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

• Published in: Mechanical systems and signal processing Vol. 39; no. 1-2; pp. 32 - 46
• Main Authors: Manktelow, Kevin, Narisetti, Raj K., Leamy, Michael J., Ruzzene, Massimo
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.08.2013
• Subjects: Computer programs; Dispersions; Finite element method; Mathematical analysis; Nonlinear dispersion; Nonlinear metamaterial; Nonlinearity; Periodic structure; Periodic structures; Phononic crystal; Tunable system; Unit cell; Wave propagation; Nonlinear metamaterial; Phononic crystal; Wave propagation; Tunable system; Nonlinear dispersion; Periodic structure
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2012.04.015

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. ► Article studies wave propagation and dispersion in nonlinear periodic. ► FEA software utilized in finding amplitude-dependent dispersion relationships. ► A perturbation approach for discrete systems extended to continuous systems. ► Two systems studied: the multilayer rod and a periodically supported membrane. ► Band gaps found to be amplitude dependent and sensitive to system parameters.