Forced vibration of a bubble spring-mass system: Nonlinear analysis and experiment

In the present study, we investigate the nonlinear forced vibration of a bubble-mass system both theoretically and experimentally, where the bubble is viewed as a spring. The mathematical model on the excited vibration is developed by assuming the contour line of the bubble being a parabola curve. The incremental harmonic balance method is used to solve the ordinary differential equation, and the high speed video camera is utilized to take photographs. The effects of the bubble volume and radius of the plate on the static compression of the spring, the amplitude–frequency curves for the fundamental and second harmonic wave, and phase–frequency curve of the fundamental wave, are all demonstrated. The results show that the spring representing the bubble is always in compression in the process of vibration, and a greater bubble volume and a smaller plate radius make the system stiffness smaller. The second harmonic wave has some different characteristics from the counterparts of the fundamental wave. We also perform an experiment to validate these theoretical analyses. This study sheds new light on the nonlinear vibration of soft system, which may be beneficial to such areas as aerospace, microgravity, and soft robotics.