Probabilistic response of an electromagnetic transducer with nonlinear magnetic coupling under bounded noise excitation

The response in terms of probability density function (PDF) of a vibration transducer, whose mechanical and electrical parts are respectively subjected to stochastic force and bounded noise excitation, is revisited in this report, both analytically and numerically. We discuss the phenomenological transitions exhibited by the PDFs as the noisy excitations parameters evolve and analyze the dependence of the mean output power (MOP) on the parameters of noisy excitations. In the weak parameter regime, using the stochastic averaging method, we show that the MOP of the transducer increases with the intensity of the electrical oscillator additive noise; however, it is independent of the mechanical oscillator additive noise intensity. Conversely, in the hard coupling regime, we show, by Monte Carlo simulations, that the PDFs and the MOP are also affected by the mechanical oscillator additive noise parameters. In particular, we find that the system exhibits the stochastic P-bifurcation only for large damping and coupling parameters. The simulations and the approximate analytical treatment are consistent in the weak parameter regime, as expected.