Natural vibrations of shallow shells of complex shape under the presence of cuts (cracks) on their surface (Q2754728)

On the basis of the Ritz variational method, the problem of natural vibrations is reduced to minimization of some functional. The main problem, considered in detail in the paper, is construction of the appropriate system of coordinate functions. The case, when the shell is clamped at one portion of the boundary, is free at the remaining part and contains a cut at the free portion of boundary, is considered. A technique ensuring construction of functions allowing ``jumps'' at the sides of the cut, is developed on the basis of R-function method, and explicit expressions for coordinate functions are constructed. Examples of coordinate functions for (i) cylindrical shell; (ii) spherical shell and (iii) shell with principal curvatures, equal in magnitude and having opposite signs, are considered. A table displaying the influence of curvature and of the cut length on the frequency is presented.