Nonlinear Flexural-Flexural-Torsional Dynamics of Inextensional Beams. I. Equations of Motion

Abstract

This paper is divided into two parts. The authors’ purpose in Part I is to formulate a set of mathematically consistent governing differential equations of motion describing the nonplanar, nonlinear dynamics of an inextensional beam. The beam is assumed to undergo flexure about two principal axes and torsion. The equations are developed with the objective of retaining contributions due to nonlinear curvature as well as nonlinear inertia. A priori ordering assumptions are avoided as much as possible in the process. The equations are expanded to contain nonlinearities up to order three to facilitate comparison with analogous equations in the literature, and to render them amenable to the study of moderately large amplitude flexural-torsional oscillations by perturbation techniques. The utilization of the order-three equations in the analysis of nonlinear beam oscillations is the subject of Part II.