Free vibrations of a viscoelastic noncircular cylindrical shell under homogeneous axial loading

Free low-frequency vibrations of a noncircular cylindrical shell subject to an axial static load are investigated. The case where the vibrations are localized near a certain generatrix, called the weakest, is considered. The complex WKB-method is used to determine the natural modes of vibrations that damp with time and drop down far from the weakest generatrix, An example on the vibration of a viscoelastic shell is considered with the relaxation rate function given and in the presence of a static axial force.