Goriachko T. Amplitude-frequency characteristics of layered plates and corrugated cylindrical shells.

This work is devoted to the development of the perturbation method in conjunction with the finite element method to determine the amplitude-frequency characteristics of layered plates and corrugated cylindrical shells for linear and geometrically nonlinear deformations. Using the quadratic approximations for the normal axis to the mid-surface and the general elasticity theory, a refined higher-order shell theory is presented, which takes into account the shear deformation and axial compression. A new methodology is developed for finding the eigenfrequencies of geometrically nonlinear vibrations of elongated cylindrical panels and corrugated shells. The linear and geometrically nonlinear vibrations are investigated for a three-layered plate and corrugated cylindrical shell. The influence of its structure and geometrical characteristics on the eigenfrequencies is analyzed.