000013081 001__ 13081
000013081 005__ 20161114160326.0
000013081 04107 $$aeng
000013081 046__ $$k2009-06-22
000013081 100__ $$aBrasil R., M.
000013081 24500 $$aNonlinear dynamic behavior of a portal frame under support excitation

000013081 24630 $$n2.$$pComputational Methods in Structural Dynamics and Earhquake Engineering
000013081 260__ $$bNational Technical University of Athens, 2009
000013081 506__ $$arestricted
000013081 520__ $$2eng$$aWe present a study of the nonlinear dynamic behavior of a simple portal frame excited by ground motion. Two vertical columns clamped in their bases supporting a horizontal beam pinned in both ends compose the structure. Nonlinearity is introduced by considering the elements shortening due to bending. A two-degrees-of-freedom mathematical model is derived via Lagrange’s formulation leading to a set of two second order differential equations with quadratic nonlinearities. The geometry and mass distribution is chosen in such a way as to render a 1:2 relationship between the frequency of the first mode (sway mode), related with the lateral motion of the vertical columns, and the frequency of the second mode (symmetrical mode), related to the vertical motions of the horizontal beam axis. This ratio may cause internal resonance between those modes with possible energy transfer. Further, we impose harmonic support motions in the vertical and horizontal directions in near resonance with the modes. Several interesting nonlinear phenomena are observed. In one case, when the support excitation frequency is near the second frequency of the structure, as its amplitude is increased the vertical motion of the horizontal beam axis will increase accordingly up to a point when it stops growing, that is, saturates. At this point, the energy pumped into the system via the second mode is transferred to the first mode, not directly excited, causing large amplitude sway motions, potentially dangerous. These are the saturation and energy transference phenomena. In another case, when the support excitation frequency is near the first frequency of the structure, as its amplitude is increased again energy transfer between modes occurs in an intermittent fashion.

000013081 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000013081 653__ $$aNonlinear dynamics, Structural Dynamics, Earthquake Engineering,. Abstract. We present a study of the nonlinear dynamic behavior of a simple portal frame excited by ground motion. Two vertical columns clamped in their bases supporting a horizontal beam pinned in both ends compose the structure. Nonlinearity is introduced by considering the elements shortening due to bending. A two-degrees-of-freedom mathematical model is derived via Lagrange’s formulation leading to a set of two second order differential equations with quadratic nonlinearities. The geometry and mass distribution is chosen in such a way as to render a 1:2 relationship between the frequency of the first mode (sway mode), related with the lateral motion of the vertical columns, and the frequency of the second mode (symmetrical mode), related to the vertical motions of the horizontal beam axis. This ratio may cause internal resonance between those modes with possible energy transfer. Further, we impose harmonic support motions in the vertical and horizontal directions in near resonance with the modes. Several interesting nonlinear phenomena are observed. In one case, when the support excitation frequency is near the second frequency of the structure, as its amplitude is increased the vertical motion of the horizontal beam axis will increase accordingly up to a point when it stops growing, that is, saturates. At this point, the energy pumped into the system via the second mode is transferred to the first mode, not directly excited, causing large amplitude sway motions, potentially dangerous. These are the saturation and energy transference phenomena. In another case, when the support excitation frequency is near the first frequency of the structure, as its amplitude is increased again energy transfer between modes occurs in an intermittent fashion.

000013081 7112_ $$aCOMPDYN 2009 - 2nd International Thematic Conference$$cIsland of Rhodes (GR)$$d2009-06-22 / 2009-06-24$$gCOMPDYN2009
000013081 720__ $$aBrasil R., M.$$iOrbolato L., M.
000013081 8560_ $$ffischerc@itam.cas.cz
000013081 8564_ $$s71560$$uhttps://invenio.itam.cas.cz/record/13081/files/CD107.pdf$$yOriginal version of the author's contribution as presented on CD, section: Nonlinear dynamics (MS).
000013081 962__ $$r13074
000013081 980__ $$aPAPER