Periodic excitation of a buckled beam using a higher order semianalytic approach

This paper considers the steady-state behavior of a transversally excited, buckled pinned–pinned beam, which is free to move axially on one side. This research focuses on higher order single-mode as well as multimode Galerkin discretizations of the beam’s partial differential equation. The convergence of the static load-paths and eigenfrequencies (of the linearized system) of the various higher-order Taylor approximations is investigated. In the steady-state analyses of the semianalytic models, amplitude–frequency plots are presented based on 7th order approximations for the strains. These plots are obtained by solving two-point boundary value problems and by applying a path-following technique. Local stability and bifurcation analysis is carried out using Floquet theory. Dynamically interesting areas (bifurcation points, routes to chaos, snapthrough regions) are analyzed using phase space plots and Poincaré plots. In addition, parameter variation studies are carried out. The accuracy of some semianalytic results is verified by Finite Element analyses. It is shown that the described semianalytic higher order approach is very useful for fast and accurate evaluation of the nonlinear dynamics of the buckled beam system.

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