Some observations on the dynamic equations of prismatic members in compression (Q1072764)

The dynamic equations governing the longitudinal, and the coupled transverse and torsional deformations of uniformly compressed elastic prismatic members are discussed. It is shown that if they are properly formulated, the modes of buckling of members with their ends simply supported and, where appropriate, free to warp are precisely the same as the modes of vibration, and that for each mode there is a very simple relation between the critical compressive stress and the natural frequency. The dynamic equations for Vlasov beams and Timoshenko beams are presented in detail.