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CivilComp Proceedings
ISSN 17593433 CCP: 99
PROCEEDINGS OF THE ELEVENTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping
Paper 179
Dynamic Stability of a Nonlinear Continuous System Subjected to Vertical Seismic Excitation J. Náprstek and C. Fischer
Institute of Theoretical and Applied Mechanics ASCR, v.v.i., Prague, Czech Republic , "Dynamic Stability of a Nonlinear Continuous System Subjected to Vertical Seismic Excitation", in B.H.V. Topping, (Editor), "Proceedings of the Eleventh International Conference on Computational Structures Technology", CivilComp Press, Stirlingshire, UK, Paper 179, 2012. doi:10.4203/ccp.99.179
Keywords: autoparametric systems, semitrivial solution, dynamic stability, system recovery, postcritical response.
Summary
A strong vertical component of an earthquake excitation in the epicenter area very often represents the most dangerous condition leading to structure collapse resulting from autoparametric resonance. This highly nonlinear dynamic process caused in the past heavy damage or collapses of towers, bridges and other structures. In the subcritical linear regime vertical and horizontal response components are independent and therefore in such a case no horizontal response component is observed. If the amplitude of a vertical excitation in a structure foundation exceeds a certain limit, a vertical response component loses stability and dominant horizontal response component arises [1]. This postcritical regime or the autoparametric resonance [2], follows from the nonlinear interaction of the vertical and horizontal response components and can lead to a failure of the structure. The seismic type broadband random nonstationary excitation can be particularly dangerous and amplify these effects.
In principle easily deformable tall structures are the most sensitive regarding effects of autoparametric resonance (chimneys, towers, etc.). Therefore the structure itself is modelled as a console with continuously distributed mass and stiffness in order to respect the whole eigenvalue and eigenform spectrum. The subsoil model respects the vertical and rocking component of the response including internal viscosity of the Voight type. A Hamiltonian functional is provided for the Lagrangian differential system linking the strongly nonlinear double degrees of freedom part with multidegree of freedom part modelling continuous console to the governing system. The system shows that horizontal and vertical response components are independent in the semitrivial regime, which is linear in such a case. Their interaction takes place as a result of the nonlinear terms in the postcritical regime only. Two generally different types of the postcritical regimes are presented in the paper: (i) the close neighbourhood of the stable state (area between the semitrivial solution stability limit and the limit of irreversibility); despite the strongly nonlinear response, the structure can regain the stable state, when excitation drops below a certain limit; (ii) if the response is beyond the limit of irreversibility, the rocking response component looses any periodic character and rises exponentially leading inevitably to a failure of the structure without a possibility of any recovery. In principle the solution method combining analytical and numerical approaches is developed and used. Its applicability and shortcomings are commented upon. Some advice for engineering applications are given and some open problems are indicated. References
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