Mass-Loading of Thickness-Excited Crystal Resonators Having Arbitrary Piezo-Coupling

Effects of mass layer dimension on a finite quartz crystal microbalance

“…Otherwise transducers are needed for the excitation and detection of acoustic modes. Specifically, when a thin layer of another material is added to the surface of a resonator, the resonant frequencies of the resonator become lower due to the inertia of the mass layer [1][2][3][4][5]. This effect has been used to make mass sensors for measuring the density and thickness of the layer.…”

Propagation of thickness-twist waves in a piezoelectric ceramic plate with unattached electrodes

“…Eqs. (9) and (10) satisfy Eqs. (4) and (5), respectively, as well as the boundary conditions at the top and bottom electrodes, i.e., the first and last equations in Eq.…”

“…Substitution of Eqs. (7), (9) and (10) into the remaining boundary and continuity conditions at x 2 = ± h in Eq. (6) yields six linear, homogeneous algebraic equations for A 1 through A 6 .…”

“…For very thin electrodes the mechanical effects of the electrodes, mass and stiffness, can all be neglected [8]. When the electrodes are not very thin, the inertia and stiffness of the electrodes need to be considered [9][10][11][12]. Recently, due to the need of device miniaturization, there has been growing research interest on electrode configurations.…”

Propagation of Thickness-Twist Waves in an Infinite Piezoelectric Plate

“…Acoustic waves in these devices are driven by an alternating voltage applied to the electrodes deposited on the plates. Therefore there has been continuing research effort on the effect of electrodes (Ballato & Lukaszek, 1974;Kosinski, 2003;Wang & Shen, 2005;Yang et al, 2005). Recently, due to the need of device miniaturization, there has been growing research interest on electrode configurations.…”