A Hybrid Control Approach for Vibration Reduction of a Tower with a Pendulum Absorber

The oscillations of tall slender towers under environmental loads are usually of large amplitude. In order to protect these structures, suitable absorbers can be installed to control or limit the amplitude of oscillation. In this paper, passive and hybrid control strategies are used to improve the dynamic response of a tall tower. A pendulum attached to the top of the tower is used as a vibration absorber. The tower is modeled as a bar with variable crosssection and concentrated masses. First, the vibration modes and frequencies of the tower are obtained analytically. The primary structure and absorber together constitute a coupled system which is discretized as a two degrees of freedom nonlinear system, using the normalized eigenfunctions and the Galerkin method. These equations are either solved numerically, using the Runge-Kutta method, or analytically by the use of the Galerkin-Urabe method. A detailed numerical analysis illustrates the influence of the system parameters on the non-linear response of the tower and the effectiveness of pendulum-type passive absorbers to control the oscillations of the system. The pendulumabsorber is particularly effective when the tower is subjected to periodic excitation. In order to improve the effectiveness of the control during the transient response and under non-periodic forces, a hybrid control system is suggested. The added control force is implemented as a non-linear variable stiffness device based on position and velocity feedback. A marked decrease in vibration amplitudes is obtained. The same is observed for velocities and accelerations. The influence of time delay, an unavoidable fact in practical problem, is also investigated. The obtained results show that this strategy of nonlinear control is attractive, has a good potential and can be used to minimize the response of slender structures under various types of excitation.