Coupled oscillations typically occur in maglev vehicle-bridge coupled systems excited by bounded noise caused by guideway irregularities. The paper employed Hamilton equations to derive the corresponding canonical transformation equations and determined the critical stable regions for two kinds of resonances using the largest Lyapunov exponents. The results show that the critical stable region between the excitation amplitude and the resonant frequency ratio is a valley shape when the system has external resonance only. When considering both internal and external resonances, the critical stable region between the excitation amplitude and resonant frequency ratio presents a small saddle shape. Energy transfers from the first to the second oscillator under with both internal and extrinsic resonance. As the guideway irregularities' coefficients increase, the maximum Lyapunov exponents of the two conditions change from negative to positive, which means that the system varies from a stable state to instability.
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