A Novel Active Vibration Control Design Methodology using Viscoelastic Constitutive Model

Abstract In this paper we incorporate a novel approach to synthesize a class of closed-loop feedback control, based on the variational structure assignment. A viscoelastic constitutive model is used to design an active feedback controller for an undamped structural system. These active components assign the phenomenology based internal strain rate damping parameters of a hypothetical viscoelastic system to the passive elastic structure but with active feedback control. Wave dispersion properties of one-dimensional beam system have been studied. Efficiency of the chosen viscoelastic model in enhancing damping and stability properties of one-dimensional viscoelastic bar have been analyzed. The variational structure is projected on a solution space of a closed-loop system involving a weakly damped structure with distributed sensor and actuator with controller. Time-frequency spectral method, which gives exact solution, independent of the number of states/nodes, is used in the analysis. In the formulation a model of cantilever beam with non-collocated actuator and sensor has been considered. The local control formulation leads to equating degree of freedom of the active closed loop system with that of viscoelastic hypothetical systems to obtain system gains. The closed loop system gains are found to be functions of the excitation frequency and the assured internal strain rate damping parameter of the target viscoelastic model. Parametric studies demonstrate an optimal local control, sub-optimal global control and also the effect of induced internal strain rate damping.

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