Frequency perturbation integral for piezoelectric quartz crystal microbalances based on scalar differential equations

Jiashi Yang

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arXiv · 2305.09894

Frequency perturbation integral for piezoelectric quartz crystal microbalances based on scalar differential equations

Jiashi Yang

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Abstract

We study frequency shifts in a piezoelectric quartz resonator induced by a surface mass layer for sensor applications. The scalar differential equations for thickness-shear modes in a quartz plate are used. A first-order perturbation analysis is performed. The frequency shift is obtained and is expressed by a perturbation integral. It produces the well-known Sauerbrey equation for mass sensitivity in the special case of a uniform mass layer. As an application of the perturbation integral, frequency shifts due to a nonuniform mass layer are calculated.

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Jiashi Yang. 2023-05-17. Frequency perturbation integral for piezoelectric quartz crystal microbalances based on scalar differential equations. https://arxiv.org/abs/2305.09894

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