Natural oscillations of general shells based on nonclassical theory

Two-dimensional equations of the dynamics of the theory of general shells and appropriate boundary conditions that make it possible to take into account the transverse shear and compression of the shell are constructed based on three-dimensional equations of elasticity theory and the Lagrange variational principle by expanding the displacements in the coordinate normal to the middle surface. Natural oscillations of a circular cylindrical shell are considered. Frequencies of natural oscillations are determined by the Bubnov-Galerkin method. The impact of different types of boundary conditions and geometric parameters of the shell on the value of natural frequencies are analyzed. Simulation results are compared with different variants of the classical theory of shells, as well as with three-dimensional elasticity theory.