD).For this two parameters optimization,the most important thing is that the inductance of the coil can be set very small and the external load resistance can be positive ,which can avoid the use of complex negative impedance circuit. If Ref.[6] were designed according to the H2 optimization of two parameters, the EMTMD can be used for multi-modal vibration control of structures without connecting negative inductance and negative resistance spontaneously.

Optimum Design of a New Tuned Inerter-Torsional-Mass-Damper Passive Vibration Control for Stochastically Motion-Excited Structures

The inerter is referred to as a two-terminal device that provides inertial forces proportional to the relative accelerations between its two terminals. It has been widely applied in vibration control due to its mass amplification effect. In this paper, a new inerter-based damper is proposed to take advantage of the mass amplification effect, which consists of the classic rack-pinion inerter in conjunction with a torsional tuned mass damper. Unlike any other topologies of inerter-based dampers, the torsional mass damper is connected to the pinion of the inerter via a rotational spring and viscous damper. As a result, the weight of the torsional mass damper can be significantly reduced. The proposed damper is applied to single-degree-of-freedom primary structures and a two degrees-of-freedom structure, and the H2 optimization is conducted to obtain the optimum tuning ratio and damping ratio analytically. When comparing the proposed damper with its counterpart reported in the literature, the proposed damper achieves 20–70% improvement when their weights are identical.

Optimum Design of a New Tuned Inerter Mass Damper (TIMD) Passive Vibration Control for Stochastically Motion-Excited Structures

The inerter that is referred to as a two-terminal device that provides resisting forces proportional to the relative accelerations between its two terminals has been widely applied in vibration control due to its mass amplification effect. In this paper, a new inerter-based damper is proposed to take advantage of the inerter, which consists of a rack-pinion inerter in conjunction with a tuned rotational inertia damper. Unlike any other inerter-based dampers, the rotational inertia damper is connected to the pinion of the inerter via a rotational spring and damper. As a result, the weight of the damper can be significantly reduced. The proposed damper is applied to single-degree-of-freedom primary structures and a two-degree-of-freedom structure and the H2 optimization is conducted to obtain the optimum tuning ratio and damping ratio analytically. When comparing the proposed damper with its counterpart reported in the literature, the proposed damper achieves 20% to 70% improvement when their weights are identical.

Exact Algebraic Solution of an Optimal Double-Mass Dynamic Vibration Absorber Attached to a Damped Primary System

This article presents exact algebraic solutions to optimization problems of a double-mass dynamic vibration absorber (DVA) attached to a viscous damped primary system. The series-type double-mass DVA was optimized using three optimization criteria (the H∞ optimization, H2 optimization, and stability maximization criteria), and exact algebraic solutions were successfully obtained for all of them. It is extremely difficult to optimize DVAs when there is damping in the primary system. Even in the optimization of the simpler single-mass DVA, exact solutions have been obtained only for the H2 optimization and stability maximization criteria. For H∞ optimization, only numerical solutions and an approximate perturbation solution have been obtained. Regarding double-mass DVAs, an exact algebraic solution could not be obtained in this study in the case where a parallel-type DVA is attached to the damped primary system. For the series-type double-mass DVA, which was the focus of the present study, an exact algebraic solution was obtained for the force excitation system, in which the disturbance force acts directly on the primary mass; however, an algebraic solution was not obtained for the motion excitation system, in which the foundation of the system is subjected to a periodic displacement. Because all actual vibration systems involve damping, the results obtained in this study are expected to be useful in the design of actual DVAs. Furthermore, it is a great surprise that an exact algebraic solution exists even for such complex optimization problems of a linear vibration system.