Dynamics of a discontinuous coupled electro-mechanical system oscillator with strong irrational nonlinearities and with two outputs

Abstract

The dynamics of the nonlinear electromechanical device, consisting of a mechanical part with two outputs and an electrical part which acts as the server is strongly investigated in the present work. The mechanical part consists of two nonlinear oscillators with strong irrational nonlinearities having smooth or discontinuous characteristics, where nonlinearity is just due to the inclination of springs, the geometric configuration, which are both elastically coupled. While the electrical part is the Rayleigh equation. By using the Lagrangian formulation, the model equations are established and used to investigate the equilibrium points and their stabilities. Nest by using the multiple time scales method, the analytical solutions are found both for the case of large amplitude and the weak amplitude, leading to interesting bifurcation sets of the equilibria by varying the control parameters, the inclination angles and driven frequency. Finally, numerical investigations of the exact equation of the system are used to justify the validity of analytical results and to find new phenomena such as chaotic impulses, chaotic bursting and the train of kink signal generations.

Fast-slow dynamics analysis in an externally excited smooth and discontinuous oscillator with a pair of irrational nonlinearities

“…However, it should be pointed out that most studies have focused on nonlinear systems with rational polynomials, while very little research has been done on the fast-slow oscillations of systems exhibiting irrational nonlinearity [30]. In fact, the dynamical system with irrational nonlinearity is frequently encountered in pendulums [30,31], buckled beams [32] electro-mechanical system oscillators [33], energy harvesting devices [34], and other practical engineering. Recently, inspired by the elastic arch described by Thompson and Hunt [35], Cao et al [36] proposed an archetypal smooth and discontinuous (SD) oscillator with irrational nonlinearity, which is a simple mass-spring system constrained to a straight line by a geometrical parameter.…”