Divergence and Flutter Instability of Damped Laminated Beams Subjected to a Triangular Distribution of Nonconservative Forces

Abstract

The divergence and flutter instability behavior of the damped laminated beams subjected to a triangular distribution of subtangential forces are investigated based on the finite element model. The formal engineering approach of the mechanics for the laminated beam theory is presented and the extended Hamilton's principle is employed to obtain the mass, damping, elastic stiffness, geometric stiffness matrices, and the load correction stiffness matrix due to the nonconservative forces, respectively. The methods for the evaluation of the divergence and flutter loads of the nonconservative systems are briefly introduced in case of considering and neglecting external and internal damping effects. Throughout numerical examples, the influence of various parameters on the dynamic instability behavior of the laminated beams is newly investigated: 1) the variation of the divergence and flutter loads due to the nonconservativeness with respect to the fiber angle change, 2) the influence the boundary condition of beams on the instability region of the divergence-flutter system, 3) the influence of external and internal damping on the flutter load by analysis of complex natural frequencies.