基于近场超声悬浮的耦合频率特性分析

Frequency Characteristics Based on Acoustic Near Film

以近声场模型为基础,提出圆形振子薄板与圆形悬浮物之间的挤压膜耦合数学方程组;利用奇异摄动理论中的渐近展开匹配法对归一化的气体运动方程进行求解,求出挤压膜压力分布的解析式,导出振子在挤压膜影响下的微分控制方程;针对模型的圆形结构,使用非常规板元(TRUNC)的改进列式对薄板控制方程进行数值求解,得出定子在弯曲振动模态下的压力振型和位移振型;分析了挤压膜厚度变化时的频率特性。分析表明,振子的驱动频率随着重物重量的增大而升高,而随着驱动频率阶数的增大,这种影响又逐渐减小。研究结果可为今后的理论推导及实验研究提供指导。

A set of coupled-differential equations of circle stator and squeeze film were achieved based on acoustic near film.The normalized gas motion equation was solved by asymptotic matching methods to the extent that pressure analytic expression in the squeeze film was achieved.On account of the circular structures,this expression was substituted into the stator equation,which was solved in turn using a new formation of triangular unconventional plate element（TRUNC element） for the structural mode shapes and present the final expressions for the pressure distributions and modal shape of the bending vibration.At last,the frequency characteristics under the different depths of squeeze film were analyzed,which proves that driving frequencies of the stator increase with weight of levitated plate.However,this effect decreases when the order of driving frequencies become higher.The test results herein will guide the theoretical and experimental researches and lay the foundation for controlling the lift force in further.