Nonlinear Response of an Inextensible, Free–Free Beam Subjected to a Nonconservative Follower Force

Abstract

A free–free beam with a compressive follower force applied to one end exhibits interesting flutter and limit cycle oscillation (LCO) responses. Here, the derivation from Lagrange's equations is given for the nonlinear inextensible beam with such a force applied. The inextensibility constraint is met with a Lagrange multiplier added to the Lagrangian, and the beam allowed three rigid body modes in planar motion in addition to its elastic deformation. The Rayleigh–Ritz modal expansion method and the Runge–Kutta method are used to calculate time histories of the forced beam response. This new model is validated against classical results for the stability boundary and new LCO bifurcation diagrams are computed.