Exact solutions for the free vibrations of open cylindrical shells with circumferentially varying curvature and thickness

An exact solution procedure is developed for determining the free vibration frequencies and mode shapes of open non-circular cylindrical shells having circumferentially varying thickness and the two opposite, curved edges supported by shear diaphragms. The remaining two edges, which are straight line segments parallel to the shell generators, may have arbitrary boundary conditions. The method is demonstrated for shells having elliptical cylindrical curvature and a thickness which varies quadratically in the circumferential direction, and straight edges which are clamped. For this symmetric configuration, vibration modes separate into symmetric and antisymmetric classes, and the exact frequencies are the roots of fourth order determinants. Numerical results are given showing the variations of frequencies and mode shapes of both symmetry classes with the shell length.