The nonlinear behavior and stability under static and dynamic loads of an inverted spatial pendulum with rotational springs in two perpendicular planes, called Augusti’s model, is analyzed in this paper. This 2DOF lumped-parameter system is an archetypal model of modal interaction in stability theory representing a large class of structural problems. When the system displays coincident buckling loads, several post-buckling paths emerge from the bifurcation point (critical load) along the fundamental path. This leads to a complex potential energy surface. Herein, we aim to investigate the influence of nonlinear modal interactions on the dynamic behavior of Augusti’s model. Coupled/uncoupled dynamic responses, bifurcations, escape from the pre-buckling potential well, stability, and space-time-varying displacements; attractor-manifold-basin phase portraits are numerically evaluated with the aim of enlightening the system complex response. The investigation of basins evolution due to variation of system parameters leads to the determination of erosion profiles and integrity measures which enlighten the loss of safety of the structure due to penetration of eroding fractal tongues into the safe basin.
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e-mail: dorlando@tecgraf.puc-rio.br
e-mail: paulo@puc-rio.br
e-mail: giuseppe.rega@uniroma1.it
e-mail: lenci@univpm.it
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October 2011
Research Papers
Influence of Modal Coupling on the Nonlinear Dynamics of Augusti’s Model
Diego Orlando,
Diego Orlando
TecGraf -Computer Graphics Technology Group,
e-mail: dorlando@tecgraf.puc-rio.br
Pontifical Catholic University of Rio de Janeiro
, PUC-Rio Rio de Janeiro, RJ 22451-900, Brazil
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Paulo B. Gonçalves,
Paulo B. Gonçalves
Department of Civil Engineering,
e-mail: paulo@puc-rio.br
Pontifical Catholic University of Rio de Janeiro
, PUC-Rio Rio de Janeiro, RJ 22451-900, Brazil
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Giuseppe Rega,
Giuseppe Rega
Dipartimento di Ingegneria Strutturale e Geotecnica,
e-mail: giuseppe.rega@uniroma1.it
Sapienza Università di Roma
, Rome 00197, Italy
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Stefano Lenci
Stefano Lenci
Dipartimento di Architettura, Costruzioni e Strutture,
e-mail: lenci@univpm.it
Università Politecnica delle Marche
, Ancona 60131, Italy
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Diego Orlando
TecGraf -Computer Graphics Technology Group,
Pontifical Catholic University of Rio de Janeiro
, PUC-Rio Rio de Janeiro, RJ 22451-900, Brazile-mail: dorlando@tecgraf.puc-rio.br
Paulo B. Gonçalves
Department of Civil Engineering,
Pontifical Catholic University of Rio de Janeiro
, PUC-Rio Rio de Janeiro, RJ 22451-900, Brazile-mail: paulo@puc-rio.br
Giuseppe Rega
Dipartimento di Ingegneria Strutturale e Geotecnica,
Sapienza Università di Roma
, Rome 00197, Italye-mail: giuseppe.rega@uniroma1.it
Stefano Lenci
Dipartimento di Architettura, Costruzioni e Strutture,
Università Politecnica delle Marche
, Ancona 60131, Italye-mail: lenci@univpm.it
J. Comput. Nonlinear Dynam. Oct 2011, 6(4): 041014 (11 pages)
Published Online: June 14, 2011
Article history
Received:
June 7, 2010
Revised:
March 18, 2011
Online:
June 14, 2011
Published:
June 14, 2011
Citation
Orlando, D., Gonçalves, P. B., Rega, G., and Lenci, S. (June 14, 2011). "Influence of Modal Coupling on the Nonlinear Dynamics of Augusti’s Model." ASME. J. Comput. Nonlinear Dynam. October 2011; 6(4): 041014. https://doi.org/10.1115/1.4003880
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