Research on Hopf bifurcation of vehicle air compressor system with single-pendulum TMD

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Abstract

Nonlinear tuned mass dampers (TMDs) are widely recognized for their superior damping performance, which stems from their broad damping bandwidth. In this study, we propose a single-pendulum TMD for application in vibration absorption within train compressors to protect critical components. However, the inherent nonlinear vibration characteristics of the TMD may undermine its damping effectiveness. To address this challenge, we develop a three-degree-of-freedom mechanical model of a train compressor integrated with a single-pendulum TMD. The equations of motion for the system are derived using the second kind of Lagrange formula. By employing the fourth-order Runge-Kutta numerical integration method and using the excitation frequency as the bifurcation parameter, we analyze the bifurcation behavior and the transition to chaos via the Poincaré cross-section method. Our results demonstrate that the system can transition to chaos through multiple routes, including multiplicative bifurcation, Hopf bifurcation, and residual-dimension bifurcation, depending on the excitation frequency. These findings provide critical insights for the dynamic design and chaotic motion prediction of single-pendulum TMD systems, offering practical guidance to enhance their reliability and performance in real-world applications.

Keywords

air compressor / tuned mass damper (TMD) / dynamic models / bifurcation / chaos

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