Vibration suppression through stiffness variation and modal disparity

Abstract

Vibration suppression is the main objective of this study. A semi-active and an active vibration control strategy based on stiffness variation are proposed for removing energy from vibrating structures. For the semi-active vibration control strategy, the notion of modal disparity is introduced and exploited as a new method of vibration suppression. For a given structure, modal disparity is a measure of the difference in the mode shapes of the structure in two stiffness states. Modal disparity is validated experimentally in a beam where stiffness variation is induced by application and removal of constraints. In dynamical systems modeled with finite degrees-of-freedom, the application of constraints transfers energy to the unmodeled high-frequency modes, where it is dissipated naturally and quickly. The removal of constraints does not dissipate energy but resets the system for the constraints to be applied again for further reduction of energy. Thus sequential application and removal of constraints eventually dissipates the energy of the system completely. It is shown that energy removal is always possible, even with a random switching schedule, except in one case where the energy is trapped in modes that span invariant subspaces with certain orthogonality properties. The optimal locations and timing of constraint application is investigated with the goal of maximizing energy dissipation through maximal energy transfer to the unmodeled high-frequency modes. For the active control strategy, cable actuators are proposed for removing energy from three-dimensional framed structures. The tension in the cables has two effects on the structure; it increases the stiffness of the structure and applies an external load on the structure. Both effects are used in the design of the active control strategy in which the cable tension is essentially switched between different levels to do negative work. Experimental results are presented to validate the efficacy of the control strategy.