Dynamic stability loss and post-critical behaviour of an auto-parametric non-linear system with three degrees of freedom

Abstract eng:
Slender structures exposed to a strong vertical component of an earthquake excitation are endangered by auto-parametric resonance effect. This non-linear dynamic process in a post-critical regime caused heavy damages or collapses of many towers, bridges and other structures due to earthquake attack in the epicenter area. If an amplitude of a vertical harmonic excitation in a structure foundation exceeds a certain limit, vertical response on the structure top looses its stability and a dominant horizontal response component arises. In subcritical linear regime only semi-trivial solution being represented by the vertical response component is observed, while horizontal components remain trivial. Therefore, vertical and horizontal response components are independent. In post-critical regime (auto-parametric resonance) the dynamic non-linear interaction of vertical and horizontal response components occurs. This process results in dominant horizontal response components leading to a failure of the structure. The broadband random nonstationary excitation of the seismic type can be particularly dangerous in this connection. Qualitatively different post-critical response types have been detected when sweeping throughout the frequency interval beyond the stability limit. Deterministic as well as chaotic response types have been observed. In general they can occur in a steady state, quasi-periodic and completely in-determined regimes including a possible energy transflux among degrees of freedom. Post-critical limit cycles are discussed. The processes of transition from semi-trivial to post-critical state have been investigated in case of time limited excitation period.

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