Chaos identification and parameter optimization for vibration suppression in composite bistable structures

An innovative composite bistable system (CBs) coupled of prestressed linear and buckled beams with fixed ends has been designed to enhance the damping and suppress the dynamic response. The dynamic equations of the system are derived by applying Hamilton's principle. When the amplitude of the harmonic excitation exceeds the critical value, the buckling beam of the bistable system enters a state of inter- and in-well combined oscillations. Chaotic motion is present. This motion disperses the vibrational energy over a wide frequency band. The vibration in the high-frequency range significantly enhances the dissipation of the viscoelastic layer, leading to an effective suppression of the system's vibration. Approximate analytical solutions and numerical validation of the chaotic and non-chaotic boundaries of the steady state vibration of the bistable system are carried out based on the harmonic balance method (HBM) and the Melnikov method. The Particle Swarm Optimisation (PSO)  algorithm is used to optimise system parameters for specific operating conditions. This optimisation process provides guidance for the design and improvement of CBs systems.