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首页> 外文期刊>IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control >Torsional vibrations of circular elastic plates with thickness steps
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Torsional vibrations of circular elastic plates with thickness steps

机译：圆形弹性板的厚度阶跃扭转振动

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摘要

This paper presents a theoretical study of torsional vibrations in isotropic elastic plates. The exact solutions for torsional vibrations in circular and annular plates are first reviewed. Then, an approximate method is developed to analyze torsional vibrations of circular plates with thickness steps. The method is based on an approximate plate theory for torsional vibrations derived from the variational principle following Mindlin's series expansion method. Approximate solutions for the zeroth- and first-order torsional modes in the circular plate with one thickness step are presented. It is found that, within a narrow frequency range, the first-order torsional modes can be trapped in the inner region where the thickness exceeds that of the outer region. The mode shapes clearly show that both the displacement and the stress amplitudes decay exponentially away from the thickness step. The existence arid the number of the trapped first-order torsional modes in a circular mesa on an infinite plate are determined as functions of the normalized geometric parameters, which may serve as a guide for designing distributed torsional-mode resonators for sensing applications. Comparisons between the theoretical predictions and experimental measurements show close agreements in the resonance frequencies of trapped torsional modes.
机译：本文提出了各向同性弹性板中扭转振动的理论研究。首先回顾了圆形和环形板上扭转振动的精确解。然后，开发了一种近似方法来分析具有厚度阶跃的圆形板的扭转振动。该方法基于近似板理论，根据Mindlin的级数展开法从变分原理得出的扭转振动。给出了具有一个厚度阶跃的圆形板中零阶和一阶扭转模态的近似解。发现在较窄的频率范围内，一阶扭转模可以被捕获在厚度超过外部区域的厚度的内部区域中。模态形状清楚地表明，位移和应力幅度均从厚度台阶处呈指数衰减。确定无穷板上圆形台面中被捕获的一阶扭转模的存在和数量，作为归一化几何参数的函数，可以作为设计用于传感应用的分布式扭转模谐振器的指南。理论预测值与实验测量值之间的比较表明，在捕获的扭转模态的共振频率中存在紧密的一致性。

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