This paper investigates numerically and experimentally clipped viscous damping with negative stiffness for semi-active cable damping. From simulations it is concluded that unclipped and clipped viscous damping with negative stiffness is equivalent to unclipped and clipped LQR. It is shown that optimized unclipped viscous damping with negative stiffness generates critical cable damping by an anti-node at the actuator position. The resulting curvature at the actuator position is larger than the curvature close to the anchors due to the disturbance forces which may lead to premature cable fatigue at the actuator position. Optimized clipped viscous damping with negative stiffness does not show this drawback, can be implemented using a semi-active damper and produces twice as much cable damping as optimal viscous damping. Close to the optimal tuning, it leads to approximately the same control force as optimal semi-active friction damping with negative stiffness, which explains the superior cable damping. The superior damping results from the negative stiffness that increases the damper motion. Clipped viscous damping with negative stiffness is validated on a strand cable with a magneto-rheological damper. The measured cable damping is twice that achieved by emulated viscous damping, which confirms the numerical results. A tuning rule for clipped viscous damping with negative stiffness of real cables with flexural rigidity is given.
This paper presents a new adaptive tuned mass damper (TMD) whose stiffness and damping can be tuned in real-time to changing frequencies of a target structure. The adaptive TMD consists of a tuned mass, a tuned passive spring and a magnetorheological (MR) damper. The MR damper is used to emulate controlled friction-viscous damping and controlled stiffness. The controlled positive or negative stiffness emulated by the MR damper works in parallel to the stiffness of the passive TMD spring. The resulting overall TMD stiffness can therefore be varied around the passive spring stiffness using the MR damper. Both the emulated stiffness and friction-viscous damping in the MR damper are controlled such that the resulting overall TMD stiffness and damping are adjusted according to Den Hartog's formulae. Simulations demonstrate that the adaptive TMD with a controlled MR damper provides the same reduction of steady state vibration amplitudes in the target structure as a passive TMD if the target structure vibrates at the nominal frequency. However, if the target structure vibrates at different frequencies, e.g. due to changed service loads, the adaptive TMD with a controlled MR damper outperforms the passive TMD by up to several 100% depending on the frequency change.
This paper presents a solution to the problem of cable vibration mitigation using a semi-active damping device. The optimal control of such a device is investigated with an evolutionary algorithm. A fitness function for the algorithm is defined, as the total energy removed from the cable by the damper in a numerical simulation. The initial and end conditions of the optimization are defined such that the solution is optimal for a single mode of vibration. The solution produced by the evolutionary algorithm is shown to outperform other popular semi-active control strategies for the given conditions, removing as much as 2.0 and 1.2 times more energy than the optimal linear viscous damper and clipped linear quadratic regulator controller, respectively. It is furthermore shown that the solution can be given as a simple control law parametrized with a single parameter. The performance of the control law derived is assessed by means of numerical simulation with a free vibration decay test. Due to the multiple modes of vibrations induced by the nonlinear damper in this test, the control law performance is slightly decreased compared to the aforementioned efficiency.
This investigation optimizes numerically a viscous-friction damper connected to a cable close to one cable anchor for fastest reduction of the total mechanical cable energy during a free vibration decay test. The optimization parameters are the viscous coefficient of the viscous part and the ratio between the friction force and displacement amplitude of the friction part of the transverse damper. Results demonstrate that an almost pure friction damper with negligibly small viscous damping generates fastest cable energy reduction over the entire decay. The ratio between the friction force and displacement amplitude of the optimal friction damper differs from that derived from the energy equivalent optimal viscous damper. The reason for this is that the nonlinearity of the friction damper causes energy spillover from the excited to higher modes of the order of 10%, i.e. cables with attached friction dampers vibrate at several frequencies. This explains why the energy equivalent approach does not yield the optimal friction damper. Analysis of the simulation data demonstrates that the optimally tuned friction damper dissipates the same energy per cycle as if each modal component of the cable were damped by its corresponding optimal linear viscous damper.
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