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On modeling of a thickness‐shear vibrating quartz crystal plate attached with micro‐beams immersed in liquid with considering couple stress effects
Author(s) -
Xie Xuan,
Xie Jiemin,
Chen Xuedong,
Hu Yuantai
Publication year - 2017
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201600092
Subject(s) - materials science , quartz , beam (structure) , vibration , boundary value problem , crystal (programming language) , resonator , shear (geology) , modulus , stress (linguistics) , quartz crystal microbalance , shear modulus , mechanics , composite material , optics , acoustics , physics , chemistry , linguistics , philosophy , optoelectronics , organic chemistry , adsorption , quantum mechanics , computer science , programming language
A coupling model for a compound quartz crystal resonator (QCR) system, consisting of a QCR under the thickness‐shear mode (TSM) vibrations and surface micro‐beam arrays immersed in liquid, is developed using the modified couple stress theory and the Hamilton's variational principle. Couple stresses are included in both governing equations of micro‐beams and the quartz crystal plate. Incorporating the boundary conditions, a set of homogeneous equations is numerically solved to get the frequency shift caused by micro‐beams for different material parameters, such as Young's modulus and material characteristic length. The normalized beam deflections are plotted and discussed. Influence of couple stresses of both micro‐beams and QCR together with their interaction on frequency shift is discussed in detail. The obtained results are useful in measuring geometrical and physical properties of micro‐beams using plate‐like acoustic wave sensors.