Effect of strain-gradients of surface micro-beams on frequency-shift of a quartz crystal resonator under thickness-shear vibrations.

With introduction of the first-order strain-gradient of surface micro-beams into the energy density function, we developed a two-dimensional dynamic model for a compound quartz crystal resonator (QCR) system, consisting of a QCR and surface micro-beam arrays. The frequency shift that was induced by micro-beams with consideration of strain-gradients is discussed in detail and some useful results are obtained, which have important significance in resonator design and applications. [ABSTRACT FROM AUTHOR]