Vibratory characteristics of cantilevered rectangular shallow shells of variable thickness

In this paper, a comprehensive study on the modeling of vibratory of variable thickness cantilevered shallow cylindrical shells of rectangular planform is carried out. Through the principle of minimum total energy, the equations of stretching and bending strain energies, kinetic energy, and the associated boundary conditions of the shells are derived. The present model is developed based on the Ritz formulation with the assumption of sets of mathematically complete admissible two-dimensional polynomials to approximate the in-plane and transverse displacement amplitude functions.