Modeling of a Vibration-Based Piezomagnetoelastic Energy Harvesting System by Using the Duffing Equation

Abstract

This article illustrates the modeling of a piezomagnetoelastic energy harvesting system. The generator consists of a piezoelectric cantilever with a magnetic tip mass. A second oppositely poled magnet is attached near the free end of the beam. Due to the nonlinear magnetic restoring force the system exhibits two symmetric stable equilibrium positions and one instable equilibrium position. The equation of motion is derived and it is shown that the system can be modeled as Duffing oscillator. An analytical approach is given to derive the Duffing parameters from the system parameters. The Duffing equation is solved for an oscillation around both equilibrium positions by using the harmonic balance method. For small orbit oscillations the equation of motion is solved by applying the fourth-order multiple scales method.

An E-shape broadband piezoelectric energy harvester induced by magnets

“…where m A , m B are the moments of the magnetic dipoles, and μ 0 is the vacuum permeability. The expression of the magnetic force used here is different with the one described in the models shown in Erturk et al (2009, 2011), Daqaq et al (2014), Ferrari et al (2010), Stanton et al (2010), and Westermann et al (2012); the specific model used in this study does not include the effect generated by the rotation of the magnets during the beam deflection. Here, we use three couples of repulsive magnets, so the relation m A = m B is valid.…”

“…Masana and Daqaq (2011) and Daqaq et al (2014) introduced other models and analysis of nonlinear structures for PEHs. Westermann et al (2012) developed a mechanical model that describes a vibration-based piezomagnetoelastic energy harvester containing a piezoelectric cantilever beam and two permanent magnets. The same type of nonlinear PEH was also introduced by Ferrari et al (2011, 2010); the experimental results of this single-magnet piezoelectric device showed a 400% improvement of the voltage generated by the converter, compared to the linear case.…”