On the dynamic stability of a pre-twisted beam subject to a pulsating axial load

Abstract

This paper is concerned with the investigation of the stability behaviour of a pre-twisted beam, subject to a pulsating axial force. The system, consisting of two coupled partial differential equations with time varying coefficients, which govern the small lateral displacements of the beam, is reduced to a Hill system, by using the Galerkin procedure. The stability of the solutions of this system is investigated by the method of Mettler. Then the equations of the boundaries of the instability regions are given in a parameter-plane. Finally, the results obtained are applied for various types of boundary conditions.