Proportional and derivative control for steady-state vibration mitigation in a piecewise linear beam system

A control using Proportional and/or Derivative feedback (PD-control) is applied on a piecewise linear beam system with a flushing one-sided spring element for steady-state vibration amplitude mitigation. Two control objectives are formulated: (1) minimize the transversal vibration amplitude of the midpoint of the beam at the frequency where the first harmonic resonance occurs, (2) achieve this in a larger (low) excitation frequency range, where the lowest nonlinear normal mode dominates the response. Experimentally realizable combinations of PD-control are evaluated for both control objectives. Eventually objective (1) is realized by applying proportional control only, whereas derivative control is selected to realize objective (2). The vibration reduction that is achieved in simulations and validated by experiments is very significant for both objectives. Current results obtained with active PD-control are compared with earlier results obtained using a passive dynamic vibration absorber

In-phase and anti-phase synchronization of oscillators with Huygens' coupling

In this experimental study, the synchronized motion observed in pairs of nonlinear oscillators coupled through a suspended rigid bar, is analyzed. In particular, the dynamics of two mass-spring-damper oscillators and the dynamics of two van der Pol oscillators are considered. It is shown that in both cases, the oscillators may exhibit in-phase and anti-phase synchronization. The experiments are executed in an experimental setup, consisting of two mass-spring-damperoscillators coupled through a suspended rigid bar. A relation between the obtained results and Huygens’ experiment of pendulum clocks is emphasized

Synchronization of weakly nonlinear oscillators with Huygens' coupling

In this paper, the occurrence of synchronization in pairs of weakly nonlinear selfsustained oscillators that interact via Huygens’ coupling, i.e. a suspended rigid bar, is treated. In the analysis, a generalized version of the classical Huygens’ experiment of synchronization of two coupled pendulum clocks is considered, in which the clocks are replaced by arbitrary self-sustained oscillators. Sufficient conditions for the existence and stability of synchronous solutions in the coupled system are derived by using the Poincar´e method. The obtained results are supported by computer simulations and experiments conducted on a dedicated experimental platform. It is demonstrated that the mass of the coupling bar is an important parameter with respect to the limit synchronous behaviour in the oscillators