Dynamically-dual vibration absorbers: a bond graph approach to vibration control

This paper investigates the use of an actuator and sensor pair coupled via a control system to damp out oscillations in resonant mechanical systems. Specifically the designs emulate passive control strategies, resulting in controller dynamics that resemble a physical system. Here, the use of the novel dynamically dual approach is proposed to design the vibration absorbers to be implemented as the controller dynamics; this gives rise to the dynamically dual vibration absorber (DDVA). It is shown that the method is a natural generalisation of the classical single-degree of freedom mass–spring–damper vibration absorber and also of the popular acceleration feedback controller. This generalisation is applicable to the vibration control of arbitrarily complex resonant dynamical systems. It is further shown that the DDVA approach is analogous to the hybrid numerical-experimental testing technique known as substructuring. This analogy enables methods and results, such as robustness to sensor/actuator dynamics, to be applied to dynamically dual vibration absorbers. Illustrative experiments using both a hinged rigid beam and a flexible cantilever beam are presented.