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

机译：泡沫弹簧质量系统的强制振动：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，我们研究了理论上和实验的气泡质量系统的非线性强制振动，其中气泡被视为弹簧。通过假设泡沫的轮廓线是抛物线曲线的轮廓线来开发激发振动的数学模型。增量谐波平衡方法用于解决常微分方程，并且高速摄像机用于拍摄照片。施加在弹簧的静态压缩上的气泡体积和半径的影响，对基本波的基本和二次谐波的幅度频率曲线以及基波的相位频率曲线。结果表明，表示气泡的弹簧总是在振动过程中压缩，更大的气泡体积和更小的板半径使得系统刚度更小。二次谐波具有来自基波对应的一些不同的特征。我们还执行实验以验证这些理论分析。本研究揭示了软系统的非线性振动上的新光，这可能有利于航空航天，微重力和软机器人等领域。 （c）2019 Elsevier Inc.保留所有权利。

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