Gro� Nachbeulantworten nichtkonservativer kontinuierlicher Systeme

Abstract

The large postbuckling response of a uniform cantilever beam subjected to a partial follower compressive load of constant magnitude is presented. The range of values of the nonconservativeness loading parameter for which a divergence instability occurs is theoretically established. The boundary between divergence and flutter instability corresponds to a double critical point where the first and second buckling loads (eigenvalues) coincide. It was also theoretically established that the critical points corresponding to these loads are stable symmetric. Except of the double critical point, the buckling loads of the first and second eigenmodes are distinct for the entire region of the nonconservativeness loading parameter. However, this is not true for the corresponding postbuckling paths. Indeed using an elastica analysis suitable for rotations up to 360°, it was found that at a certain critical tip rotation depending on the value of the nonconservativeness parameter the first and second postbuckling modes meet each other asymptotically. Numerical results have been obtained using various approximate analytic techniques which are checked by the method of elliptic integrals as well as the numerical schemes of Adams and Runge-Kutta.