Computerized symbolic solution for a nonconservative system in which instability occurs by flutter in one range of a parameter and by divergence in another
The instability of a uniform column which is simply supported at one end, resting on a support at some intermediate location q, and has the other end subjected to a follower force is studied. The problem is solved by the Galerkin method in conjunction with computerized symbolic algebra. It is shown that there exists a location for the intermediate support at \(q=q^*\) so that the structure loses its stability by flutter for \(q<q^*\), and by divergence for \(q>q^*\). At \(q=q^*\) the critical load undergoes a jump, implying the transition of the instability mode from flutter to divergence. Moreover, the location \(q=q^*_+\) is an optimal location in the sense that the critical load assumes a maximum.
resting on a support at some intermediate location
transition of the instability mode from flutter to divergence
scientific article; zbMATH DE number 3982655
scientific article