Nonlinear frequency response analysis and optimization of vibration systems with air springs and auxiliary chambers

Vibration isolation systems incorporating air springs with auxiliary chambers (ASAC) exhibit complex vibration responses due to the nonlinear characteristics inherent in air springs. However, the underlying mechanisms of these nonlinear behaviors remain poorly understood. This study presents a dynamic model for ASAC and its vibration system, accounting for the gas polytropic process within two air chambers and the transient airflow characteristics in the flow passage. A test bench was built to measure the transmission rate of the system for model validation. Experimental results show that the transmission rate is dependent on both frequency and amplitude, where the orifice-type system exhibits a single resonance peak, while the pipe-type system shows two. Under varying excitation amplitudes, the response curves of the orifice-type system intersect at one amplitude-independent point, while the pipe-type intersects at two. Then, closed-form expressions for the resonance peaks and amplitude-independent points are derived, explaining the mechanisms of the nonlinear responses. The effects of damping ratio, stiffness ratio, and natural frequency ratio on the transmission rate are analyzed. Finally, a novel optimization strategy leveraging the characteristics of the amplitude-independent point is proposed to minimize the acceleration transmission rate across the entire frequency range. These findings provide guidelines for optimizing the design of vibration isolation systems with ASAC.