Dynamic stability and response of fluttered beams subjected to random follower forces

Abstract

This paper presents a study of non-linear response of a fluttered, cantilevered beam subjected to a random follower force at the free end. The random follower force is characterized as the sum of a post-critical static force and a stationary process with a zero mean. First, the Ritz–Galerkin method is applied to yield a set of discretized system equations. The system equations are then partially uncoupled by a special modal analysis based on normal modes of the corresponding linear, autonomous system at the onset of fluttering. Next, the stochastic averaging method is utilized to get Ito's differential equation governing the amplitude of the fluttered mode. Finally, the probability density function for the amplitude of the fluttered mode is obtained by solving the FPK equation. Numerical results show that the probability density function for the amplitude of the fluttered mode is determined by the sample behavior of the beam near the trivial equilibrium configuration.