Dynamic Instability of Follower Forced Euler Bernoulli Cantilever Beam With Tip Mass

Abstract

This work focuses on the stability analysis of an Euler Bernoulli cantilever beam with a tip mass at the free end, subject to a follower force. This can serve as a viable model for analysis of elastic instability occurring due to fluid-structure interaction of structural components submerged in fluids and gases. A linear model with appropriate boundary conditions is developed using the energy formulation. The characteristic equation of the linear model establishes the relationship between the pulsation of the beam and the magnitude of applied follower force. The evolution of temporal eigenvalues with respect to the magnitude of the follower force helps in evaluation of the critical follower forces responsible for different modes of instability. The presented model demonstrates the existence of only dynamic instability in the system. Furthermore, the model predicts that both types of the dynamic instability i.e., flutter and divergence, are possible in the system.