Exact supercritical vibration of traveling orthotropic plates using dynamic stiffness method

Axially traveling plates are used in modeling the transverse vibration of a variety of physical systems, e.g. band saw blades, power transmission belts, steel plates in galvanizing line, paper handling and textile manufacturing. In this paper the Dynamic Stiffness Method (DSM) is employed to analyze the free vibration of traveling orthotropic plates in supercritical speeds. Critical speeds are defined as those axial speeds where the system vibration has a vanishing eigenvalue and is subject to a buckling instability. Transport speeds above the lowest critical speed are termed supercritical. Based on classical plate theory, a dynamic stiffness matrix is formed by frequency dependent shape functions which are exact solutions of the governing differential equations. It eliminates spatial discretization error and is capable of predicting several natural modes by means of a small number of degrees of freedom. This stiffness matrix is a complex matrix and contains axial speed, in-plane forces and free vibration eigenvalues which are generally complex. To extract these complex eigenvalues, an algorithm is required to search in the wodimensional plane of complex numbers. In the current study, use is made of such an algorithm. With a few test cases, the reliability of the formulation and the solution procedure is shown.

Keywords:

Dynamic Stiffness Method , Axially moving , Orthotropic plate , Supercritical speed