A nonlinear analysis of surface acoustic waves in isotropic elastic solids

•Formulation of surface acoustic waves with kinematic nonlinearity in elastic solids.•Nonlinear differential equations are simplified with the extended Galerkin method.•Nonlinear boundary conditions are considered through integrations over the physical and time domains.•Wave properties are obtained by solving nonlinear algebraic equations.•Approximate analytical solutions are consistent with nonlinear finite element analysis.•A novel procedure of nonlinear wave analysis is presented and validated. 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. It is inevitable that the smaller resonators will be under a strong electric field with induced 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 relation 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. It is shown that if the amplitude is small enough, the nonlinear results are consistent with the linear results, demonstrating an alternative procedure for nonlinear analysis of SAW devices working in nonlinear state.