Stability of a Pin-Ended Bar in Torsion and Compression

Abstract

The stability of a uniform pin-ended bar having equal principal stiffnesses, subjected to combined torsion and compression, is studied via the direct method of Liapunov for cases in which the torque vector is circulatory; i.e., the torque vector does not bisect the angle between the undeformed and deformed axes of the bar. Liapunov functionals are presented and applied to both the case of a viscous environment and the case of a viscoelastic environment. Several simple stability and instability criteria are obtained in terms of the system parameters.