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

Chains of nonlinear shear indeformable beams with distributed mass, resting on movable supports, are considered. To determine the dynamic. c response of the system, the transfer-matrix 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 x(k+1) = F(x(k)) expressed in. terms of the state variables x(k) 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.