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.

Variable-Length Pendulum-Based Mechatronic Systems for Energy Harvesting: A Review of Dynamic Models

“…Additionally, the review highlighted that numerical investigations have confirmed the feasibility of energy harvesting, particularly noting the improved efficiency associated with shorter, reduced pendulum lengths. This conclusion is supported by both numerical simulations and experimental results [2,7,8].…”

“…In this section, how electromagnetic coupling proves effective is discussed, as studied in [82] and applied to variable-length pendulums for various engineering applications in [7].…”

“…It is important to mention that, due to symmetry, no lateral force is exerted when the cylindrical magnet moves along the coil axis [74,87]. However, the frame structure can be configured to induce a slight vertical motion in the event of significant deflection [7,88].…”

“…When substituting Equation (7) into Equation ( 8), a variable of the magnetic field at an arbitrary point P along the x-axis is described as follows:…”

“…This design stems from adapting the swinging Atwood machine, incorporating multiple pendulums within a 4-DOF system. This section presents the derivation of a mathematical model for the four-degree-offreedom mechanical system shown in Figure 18, which was used to simulate an extended swinging Atwood's machine (SAM) based on the equations of motion derived in [2,7]. As a result of the complexity of the mathematical model and practical considerations, two independent approaches were utilized to deduce the equations of motion governing the dynamics of the proposed prototype SAM.…”