Vibration and stability of non-conservative follower force systems

Abstract

The equation which Hamilton called the “Law of Varying Action”, is applied to obtain direct analytical solutions to stationary, conservative and non-conservative follower force systems with various loadings and various constraints. The magnitude of the load required to produce buckling at zero frequency and/or to produce flutter, i.e., instability at non-zero frequency, is calculated. Frequency response curves and mode configurations are presented. Results from the direct analytical solution are compared to results from exact solutions for the few exact solutions which could be found in the literature. Several examples involving applied follower couples, both discrete and continuous, to which no published solutions could be found, are also presented. The paper clearly demonstrates the simplicity, generality, and accuracy available from Hamilton's law.