Bending vibration of flexible structures can be suppressed passively using piezoelectric electromechanical transducers and optimally tuned LR circuits. Since these systems include both mechanical and electrical elements, the governing equations consist of electrically coupled equations of motion. This paper describes a new method for deriving the governing equations that describe a system's vibration suppression based on the equilibrium of force principle and using an equivalent mechanical model of a piezoelectric element. Both series and parallel LR circuits are considered in the modeling approach. The optimum values for a mechanical vibration absorber can be formulated by using the two fixed points method. However, exact optimal values for the resistances of the LR circuits have not been formulated in the research literature thus far, and approximate values have been used. Analytical formulations are derived in this paper, and optimum values of the LR circuits are presented, not only in displacement, but also in terms of velocity and acceleration. The effects of the stiffness of the adhesive bond between the host structure and piezoelectric element, the dielectric loss in a piezoelectric element, and the internal resistance of an inductor are considered in the theoretical analysis. The effectiveness of the described analytical method is validated through simulations and experiments.

Semi-active systems with variable stiffness and damping have demonstrated excellent performance. However, conventional devices for controlling variable stiffness are complicated and difficult to implement in most applications. To address this issue, a new configuration using two controllable dampers and two constant springs is proposed. This paper presents theoretical and experimental analyses of the proposed system. A Voigt element and a spring in series are used to control the system stiffness. The Voigt element is comprised of a controllable damper and a constant spring. The equivalent stiffness of the whole system is changed by controlling the damper in the Voigt element, and the second damper which is parallel with the other elements provides variable damping for the system. The proposed system is experimentally implemented using two magnetorheological fluid dampers for the controllable dampers. Eight different control schemes involving soft suspension, stiff suspensions with low and high damping, damping on-off (soft and stiff), stiffness on-off (low and high), and damping and stiffness on-off control are explored. The time and frequency responses of the system to sinusoidal, impulse and random excitations show that variable stiffness and damping control can be realized by the proposed system. The system with damping and stiffness on-off control provides excellent vibration isolation for a broad range of excitations.

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A vibration isolation system with variable damping and stiffness control is practical and has good performances. However, conventional devices of variable stiffness are usually complicated. A magnetorheological (MR) fluid damper only needs a small electric current to provide the magnetic field. It is easy to achieve variable damping with an MR damper in vibration systems. In this paper, two MR fluid dampers in series were used to achieve the variable damping and stiffness for the system. The passive, variable damping, variable stiffness, and variable damping and stiffness systems were investigated in experiment and theoretical calculation. The time and frequency responses to sinusoidal, sweep and random inputs showed that the system with a variable damping and stiffness had better properties.

In the authors' previous study, we proposed a novel shock vibration control method using the active momentum exchange impact damper (AMEID). By using this method, the shock vibration of the vibratory system is greatly reduced by transferring part of its momentum to the damper mass. This feature is effective for suppressing the first large peak value of the acceleration response due to a shock load. However, the validity of AMEID for actual implementations has not yet been investigated. In this paper, the active control of shock vibration using AMEID under real conditions is evaluated by simulation and experiment. A onedegree-of-freedom vibratory system is used as the controlled object. The controller is designed using the linear quadratic regulator optimal control theory. Reductions in the acceleration response and transmitted force to the base are investigated using simulations. Experiments are carried out to verify the simulation results.

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Most passive vibration isolation systems are composed of springs and dampers. Although it is possible to improve the isolation performance by active vibration control, the complexity, power requirements and cost of such a system have restricted its use. A vibration isolation system with variable damping is practical and has good performance in the high frequency region, but it was found not to improve the responses in the low frequency region. On the base of a damping on-off control method, a stiffness on-off control method and a combination of damping and stiffness on-off control method were proposed. Comparison of the responses among the proposed methods and the conventional methods showed that the damping and stiffness on-off control method had the best isolation properties in the whole frequency region. A new system with controllable dampers of two Voigt elements in series was used to achieve the proposed idea.