LAUSR

In this examination, the free vibrations of complete composite shells with rectangular openings based on first-order shear deformation theory have been studied. The equations are generally written in such a way that they can be converted to any of Donnell, Love, or Sanders theories. To study the shell with the opening of the problem-solving space, it is elementalized in such a way that the boundary conditions and loading are uniform at the edges of each element. For each element, the governing equations, the boundary conditions of the edges, and the compatibility conditions at the common boundary of the adjacent elements are discretized by the generalized differential quadrature method in the longitudinal and peripheral directions, and by assembling them, a system of algebraic equations is formed. Finally, the natural frequency of the structure is calculated using the solution of the eigenvalue. To validate this method, the results are compared with the results of some articles as well as the results of Abaqus finite element software. After ensuring the efficiency of the present method, it has been used to study the effect of different parameters on the vibrational behavior of shells with and without apertures. These studies show that relatively small openings (c/L <0.3) have little effect on the natural frequency of the shell, regardless of the material and the porcelain layer of the shell. While reducing the ratio of length to radius or increasing the thickness of the shell is also effective in reducing the effects of opening. In addition, the effect of peripheral openings is far less than longitudinal openings.