The linear control of a parametrically excited impacting flexible link in rotational motion is considered. The equation of motion for such a system contains time-periodic coefficients.To suppress the vibrations resulting after impact with an external rigid body, a linear controller is designed via Lyapunov-Floquet transformation. In this approach, the equations of motion with time-periodic coef...

– We consider a population of parametrically excited globally coupled oscillators in a weakly nonlinear state. The instabilities of collective modes lead to a traveling-wave regime, where intensities of oscillations of each oscillator vary periodically in time. For large excitation amplitudes a frozen state with nearly uniform oscillation intensities is observed. Ensembles of coupled oscillator...

Consider a linear autonomous Hamiltonian system with a time-periodic bound state solution. In this paper we study the structural instability of this bound state relative to time almost periodic perturbations which are small, localized, and Hamiltonian. This class of perturbations includes those whose time dependence is periodic but encompasses a large class of those with finite (quasi-periodic)...

The global bifurcations and chaotic dynamics of a string-beam coupled system subjected to parametric and external excitations are investigated in detail in this paper. The governing equations are firstly obtained to describe the nonlinear transverse vibrations of the string-beam coupled system. The Galerkin procedure is introduced to simplify the governing equations of motion to ordinary differ...