Computational aspects of the ritz method for vibration of shallow shells

Abstract

The present research deals with the linear, elastic free vibration analysis of thin, moder-ately thick and thick shallow shells. A new derivation of energy functional and method of solution based on the principle of extremum energy are developed. The classical Kirchhoff-Love thin shell theory is employed to formulate the strain and kinetic en-ergy expressions for the thin shell studies while the refined first-order and higher-order theories are proposed for the moderately thick and thick shells investigations.