Analysis of a Monolithic, Two-Dimensional Array of Quartz Crystal Microbalances Loaded by Mass Layers With Nonuniform Thickness

Authors

Nan Liu, University of Nebraska-LincolnFollow
J. S. Yang, University of Nebraska-LincolnFollow
Ji Wang, Ningbo University

Document Type

Article

Date of this Version

2012

Citation

IEEE Transactions on Ultrasonics, Ferroelectrics, and Fr 746 equency Control, vol. 59, no. 4, April 2012; DOI: http://dx.doi.org/10.1109/TUFFC.2012.2252

Comments

Copyright 2012 IEEE

Abstract

We study free thickness-shear vibrations of a monolithic, two-dimensional, and periodic array of quartz crystal microbalances loaded by mass layers with gradually varying thickness. A theoretical analysis is performed using Mindlin’s two-dimensional plate equation. It is shown that the problem is mathematically governed by Mathieu’s equation with a spatially varying coefficient. A periodic solution for resonant frequencies and modes is obtained and used to examine the effects of the mass layers. Results show that the vibration may be trapped or untrapped under the mass layers. The trapped modes decay differently in the two in-plane directions of the plate. The mode shapes and the decay rate of the trapped modes are sensitive to the mass layer thickness.