A Transfer matrix-perturbation approach to the dynamics of chains of nonlinear sliding beams

Angelo Luongo (1) , Francesco Romeo (2)

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

Chains of nonlinear shear indeformable beams with distributed mass, resting on movable supports, are considered. To determine the dynamic response of the system, the transfermatrix approach is merged with the harmonic balance method and a perturbation method, thereby transforming the original space-temporal continuous problem into a discrete one-dimensional map Xk+1=F(Xk) expressed in terms of the state variables xk at the interface between adjacent beams. Such transformation does not imply any discretization, because it is obtained by integrating the single-element field equations. The state variables consist of both first-order variables, namely, transversal displacement and couples, and second-order variables, which are longitudinal displacement and axial forces. Therefore, while the linear problem is monocoupled, the nonlinear one becomes multicoupled. The procedure is applied to determine frequency-response relationship under free and forced vibrations.

Domaines: Autre

Angelo Luongo, Francesco Romeo. A Transfer matrix-perturbation approach to the dynamics of chains of nonlinear sliding beams. Journal of Vibration and Acoustics, 2006, 128 (2), pp.190-196. ⟨hal-00790182⟩