摘要
For quartz crystal resonators of thickness-shear type,the vibration frequency and mode shapes reflect the basic material and structural properties of a quartz crystal plate and the variation with time under attack by erosive gases and liquids that can cause surface and internal degradation in a graded form.Such gradual effects,in turn,will change surface conditions through elastic constants and stiffness and more importantly the gradient of such properties across the thickness with certain depth.Now we study the thickness-shear vibrations of functionally graded material plates with properties of the popular AT-cut quartz crystal varying across the thickness in a general pattern represented by both sine and cosine components of the thickness.The vibration solutions are obtained through the Fourier expansion of the plate deformation.
基金
the National Natural Science Foundation of China(Grant Nos.10932004,11072116,and 11372145)
K.C.Wong Magna Fund administered by Ningbo University
A dditional supports are from the Research Project Foundation of Zhejiang Department of Education(Grant Nos.Y201636501 and Y201738413).
