Nonlinear dynamics of slender rods

Abstract

The nonlinear equations of motion of a rod undergoing small strains and moderate elastic rotations are derived. The derivation uses a variational approach and the equations of motion are obtained by applying Lagrange's equations. The results of a recently developed principal curvature transformation are employed to account for the structural aspects. Generalized coordinates are also used to establish an efficient analysis method. By a direct perturbation of the nonlinear equations of motion, the relations governing the small vibrations of a rod superimposed on finite static deformations are obtained. The theory is validated by comparing its results with experimental results available in the literature. Good agreement is obtained. In addition, the influences of nonlinear effects on such vibrations are pointed out and discussed.