Vibration analysis, stability assessment, and chaotic behavior of a damped oscillator coupled with a spherical pendulum and a piezoelectric transducer

Abstract

Abstract This research explores the dynamics of an innovative three-degrees-of-freedom (3-DOF) spherical pendulum (SP) system integrated with a piezoelectric device to improve energy harvesting (EH) efficiency. The proposed model features a damped Duffing oscillator as the central component, coupled with a piezoelectric energy harvester and an attached SP. Lagrange’s equations are utilized to derive the system’s nonlinear differential governing equations. Analytical solutions (AS) are obtained using the multiple scales method (MSM) to achieve higher-order approximations. These solutions are then compared with numerical results to validate their accuracy and enhance the overall clarity of the analysis. Moreover, solvability criteria and characteristic exponents under resonant conditions are obtained. The stability of the steady-state solutions is analyzed using the Routh–Hurwitz criteria (RHC) and frequency response curves, providing deeper insights into the system’s behavior. Moreover, the basins of attraction have been simulated to analyze the behavior of the system’s nonlinear dynamics and its sensitivity to initial conditions. Additionally, the nonlinear stability analysis reveals both stable and unstable regimes, with resonance curves and time histories constructed for various parameter values. Furthermore, the phase portraits, graphs of bifurcation, and maps of Poincaré present a thorough view of the system’s dynamics that capture quasi-periodic and chaotic phenomena. This research has broad practical usages, evidenced by real-world applications of EH, including the power watch, power pucks, self-powered switches, Boeing wireless sensor nodes, and electrochemistry EH. The diversity and potential impact represented by these examples show the versatility of the proposed system in advancing EH technologies.

Topics & Concepts