Experimental switching between coexisting attractors in the yoke-bell-clapper system

Area of Science:

• Mechanical Engineering
• Nonlinear Dynamics
• Acoustics

Background:

• The yoke-bell-clapper system exhibits multistability, presenting two coexisting solutions.
• One solution involves a single impact per motion period, producing sound, while the other has no impacts and is silent.
• Understanding and controlling these states is crucial for engineering design.

Purpose of the Study:

• To experimentally demonstrate and control attractor switching in a real-world swinging bell system.
• To validate the effectiveness of the time-dependent stability margin method for predicting and inducing state changes.
• To address issues of incorrect operation (lack of impact) in mechanical systems.

Main Methods:

• Numerical analysis using the time-dependent stability margin method to identify sensitive regions of the system's trajectories.
• Experimental investigation involving targeted perturbations applied to the clapper at specific times.
• Real-world mechanical system analysis, avoiding idealized models.

Main Results:

• The time-dependent stability margin method successfully identified trajectories prone to perturbation.
• Experimental application of precisely timed perturbations effectively switched the system between the impact (sound) and no-impact (silent) attractors.
• The study confirmed the ability to transition the bell from incorrect (silent) to correct (impact) operation.

Conclusions:

• Precise timing of external perturbations allows for controlled switching between coexisting attractors in a multistable mechanical system.
• The time-dependent stability margin method is a valuable tool for analyzing and controlling complex nonlinear systems.
• This research contributes to the understanding of multistability in engineering design, particularly for systems previously considered simple.