Dynamic Stability of Thin‐Walled Structural Members under Periodic Axial Torque

Members of framed structures which are influenced by the dynamic torsional moment from other members connected to the end of the member and structural members like the rotor of a helicopter which experience a twisting moment due to flow are studied. The dynamic stability of those members with a thin‐walled cross section under periodic follower and unidirectional axial torques is investigated. The basic equation of motion of these members becomes a Hill equation, and the parametrically excited unstable vibration occurs in this system. Stability maps of simple parametric resonance are illustrated by using the Bolotin method, and the dynamic stability of various types of members may be estimated from numerical results. The analytical method presented can be applied to analysis members with various boundary conditions and various load conditions.