Exact free vibration analysis of axially moving viscoelastic plates

In this paper, an exact finite strip method is developed for the free vibration analysis of axially moving viscoelastic plates. Using the differential equation that governs the vibration of plates traveling at a constant axial speed, and utilizing the rheological models to model the viscoelastic behavior of materials, the exact stiffness matrix of a finite strip of plate is extracted in the frequency domain. Terms of this matrix are implicit functions of the eigenvalues of free vibration, in-plane forces, viscoelasticity parameters, axial speed and the geometry of the plate. By assembling the stiffness matrices of these finite strips, the global stiffness matrix of a plate moving on intermediate rollers is obtained, from which the eigenvalues defining the free vibration of the plate are extracted within the domain of complex numbers using a suitable algorithm. These values (that represent the exact frequencies of the plate vibration and damping) can be used as a benchmark to evaluate the accuracy of other numerical techniques. Finally, by presenting a set of numerical examples, the effects of axial speed and viscoelastic parameters on the free vibration of moving plates are examined in this paper.