Vibrations of compound shells of revolution with elliptical toroidal members

Vibrations of thin-walled systems compound of coaxial conjugate shells of revolution of different shapes with torus-elliptical members are analyzed. The shells can be composed of one or several layers, of isotropic and orthotropic materials with variable geometric and stiffness characteristics along a generatrix-meridian. Small undamped vibrations of such systems are studied using the classical Kirchhoff-Love theory. To solve the appropriate eigen-value two-dimensional problems, the numerical-analytical technique, which includes the Fourier variable-separation method, incremenal search method (Δ(λ) -method), and the orthogonal sweep method with solving Cauchy's problems by the fifth-order Runge-Kutta scheme, is developed. It is shown by a number of examples that vibrations of the shell system as a single whole have qualitative features in comparison with vibrations of its separate members.