Finite-element algorithms for calculation of natural vibrations of three-dimensional shells

The natural oscillations of thin-walled structures are studied using two variants of the finite-element method. In the first variant, the shell is represented as a set of planar elements, which are under the action of both membrane and bending forces. The second variant is based on the equations of the theory of elasticity. Domain discretization is carried out using the 8-node finite element and incompatible displacement modes. In the numerical experiments, cylindrical, elliptical and open shells are considered. The influence of different boundary conditions and geometrical parameters on natural vibration frequencies is taken into account. The advantages and disadvantages of each approach are discussed.