圆板振子超谐分岔和混沌运动的实验研究

Experiments on Superharmonic Bifurcation and Chaotic Motion of a Circular Plate Osciliator

设计了非线性圆板混沌实验振动台 .就轴对称圆板在简谐载荷作用下的非线性动力学行为进行了较为系统的实验研究、理论分析和数值计算 .对基础作简谐运动 ,周边固支圆板 ,进行了实验 .通过测量时间—中心挠度的加速度曲线 ,进行快速傅立叶变换 (FFT)分析 ,实验发现了对称破缺 ,超谐分岔 ,调幅调相等复杂现象 ;对基础作简谐运动 ,周边固支 ,中心加质量块的圆板 ,进行了实验 .通过测量时间—周边应变曲线 ,进行 FFT分析 ,实验发现了混沌。

In this paper experimental evidence is presented for the chaotic type non-periodic motions of a deterministic circular plate. The nonlinear dynamic behaviors of symmetric circular plates under a harmonic excitation are studied by experimental techniques, analytic techniques and numerical techniques. Axisymmetric nonlinear flexural vibration of a circular plate clamped at its edge, excited by the periodic motion of its supporting base, are investigated experimentally. The system′s complicated phenomena, such as symmetry breaking and superharmonic bifurcation are observed by monitoring the acceleration of the concentric deflection of the circular plate, and experimental fast Fourier transform of motion data. Axisymmetric nonlinear flexural vibration of a circular plate with concentric rigid mass, clamped at its edge, excited by the periodic motion of its supporting base, are investigated experimentally. The system′s complicated dynamic behaviors, such as chaos, symmetry breaking and restoration, superharmonic bifurcation, are observed by watching the strain at clamped edge of the circular plate as a function of time, and experimental FFT of motion data. The results of the analog computer study agree well with the experiments in qualitative analysis. Our observation is that the symmetry breaking phenomena in a symmetric construction are the omen of chaos. If the solution of the dynamical systems having a symmetry is one of the following four cases: 1) even order superharmonic solution; 2) even order subharmonic solution; 3) even order super-subharmonic solution; 4) even order sub-superharmonic solution, then the symmetric breaking phenomena will appear. Before the chaos occurs, one of the above four solutions mast take place.