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首页> 外文期刊>IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control >Consideration of stiffness and mass effects of relatively thicker electrodes with Mindlin plate theory
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Consideration of stiffness and mass effects of relatively thicker electrodes with Mindlin plate theory

机译：用Mindlin板理论考虑相对较厚的电极的刚度和质量效应

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Mindlin plate theory has been widely used in the high-frequency vibrations of piezoelectric crystal plates with emphasis on its applications in crystal resonator analysis and design. The plate equations were derived without considering the effect of electrodes from the beginning. But continuing efforts have been made to include the mechanical effect, or the mass loading, through the consideration of the mass ratio of the electrodes and crystal blank. Such a consideration has been effective for relatively thin electrodes before, but the ever-increasing mass ratio has been pressing further improvement to take into account relatively thicker electrodes. To extend Mindlin plate equations for these applications, we derive the plate equations systematically with the approximation of displacements in electrodes with those in the crystal blank. As a result, both mass and stiffness effects of electrodes are considered through ratios of the thickness, density, and elastic constants of the electrodes to those of the crystal blank, respectively, and the plate equations are modified accordingly. A practical design of the electrodes and crystal blank are analyzed to demonstrate the necessity of such modifications to Mindlin plate equations.
机译：Mindlin板理论已广泛用于压电晶体板的高频振动，重点是其在晶体谐振器分析和设计中的应用。从一开始就没有考虑电极的影响就得出了板式方程。但是，通过考虑电极和晶体坯的质量比，已经做出了不断的努力以包括机械效应或质量负载。这样的考虑以前对于较薄的电极是有效的，但是考虑到相对较厚的电极，不断增加的质量比已迫使进一步改进。为了将Mindlin平板方程扩展到这些应用，我们系统地推导了平板方程，其中电极中的位移与晶体坯中的位移近似。结果，分别通过电极的厚度，密度和弹性常数与晶体毛坯的厚度，密度和弹性常数之比来考虑电极的质量和刚度效应，并相应地修改板式。分析了电极和晶体坯料的实际设计，以证明对Mindlin平板方程式进行此类修改的必要性。

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