Vibration suppression in harmonically forced viscously damped systems is considered using a new vibration absorber setup. The absorber is placed between the primary system and the supporting ground. The optimal absorber parameters are obtained with the aim of minimizing the maximum of the primary system frequency response. For a given damping ratio of the primary system and mass ratio of the system, the optimal stiffness and damping ratios of the absorber are calculated numerically. Two different numerical approaches are used in solving the problem; the first is based on the genetic algorithm technique and the second on the downhill simplex method. It is shown that an optimal mass ratio exists and it is calculated along with the corresponding absorber parameters for a range of the primary system damping ratio. The utmost optimal parameters associated with the optimal mass ratios are tabulated to be used for the design of such absorbers. The absorber efficiency is discussed and it is shown that this absorber becomes detrimental as the mass ratio is increased or when damping in the primary system is high. The proposed and classical absorbers efficiencies are compared.
We investigate the use of cable tension for active vibration control in frame structures. A general formulation for this class of systems is developed using finite elements, which includes the dynamics of the structure and the effects of cable-structure interactions. It is found that the cable tension has two distinct effects on the structure. The first is a parametric effect in which the cable tension changes the stiffness of the structure, and the second is a direct effect that provides an external force on the structure. Based on this model, a general control scheme is developed that uses cable actuation to take advantage of these effects, both separately and together. The control scheme for all cases is based on modal amplitudes, and it applies and releases tension in such a manner that vibration energy is removed from the modes of the structure over a prescribed frequency range that depends on the bandwidth(s) of the actuator(s). The stability of the controlled systems is proven using nonlinear control theory. In addition, a method is developed for determining the optimal placement of cables for parametric stiffness control, which is verified via simulations. Finally, an experimental realization of the direct force control is tested on a frame structure and compared with simulations, demonstrating its effectiveness.
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