Numerical and Experimental Studies on a Bistable Oscillator Coupled with a Resonator for Vibration Attenuation and Chaos Prediction

In this study, we develop and investigate an analytical model of a bistable damped oscillator coupled with a linear resonator,supported by numerical simulations and experimental validation. Bistability is realised through slender beams buckled underaxial compression, forming the core of the system. The proposed analytical and numerical tools can capture the key nonlineardynamics of the coupled system. The response of the bistable oscillator–linear resonator system under external excitationis initially analysed and compared with that of a stand-alone oscillator. By varying excitation amplitude and frequency, arich spectrum of nonlinear behaviours is revealed—from intrawell oscillations to interwell transitions and bifurcations—andis thoroughly characterised. The integration of a linear resonator is shown to enhance vibration attenuation across multiplefrequency bands and improve the predictability of chaotic regimes. Experimental validation is then conducted using additivelymanufactured pre-buckled bistable beams and linear resonators. Nonlinear system identification confirms the influence offriction and complex damping, aligning well with predictions. Tests which compare oscillators with linear and bistable beamscoupled to resonators demonstrate the effectiveness of pre-buckled beams in producing bistable springs. Finally, simulationaccuracy is shown to degrade significantly close to chaotic response regimes, emphasising the sensitivity of bistable systemsto parameter variations, test conditions, and manufacturing tolerances.