On nonlinear dynamics of planar shear indeformable beams

Angelo Luongo (1) , Giuseppe Rega (2) , Fabrizio Vestroni (2)

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

The planar forced oscillations of shear indeformabie beams with either movable or immovable supports are studied through a unified approach. An exact nonlinear beam model is referred to and a consistent procedure up to order three nonlinearities is followed. By eliminating the longitudinal displacement component through a constraint condition and assuming one mode, the problem is reduced to one nonlinear differential equation. A perturbational solution in the neighborhood of the resonant frequency is determined and the stability of the steady-state solutions is studied. The dependence of the phenomenon on the geometrical and mechanical characteristics of the system is put into light and the frequency-response curves for different boundary conditions are furnished.

Domaines: Autre

Angelo Luongo, Giuseppe Rega, Fabrizio Vestroni. On nonlinear dynamics of planar shear indeformable beams. Journal of Applied Mechanics, 1986, 53 (31-32), pp.619-624. ⟨hal-00789126⟩