Nonlinear time domain and stability analysis of beams under partially distributed follower force

Abstract

• A geometrically exact beam formulation is used to obtain the stability and nonlinear time domain analysis. • A wide range of beams with different flexibility ratios are utilized in this investigation. • The behavior of the eigenvalues at pre- and post-instability as well as the frequency and time domain results are obtained. • The stability and nonlinear behavior are highly affected by partially follower forces length and position. This paper aims to investigate linear and nonlinear behavior of beams subjected to externally applied partially distributed follower forces. In this investigation, the nonlinear composite beam theory of Hodges is used. The system of nonlinear equations is linearized about the equilibrium, or rest structure state, and the linear system is solved numerically. The effects of follower force position on the behavior of eigenvalues at pre- and post-instability are reported. Additionally, the contours of critical follower force are obtained by changing the position of follower force in span-wise and chord-wise directions. The effects of different parameters such as the length, and position of follower force and the ratios of stiffnesses on the critical follower force as well as the nonlinear limit cycle oscillation (LCO) are reported. The obtained results indicate that the length and the position of the partially distributed follower forces considerably affect the stability of the beam.