Vibration Equations of an Orthotropic Shell, Wrapped Around a Drum, ConsideringResidual Stress Effects

In this paper, the governing vibration equations of anorthotropic, thin rectangular plate wrapped around a porousdrum are developed considering residual stress effects. It isassumed that the plate is under tension from two sides andwrapped continuously around a cylindrical drum so that thewrapped portion behaves like a circular cylindrical shell.At first, the Lame' parameters are obtained for a cylindricalshallow shell in cylindrical coordinate system. Then, equationsof motion are derived by utilizing the virtual work principlebased on the Love assumptions.Finally, a more complete set of vibration equations is obtainedby applying the simplifications of the Donnell-Mushtari-Vlasov theory. The weak form of equations is extracted and theprocedure to derive frequency equation is developed. Theresulting equations are compared with the previously availableones that are derived under more stringent assumptions and thedifferences are expounded.

کلیدواژه ها:

Vibrations ، Shells ، Orthotropic ، Residual stress