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

机译：气泡弹簧-质量系统的强迫振动：非线性分析和实验

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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. (C) 2019 Elsevier Inc. All rights reserved.
机译：在本研究中，我们在理论和实验上研究了气泡-质量系统的非线性强迫振动，其中气泡被视为弹簧。通过假设气泡的轮廓线是抛物线曲线来建立关于激发振动的数学模型。增量谐波平衡法用于求解常微分方程，高速摄像机用于拍照。证明了气泡体积和板半径对弹簧的静态压缩，基波和二次谐波的幅频曲线以及基波的相频曲线的影响。结果表明，代表气泡的弹簧在振动过程中始终处于压缩状态，较大的气泡体积和较小的板半径使系统刚度较小。二次谐波具有与基波对应物不同的特性。我们还进行了实验以验证这些理论分析。这项研究为软系统的非线性振动提供了新的思路，这可能对航空航天，微重力和软机器人等领域有益。 （C）2019 Elsevier Inc.保留所有权利。

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