Dynamic stability of shear-flexible beck’s columns based on Engesser’s and Haringx’s buckling theories

Based on Engesser’s and Haringx’s buckling theories for shear-flexible columns, dynamic stability behaviors of damped Beck’s columns subjected to sub-tangential follower forces are intensively investigated using fifth-order Hermitian beam elements. For this purpose, dimensionless equations of motion for the non-conservative systems are firstly derived based on the buckling approaches of Engesser and Haringx. FE procedures using the shear-flexible Hermitian interpolation functions are next presented by obtaining the mass matrix, the internal and external damping matrices, the elastic and the geometric stiffness matrices, and the load correction stiffness matrices due to sub-tangential follower forces, respectively. Evaluation schemes for flutter and divergence loads of non-conservative systems are described and the static buckling loads and natural frequencies of the shear-flexible beam-columns are compared through numerical examples using the two buckling theories. Finally, the influences of sub-tangentiality, shear deformation and Rayleigh damping on the dynamic stability of the non-conservative system are investigated and compared based on two buckling approaches.