Thickness-shear vibration of an elastic plate carrying an array of rigid microbeams with consideration of couple stresses

We study thickness-shear vibration of an elastic plate carrying an array of rigid microbeams with their bottoms attached to the top surface of the plate. The beams undergo rigid-body translation and rotation when the plate is in thickness-shear motion. The plate is modeled by the couple-stress theory of elasticity to properly take into account both the shear forces and the bending moments at the bottoms of the beams. A equation that determines the resonant frequencies of the structure is derived. Analytical and numerical examinations of a few special cases of the general frequency equation reveal a few basic effects of the microbeams and the couple stress. The results are useful in measuring geometric/physical properties of the microbeams using plate thickness-shear mode acoustic wave sensors.