Geometrically Exact, Fully Intrinsic Analysis of Pre-Twisted Beams Under Distributed Follower Forces

This paper studied the dynamic behavior of pre-twisted beams subjected to applied, distributed follower forces. The analysis was based on geometrically exact, fully intrinsic nonlinear composite beam theory, which is capable of analyzing the dynamic behavior of a general, nonuniform, initially curved and twisted, anisotropic beam undergoing large deformation. The equations of motion are independent of displacement and rotation variables, and singularities caused by finite rotation are avoided. The system of nonlinear equations was linearized about a trim solution state, and the linear system governing dynamic stability was solved numerically. The Hopf bifurcation point and behavior of the eigenvalues both pre- and post-instability were determined, and nonlinear limit-cycle oscillations were analyzed in the time domain. The results obtained show that the nonconservative instability problem of the beam is highly affected by pre-twist, as well as by the magnitude and orientation of the applied, distributed follower forces.