Dynamic stability of a vertically excited non-linear continuous system

Easily deformable tall structures exposed to a strong vertical component of an excitation are endangered by auto-parametric resonance effect. This non-linear dynamic process in a post-critical regime might contribute to various damages caused by a kinematic excitation. Vertical and horizontal response components are independent on the linear level. However their interaction takes place due to non-linear terms in post-critical regime. Two generally different types of the post-critical regimes are presented: (i) post-critical state with possible recovery and (ii) exponentially rising horizontal response leading to a collapse. A special attention is paid to processes of transition from semi-trivial to post-critical state in case of time limited excitation period as it concerns the seismic processes. Solution method combining analytical and numerical approaches is developed and used. Its applicability and shortcomings are commented. A few hints for engineering applications are given.