Energy harvesting from a non-linear standing beam–mass system: Two- versus one-mode approximations. (May 2017)

• Record Type: Journal Article
• Authors: Mousavi Lajimi, S Amir; Friswell, Michael I
• Is Part Of: Journal of intelligent material systems and structures. Volume 28:Number 8(2017)
• Page Start: 1010
• Page End: 1022
• Publication Date: 2017-05
• Subjects: Energy harvesting -- piezoelectric -- bi-stable -- bifurcation diagram -- Poincaré section -- frequency–response curve; Smart materials -- Periodicals; Intelligent control systems -- Periodicals; Artificial intelligence -- Periodicals; Matériaux intelligents -- Périodiques; Commande intelligente -- Périodiques; Intelligence artificielle -- Périodiques; 620.11
• DOI: 10.1177/1045389X16667852
• Languages: English
• ISSNs: 1045-389X

Abstract

We investigate the effect of including the second mode of natural vibration on the computed response of a forced non-linear gravity-loaded beam–mass structure used for non-linear piezoelectric energy harvesting. Using the method of assumed-modes and Lagrange's equations, we develop the discretized equations of generalized coordinates of the system including the electro-mechanical equation. The equation of motion is further simplified to find the single-mode approximation. The phase-portraits, time-histories, Poincaré sections, and frequency–response curves of the system are computed. It is shown that the number of mode shapes affects the response, and it is required to include higher modes to improve the analytical–computational results. The system shows distinct behavior varying from a linear single-frequency response to a multi-frequency chaotic response. The average power across the load resistor consequently shows a noticeable variation depending on the characteristics of the overall system response.