Melnikov theoretic methods for characterizing the dynamics of the bistable piezoelectric inertial generator in complex spectral environments

• Published in: Physica. D Vol. 241; no. 6; pp. 711 - 720
• Main Authors: Stanton, Samuel C., Mann, Brian P., Owens, Benjamin A.M.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15.03.2012
• Subjects: Bistable; Broadband; Chaos theory; Duffing–Holmes; Dynamical systems; Excitation; Generators; Inertial; Mathematical analysis; Mathematical models; Melnikov theory; Piezoelectric energy harvesting; Piezoelectricity; Piezoelectric energy harvesting; Bistable; Duffing–Holmes; Dynamical systems; Melnikov theory
• ISSN: 0167-2789; 1872-8022
• DOI: 10.1016/j.physd.2011.12.010

Piezoelectric energy harvesters exploiting strong mechanical nonlinearities exhibit intrinsic suitability for one of several modern challenges in vibratory energy harvesting: consistent kinetic performance in the presence of broadband environmental excitation. In particular, the bistable piezoelectric generator has been prolifically examined. However, most of the relevant literature relies on numerical simulation of specific experimental realizations to demonstrate superior performance. Due to the complexities and lack of analytical solutions for such designs, streamlined methods for parameter optimization,potential well shaping, optimal electromechanical coupling considerations, and other design methodologies are thus inhibited. To facilitate future innovation and research, this paper employs techniques from chaotic dynamical systems theory to provide a simplified analytical framework such that deeper insight into the performance of the bistable piezoelectric inertial generator may be obtained. Specifically, Melnikov theory is investigated to provide metrics for which homoclinic bifurcation may occur in the presence of harmonic, multi-frequency, and broadband excitation. The analysis maintains full consideration of the electromechanical coupling and electrical impedance effects and predicts that for range of dimensionless electrical impedance values, the threshold for chaotic motion and other high-energy solutions is significantly influenced. ► Melnikov theory provides simplified metrics for a class of multi-stable harvesters. ► Nonlinear piezoelectricity and nonlinear damping are modeled. ► Critical impedance load and excitation frequency ranges are identified. ► Nonlinearity offers enhanced capabilities in broadband environments.