Parametric Torsional Stability of a Bar Under Axial Excitation

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Abstract
A study is made on the parametric torsional stability of an elastic cantilever of rectangular cross section under dynamic axial loading. The coupling between the longitudinal and torsional motions exists due to the “shortening effect.” The problem is so formulated that the stability of torsional vibrations is represented by a Mathieu equation, the stability of which is well known. The effect of longitudinal vibrations on the torsional stability is investigated. The steady-state torsional-vibrational response curves are given analytically, and the effect of longitudinal damping on the boundary of stability and the steady-state response curves is also determined.

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