Wave propagation in periodic buckled beams. Part I: Analytical models and numerical simulations

• Periodic buckled beams are dispersive and nonlinear structures.
• Long-wave propagation is described by the Boussinesq and strongly-nonlinear models.
• The solitary wave behavior changes with the support types and buckling level.
• Compressive/tensile supersonic/supersonic solitary waves are predicted.
• Finite element simulations of the structure are used for validation purpose.

Periodic buckled beams possess a geometrically nonlinear, load–deformation relationship and intrinsic length scales such that stable, nonlinear waves are possible. Modeling buckled beams as a chain of masses and nonlinear springs which account for transverse and coupling effects, homogenization of the discretized system leads to the Boussinesq equation. Since the sign of the dispersive and nonlinear terms depends on the level of buckling and support type (guided or pinned), compressive supersonic, rarefaction supersonic, compressive subsonic and rarefaction subsonic solitary waves are predicted, and their existence is validated using finite element simulations of the structure. Large dynamic deformations, which cannot be approximated with a polynomial of degree two, lead to strongly nonlinear equations for which closed-form solutions are proposed.