Shear vibration of a crystal plate carrying an array of microbeams

We study shear vibration of a rotated Y-cut quartz crystal plate carrying an array of microbeams with their bottoms fixed to the top surface of the plate. The beams undergo flexural vibrations when the plate is in shear motion. The plate is modeled by the theory of anisotropic elasticity. The beams are modeled by the Euler–Bernoulli theory for beam bending. A frequency equation that determines the resonant frequencies of the structure is derived. An analytical solution on beam-induced frequency shift is obtained using a perturbation procedure. It is shown that the frequency shift may be used to measure geometric/physical properties of the beam array. A vibrating crystal plate carrying a beam array may also be considered for application as an ultrasonic brush.