A non-linear model for the dynamics of open cross-section thin-walled beams--Part II: forced motion

Angelo Di Egidio (1) , Angelo Luongo (1) , Fabrizio Vestroni (2)

1 DICEAA - Dipartimento di Ingegneria Civile, Edile-Architettura, Ambientale
2 DISG - Dipartimento di Ingegneria Strutturale e Geotecnica

The discrete equations developed in Part I are here used to analyze the non-linear dynamics of an inextensional shear indeformable beam with given end constraints. The model takes into account the non-linear effects of warping and of torsional elongation. Non-linear 3D oscillations of a beam with a cross-section having one symmetry axis is examined. Only terms of higher magnitude are retained in the equations, which exhibit quadratic, cubic and combination resonances. A harmonic load acting in the direction of the symmetry axis and in resonance with the corresponding natural frequency, is considered. Steady-state solutions and their stability are studied; in particular the effects of non-linear warping and of torsional elongation on the response are highlighted.

Domaines: Autre

Angelo Di Egidio, Angelo Luongo, Fabrizio Vestroni. A non-linear model for the dynamics of open cross-section thin-walled beams--Part II: forced motion. International Journal of Non-Linear Mechanics, 2003, 38 (7), pp.1083-1094. ⟨hal-00797963⟩