Finite-element based perturbation analysis of wave propagation in nonlinear periodic structures

Abstract

Wave propagation in continuous, periodic structures subject to weak nonlinearities is studied using a finite-element discretization of a single unit cell followed by a perturbation analysis. The dispersion analysis is integrated with commercial finite-element analysis (FEA) software to expedite nonlinear analysis of geometrically-complex unit cells. A simple continuous multilayer system is used to illustrate the principle aspects of the procedure. A periodic structure formed by membrane elements on nonlinear elastic supports is used to demonstrate the versatility of the procedure. Weakly nonlinear band diagrams are generated in which amplitude-dependent bandgaps and group velocities are identified. The nonlinear dispersion analysis procedure described, coupled with commercial FEA software, should facilitate the study of wave propagation in a wide-variety of geometrically-complex, nonlinear periodic structures.