Nonlinear Responses of a Magnetoelastic Beam in a Step-Pulsed Magnetic Field

Abstract

A theoretical study is carried out on the dynamics of a magnetoelastic beam being in a step-pulsed magnetic field. For this aim, the magnetic potential and elastic energies are determined for the beam and partial differential equations are established according to Hamilton's principle. It is proven that the magnetoelastic beam can give a variety of complex behavior in the case of step-pulsed field excitations. An intermediate regime of two-well chaos is observed. Theoretical findings were found to be in a good agreement with the experimental results for the specific system parameters.

Explorations of displacement and velocity nonlinearities and their effects to power of a magnetically-excited piezoelectric pendulum

“…Some vibration-based features of an elastic beam were described in a previous study by the author of present paper (see [22]). In the present problem, an external magnetic field obtained by an electromagnet is considered to affect a ferromagnetic knob attached to a piezoelectric layer (Fig.…”

“…It was proved [21,22] that an electromagnet could create a static and inhomogeneous magnetic field near the tip of the magnetoelastic beam. The dynamics of the pendulum-like beam consists of a certain elastic force, gravitational force and magnetic force.…”

“…The dynamics of the pendulum-like beam consists of a certain elastic force, gravitational force and magnetic force. Since the elastic force is much higher than the gravitational force, the effects of elastic and magnetic forces can be considered dominantly as in our papers [20][21][22]. In order to show all affecting forces on the pendulum tip, an equivalent electromechanical system has been produced as in Fig.…”

“…Following our earlier studies [21,22,33] and using the model in Fig. 4, one can arrive at the system equations for the pendulum system.…”

“…According to literature, the dynamic responses of beams can be different in terms of external excitations and system parameters and this reality obviously affects the energy harvesting mechanism of the proposed system. In previous papers [21,22], we studied such complicated responses of a magnetoelastic beam in a step-pulsed magnetic field, experimentally and theoretically. A numerous dynamic responses including periodic and chaotic ones were observed.…”