This paper is devoted to the study of periodic solutions for a semilinear Euler-Bernoulli beam equation with variable coefficients. Such mathematical model may be described infinitesimal, free, undamped in-plane bending vibrations thin straight elastic beam. When frequency $\omega =\frac{2\pi}{T}$ rational, some properties operator coefficients are investigated. We obtain existence when nonline...

A driven anharmonic oscillator is described which exhibits period doubling and chaotic behavior. The measured behavior of the oscillator under successive period doublings is in quantitative agreement with a recent theory which describes the behavior of nonlinear systems. Both the scalirg and the convergence rate predicted by the theory are verified by the experiment. The oscillator also exhibit...

An artificial system is studied consisting of salt solutions of different concentrations separated by a porous, "charged" membrane, through which a constant electric current is passed. Experiments on such systems demonstrate rhythmic variations of the transmembrane potential and the membrane resistance, which are concomitant with an oscillatory streaming of water solution across the membrane. T...

Details of electronic circuitry to define Poincaré planes in the phase space of nonlinear electronic systems are presented. It allows an experimental setup to capture data at every moment the system’s orbit crosses the Poincaré plane. We illustrate how the circuit is used in an experimental setup that allows us (i) to reconstruct bifurcation cascades and to disclose induced first return chaotic...

Nonlinear elastic effects play an important role in the dynamics of microelectromechanical systems (MEMS). A Duffing oscillator is widely used as an archetypical model of mechanical resonators with nonlinear elastic behavior. In contrast, nonlinear dissipation effects in micromechanical oscillators are often overlooked. In this work, we consider a doubly clamped micromechanical beam oscillator,...