振荡器驱动方板的有限元模型和克拉尼图形

Finite Element Models and Chladni Figures of Oscillator-driven Square Plates

振荡器驱动的方板在稳态振动时所形成的克拉尼图形(驻波节线图形)在噪声源识别和颗粒移动操控等领域得到广泛应用。现有的对方板克拉尼图形的研究多采用实验和近似的理论分析方法。基于参数分析建立振荡器驱动方板的简化有限元模型和适当的边界条件,进而通过固有频率和振型分析,根据振型有效质量的大小预测和再现多组实验中出现的共振频率和克拉尼图形。对薄板在任意驱动频率下的稳态振动,通过振型叠加法快速准确计算出其振幅节线图形,与实验中相同频率下的克拉尼图形几乎相同。振荡器驱动的方板在共振频率下的克拉尼图形可解释为固有频率对应的振型,在非共振频率下的克拉尼图形可以解释为多个振型的叠加。通过建立具有适当边界条件的有限元模型,对振荡器驱动方板的克拉尼图形给出具有明确物理意义解释。

The Chladni figures(standing wave nodal pattern)formed by the oscillator-driven square plate during steady-state vibration have a wide application in the fields of noise source identification and particle movement control.Experiments and approximate theoretical analysis are used in most of the existing research on the Chladni figures of the square plate.In the present work,a simplified finite element model with appropriate boundary conditions for the oscillatordriven square plate is established based on parametric analysis.Through natural frequency and mode shape analysis,the resonant frequencies and Chladni figures in multiple sets of experiments are almost perfectly predicted and reproduced by the effective mass of the mode shape.For the steady-state vibration of the square plate at any given frequency,the amplitude nodal pattern can be quickly and accurately calculated by the mode shape superposition method,which is almost identical to the Chladni figures at the same frequency in the experiment.The Chladni figures of the oscillator-driven square plate at the resonant frequency can be interpreted as the mode shape corresponding to the natural frequency,and the Chladni figures at the non-resonant frequency can be interpreted as the superposition of multiple mode shapes.The main contribution of this paper is that a clear physical interpretation of the Chladni pattern of the oscillator-driven square plates is given by establishing a finite element model with appropriate boundary conditions.