Free Vibration Analysis of Closed Cans Using a Collocation-Interpolation Method

A free vibration analysis of a closed can based on the first order shear deformation theory is developed. A closed can is a cylindrical shell capped by circular plates at both ends. The circular plates are modeled by flattening conical shells by setting the semi-apex angle to be the right angle. The Chebyshev polynomials of the first kind are employed as the admissible functions for the displacements and rotations, and the equations of motion are collocation-interpolated to yield the system of algebraic equations. Flattened conical and a cylindrical shell segments are modeled separately, and the numbers of expansions of each shell segment are larger than those of intended degrees of freedom such that the surplus expansions accommodate the compatibility conditions. Numerical examples are provided to demonstrate the robustness of the present method.