A Nonlinear Analysis of Surface Acoustic Waves in ST-cut Quartz Crystals

With the fast evolution of wireless and networking communication technology, applications of surface acoustic wave (SAW), or Rayleigh wave, resonators are proliferating with fast shrinking sizes and increasing frequencies. The smaller resonators under a strong electric field will inevitably induce large deformation, which has to be described in wave propagation equations with the consideration of nonlinearity. In this study, the formal nonlinear equations of motion are constructed by introducing the nonlinear constitutive relations and strain components in a standard procedure, and the equations are simplified by the extended Galerkin method through the elimination of harmonics. The wave velocity of the nonlinear SAW is obtained from approximated nonlinear equations and boundary conditions through a rigorous solution procedure. If the amplitude is small enough, the nonlinear results are consistent with the linear results, demonstrating an alternative procedure for the nonlinear analysis of SAW devices.