Three Dimensional Nonlinear Global Dynamics of Axially Moving Viscoelastic Beams

Abstract

The threedimensional nonlinear global dynamics of an axially moving viscoelastic beam is investigated numerically, retaining longitudinal, transverse, and lateral displacements and inertia. The nonlinear continuous model governing the motion of the system is obtained by means of Hamilton's principle. The Galerkin scheme along with suitable eigenfunctions is employed for model reduction. Direct timeintegration is conducted upon the reducedorder model yielding the timevarying generalized coordinates. From the time histories of the generalized coordinates, the bifurcation diagrams of Poincarأ© sections are constructed by varying either the forcing amplitude or the axial speed as the bifurcation parameter. The results for the threedimensional viscoelastic model are compared to those of a threedimensional elastic model in order to better understand the effect of the internal energy dissipation mechanism on the dynamical behavior of the system. The results are also presented by means of time histories, phaseplane diagrams, and fast Fourier transforms (FFT).