A double variable-length pendulum with counterweight mass, kinematic excitation and electromagnetic forcing

Abstract

This study introduces a novel double variable-length cable pendulum model and experimental setup featuring elastic suspension and counterweight mass. Our main goal is to investigate the complex dynamics resulting from variable length’s impact on vibration frequency and amplitude. Through numerical simulations and experiments, we explore the system’s response to different external forces. Utilizing methods like phase plots, bifurcation diagrams, and Lyapunov exponents, we delve into nonlinear dynamics. We also use vision-based techniques to assess friction damping-related vibrations and magnetic field interactions. The results reveal diverse behaviors, including chaotic and periodic oscillations, shedding light on control functions and parameter relationships. The developed cable system captures intricate nonlinear dynamics and attains stable vibration modes, as confirmed by vision-based measurements. This platform can analyze and control irregular dynamics in systems with elastically suspended weights driven by motors or mobile cranes. Its nature, encompassing kinematic excitation, electromagnetic interactions, and sliding friction, allows for exploring complex nonlinear dynamics. The system’s capacity to modulate vibration frequencies contributes to mitigating persistent vibrations.