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In this paper, vibration equations of an orthotropic, thin rectangular plate wrapped around a porous drum are developed, considering residual stress effects. It is assumed that the plate is subjected to tension from both opposite sides and wrapped continuously around a cylindrical drum so that the wrapped portion behaves like a circular cylindrical shell. First of all, the Lame’ parameters, required to constitute the geometry relations, are established for typical cylindrical shallow shell in cylindrical coordinate system. Then, the equations of motion are derived by utilizing the stored strain energy principle based on the Love assumptions. Finally, a set of more complete vibration equations is introduced by applying the simplifications of the Donnell-Mushtari-Vlasov theory. The equations derived under more stringent and precise assumptions are compared with those obtained and available in literature, and the discripancies are highlighted. The present study only aims to mathematically develop the governing relationships, where a numerical solution separately done by the authors can be found in other literature in which vibrational behavior has been completely discussed for moving and stable anisotropic wrapped plates.

Developing Vibration Equations of an Orthotropic Wrapped Shell, Considering Residual Stress Effects; A Mathematical Approach