RELATIONSHIP BETWEEN THE EQUILIBRIUM AND MOTION EQUATIONS FOR A THIN ELASTIC BEAM

Abstract

The nonlinear equilibrium equations for a thin elastic rod with ends fixed by external forces can be solved exactly. Due to the large displacements, a nonlinear effect sets in. The localized solutions are cnoidal and solitonic waves. The rod deviates from a plane when the torsion exists. In this paper, the conditions for which the motion equations are equivalent to the equilibrium equations, are determined.  If these conditions are fulfilled the exact solutions of the motion equations of the thin elastic beam can be determined from the exact solutions of the equilibrium equations.