Revisited the Critical Load Assessment of Huang et al. on Willems Tested Beck Column

Dynamic stability of elastic structures is a fascinating topic. Many researchers have examined the problem theoretically considering a cantilever column under a tip-concentrated tangential load, the so-called Beck column. Experimental verification is demanded since the critical load of Beck column is found to be approximately eight times to that of the classical Euler column. Different types of testing procedures are being adopted to create the follower force. Among them, notable Willems experimentation provides the critical load close to that of Beck column. Investigations made by other researchers indicate the controversy associated with modeling and testing of Willems on Beck column. Such an intriguing problem of structures loaded by non-conservative forces is revisited here through a simple mathematical formulation. This paper confirms the adequacy of Willems approach on Beck column and the wrong critical load assessment of others. It indicates the possibility on the practical realization of follower forces

Dynamic Stability and Response of Inclined Beams Under Moving Mass and Follower Force

This paper is concerned with the dynamic stability and response of an inclined Euler–Bernoulli beam under a moving mass and a moving follower force. The extended Hamilton’s principle is used to derive the governing equation of motion and the boundary conditions for this general moving load/force problem. Considering a simply supported beam, one can solve the problem analytically by approximating the spatial part of the deflection with a Fourier sine series. Based on the formulation and method of solution, sample dynamic responses are determined for a beam that is inclined at 30[Formula: see text] with respect to the horizontal. It is shown that the dynamic response of the beam under a moving mass is rather different from an equivalent moving follower force. Also investigated herein are the dynamic stability of inclined beams under moving load/follower force which are described by four key variables, viz. the speed of the moving mass/follower force, concentrated mass to the beam distributed mass, vibration frequency and the magnitude of the moving mass/follower force. The critical axial load and the critical follower force are different when they are located at different positions in the beam; except for the special case when they are at the end of the beam.