摘要:
具有光滑与不连续转迁特征的SD振子发现和提出以来, 引起了广泛关注. 基于双稳系统大位移特征的测量法困难, SD振子的实验研究还未见报道. 该文提出并设计了具有SD振子系统光滑特征的非线性实验装置, 用实验的方法揭示由几何关系产生的强非线性系统的非线性动力学行为. 设计的非线性实验装置基本振动参数均有良好的可调性和可测量性, 对SD振子在不同频率及幅值的简谐激励作用下的非线性动力学响应进行了实验研究. 为克服大位移测量难题, 研究采用高速摄像机采集振子振动视频信号并进行分析. 结果表明, SD振子系统在一定的参数条件下会产生周期振动、周期5振动及混沌运动等复杂非线性动力学现象, 在相同实验参数条件下进行了数值仿真, 仿真结果与实验结果一致.
Abstract:
Since the discovery of SD oscillator in 2006, which allows the transition from smooth to discontinuous dynamics of strongly geometric nonlinearity, a variety of significant phenomena have been explored through theoretical research. However, there has no report in literature about the experimental research due to the barrier of large displacement associated with bistability. Here in this paper, we propose an experimental rig of SD oscillator, which is smooth at the first stage, to investigate the nonlinear dynamic responses experimentally under the harmonic excitation with different excitation frequencies and amplitudes. Vibration parameters existed in the rig are measurable and adjustable. Vibration signals are collected by a high speed camera to overcome the conventional barrier. The experimental results presented in this paper showed the excellent agreement with the analytical results, periodic vibration, period-5 solution and chaotic phenomena under the chosen certain parameters.
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