Axially Moving Beam

In this paper, the Incremental Harmonic Balance (IHB) method is formulated for the nonlinear vibration analysis of axially moving beams. The Galerkin method is used to discretize the governing equations. A high dimensional model that can take nonlinear model coupling into account is derived. The forced response of an axially moving strip with internal resonance between the first two transverse modes is studied. Particular attention is paid to the fundamental, superharmonic and subharmonic resonance as the excitation frequency is close to the first, second or one-third of the first natural frequency of the system. Numerical results reveal the rich and interesting nonlinear phenomena that have not been presented in the existent literature on the nonlinear vibration of axially moving media.

A simplified model of the belt motion with small strains is proposed. The main purpose of the modeling is to show the effects arising when the line of action of friction forces is shifted to the belt’s middle axis. The prestressed shearable model of the belt is used in this study. The differential equations of the steady state motion are integrated and combined together with the boundary conditions into two nonlinear systems of algebraic equations corresponding to the different cases of the belt behavior: presence and absence of a sliding segment. The nonlinearity results from the fact that the boundaries of the contact segments are a priori unknown. The case without sliding requires introduction of a concentrated force at the point where the belt leaves the pulley. Considerable effects of the assumptions of contact characterization on the simulation results are demonstrated.