000013279 001__ 13279
000013279 005__ 20161114160334.0
000013279 04107 $$aeng
000013279 046__ $$k2009-06-22
000013279 100__ $$aNaprstek, J.
000013279 24500 $$aDynamic stability loss and post-critical behaviour of an auto-parametric non-linear system with three degrees of freedom

000013279 24630 $$n2.$$pComputational Methods in Structural Dynamics and Earhquake Engineering
000013279 260__ $$bNational Technical University of Athens, 2009
000013279 506__ $$arestricted
000013279 520__ $$2eng$$aSlender 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.

000013279 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000013279 653__ $$adynamic stability, auto-parametric response, non-linear dynamics, semi-trivial solution, post-critical response. Abstract. 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.

000013279 7112_ $$aCOMPDYN 2009 - 2nd International Thematic Conference$$cIsland of Rhodes (GR)$$d2009-06-22 / 2009-06-24$$gCOMPDYN2009
000013279 720__ $$aNaprstek, J.$$iFischer, C.
000013279 8560_ $$ffischerc@itam.cas.cz
000013279 8564_ $$s4645054$$uhttps://invenio.itam.cas.cz/record/13279/files/CD419.pdf$$yOriginal version of the author's contribution as presented on CD, section: Nonlinear dynamics.
000013279 962__ $$r13074
000013279 980__ $$aPAPER