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There are two types of dynamic vibration absorbers (DVAs) for vibration reduction of a pendulum structure. The first one moving in the tangential direction of the pendulum's orbit can reduce all kinds of vibrations but the effectiveness is quite poor when the DVA locates near the centre of oscillation. Conversely, the second one moving in the normal direction of the pendulum's orbit can only reduce large vibration but has a good effect when the DVA's location is near the centre of oscillation. In this article, the authors propose the DVA, which can move in the normal and tangential directions at the same time. The proposed DVA can overcome the shortcoming of two DVAs moving in only one direction. Because the system's non-linearity is quite complex, a numerical method is used for obtaining the optimal parameters. Then, the authors introduce the convenient empirical formulas of optimal parameters based on the numerical results. The effect of the proposed DVA is demonstrated by the numerical calculations of free vibration of a ropeway gondola.

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This paper addresses an on-off damping tuned liquid column damper (TLCD) regulated by a general controller. This general controller can represent many conventional controllers such as groundhook, skyhook, bang-bang, or linear clipping controller. Due to the on-off damping and quadratic damping of the TLCD the system is complex nonlinear. To cope with those nonlinearities, this paper presents a simple approximated solution by solving a scalar algebraic equation. Outcomes of numerical simulations verify the proposed approximated solution. Moreover, the approximated solution is useful to clarify the condition of robust controllers, to speed up the optimization of the general controller, and to conduct any parametric study. Based on a parametric study, an empirical formula for the optimized parameters of the general on-off damping controller is derived. In a case study of an earthquake excited five degree-of-freedom shear frame the simplicity, robustness, and effectiveness of the semi-active TLCD with optimized parameters is illustrated, considering limited noisy measurements, time delay, modeling error, and nonlinear TLCD behavior.