An improved theoretical approach is proposed to predict the dynamic behavior of long, slender and flexible microcantilevers affected by squeeze-film damping at low ambient pressures. Our approach extends recent continuum gas damping models (Veijola 2004 J. Micromech. Microeng. 14 1109-18, Gallis and Torczynski 2004 J. Microelectromech. Syst. 13 653-9), which were originally derived for a rigid oscillating plate near a wall, to flexible microcantilevers for calculating and predicting squeeze-film damping ratios of higher order bending modes at reduced ambient pressures. Theoretical frequency response functions are derived for a flexible microcantilever beam excited both inertially and via external forcing. Experiments performed carefully at controlled gas pressures are used to validate our theoretical approach over five orders of the Knudsen number. In addition, we investigate the relative importance of theoretical assumptions made in the Reynolds-equation-based approach for flexible microelectromechanical systems.
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机译：提出了一种改进的理论方法来预测在低环境压力下受挤压膜阻尼影响的细长细长柔性悬臂梁的动力学行为。我们的方法扩展了最近的连续气体阻尼模型（Veijola 2004 J. Micromech。Microeng。14 1109-18，Gallis和Torczynski 2004 J. Microelectromech。Syst。13 653-9），该模型最初是为壁附近的刚性振动板得出的。到柔性微悬臂梁，用于在降低的环境压力下计算和预测高阶弯曲模式的挤压膜阻尼比。理论上的频率响应函数是针对通过惯性和通过外力激发的柔性微悬臂梁得出的。在受控气体压力下仔细执行的实验用于验证我们对Knudsen数的五个数量级的理论方法。此外，我们调查了基于雷诺方程的方法对柔性微机电系统所做的理论假设的相对重要性。
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