Theoretical and non-dimensional investigations into vibration control using viscoelastic and endochronic elements

Abstract

Theoretical and non-dimensional investigations have been performed to study the vibration control potential of approaches that are not only based on viscoelastic but also on endochronic elements. The latter are known from the endochronic theory of plasticity and provide the possibility of establishing rate-independent schemes for vibration control. The main question that has to be answered is: Can rate-independent damping be efficiently used to reduce mechanical vibrations? To answer this question, non-dimensional models for dynamical systems are derived and analyzed numerically in the time domain as well as in the frequency domain. The results are used to compare the performance of an optimally tuned endochronic absorber to the performance of an optimally tuned dynamic absorber with viscoelastic damping. Based on a novel closed-form representation for non-linear systems with endochronic elements, it has been possible to prove that the rate-independent control of vibration results in an overall control profit that is close to the control profit obtained by the application of well-established approaches. It has also been found that the new concept is advantageous if anti-resonances have to be considered in broadband vibration control. Based on these novel findings, a practical realization in the context of active vibration control is proposed in which the rate-independent control law is implemented with an appropriate signal processing hardware.