Vibrations of composite laminated doubly-curved shells of revolution with elastic restraints including shear deformation, rotary inertia and initial curvature

In this paper, the modified Fourier series method is applied to study the vibration behavior of composite laminated doubly-curved shells of revolution with elastic restraints. The theoretical formulation is based on the first order shear deformation shell theory considering the effects of the rotary inertia and initial curvature. In summary, the shell energy functional, written in terms of stress resultants and mid-surface strains, is expressed as a function of five displacement components by using the constitutive and kinematic relationships. Each displacement of the shell is then expanded as a superposition of the standard cosine Fourier series and several auxiliary functions introduced to remove any potential discontinuous of the original displacement and its derivatives at the ends. The desired solutions are obtained by using the variational operation. The convergence and accuracy of the presented solutions are validated, with good agreement observed. A systematic parametric study is also performed regarding the effects of the boundary conditions, lamination schemes, material and geometrical parameters. Finally, a variety of new vibration results including frequencies and mode shapes for circular toroidal, elliptical, paraboloidal and hyperbolical shells with classical and elastic boundary conditions as well as different geometric and material parameters are also presented, which may serve as benchmark solutions for the future researches.