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) ...

We show that time-delayed feedback methods, which have successfully been used to control unstable steady states or periodic orbits, provide a tool to control Hopf bifurcation for a small-world network model with nonlinear interactions and time delays. We choose the interaction strength parameter as a bifurcation parameter. Without control, bifurcation will occur early; meanwhile, ...

In this paper, we discuss existence, stability, and symmetry of solutions for networks of parametrically forced oscillators. We consider a nonlinear oscillator model with strong 2:1 resonance via parametric excitation. For uncoupled systems, the 2:1 resonance property results in sets of solutions that we classify using a combinatorial approach. The symmetry properties for solution ...

In the classical multiple scales perturbation method for ordinary difference equations (O Δ Es) as developed in 1977 by Hoppensteadt and Miranker, difference equations (describing the slow dynamics of the problem) are replaced at a certain moment in the perturbation procedure by ordinary differential equations (ODEs). Taking into account the possibly different behavior of the ...

An electromechanical system with flexible arm is considered. The mechanical part is a linear flexible beam and the electrical part is a nonlinear self-sustained oscillator. Oscillatory solutions are obtained using an averaging method. Chaotic behavior is studied via the Lyapunov exponent. The synchronization of regular and chaotic states of two such devices is discussed and the ...

Recently, geometric singular perturbation theory has been extended considerably while at the same time producing many new applications. We will review a number of aspects relevant to non-linear dynamics to apply this to periodic solutions within slow manifolds and to review a number of non-hyperbolic cases. The results are illustrated by examples.

Many dynamical systems are subject to some form of non-smooth or discontinuous nonlinearity. One eminent example of such a nonlinearity is friction. This is caused by the fact that friction always opposes the direction of movement, thus changing sign when the sliding velocity changes sign. In this paper, a structure with friction-based seismic base isolation is regarded. Seismic ...

In this paper, we analyze the interaction between friction-induced vibrations and self-sustained lateral vibrations caused by a mass-unbalance in an experimental rotor dynamic setup. This study is performed on the level of both numerical and experimental bifurcation analyses. Numerical analyses show that two types of torsional vibrations can appear: friction-induced torsional ...