An Analytical Solution to Vibration Analysis of cylindrical Shells

Abstract

simplified beam models can anticipate the dynamic behavior of a cylindrical shell in a variety of applications. The goal of this work is to identify the design parameters that allow a cylindrical shell to function like a beam. The governing equations for long cylinders with simply-supported boundary conditions at both ends are produced using the Hamilton's principle, along with the analytical solution for both the Flugge and Donnell-Mushtari shell theories. Next, the shell-to-beam transition conditions for both theories are determined by equalizing the vibration frequencies of the shell and the beam. The finite element approach is used to determine the ideal transition conditions with the fewest approximations possible, taking into consideration the effects of shear distortion and the shell's rotatory inertia. Lastly, the frequency response and the transition parameters are examined in relation to boundary conditions. The requirements that were established just state whether or not the shell may be taken to be a beam under particular geometrical and material circumstances.