Effects of Boundary Conditions on the Parametric Resonance of Cylindrical Shells under Axial Loading

T.Y Ng,K.Y Lam

doi:10.1155/1998/898321

Abstract

In this paper, a formulation for the dynamic stability analysis of circular cylindrical shells under axial compression with various boundary conditions is presented. The present study uses Love’s first approximation theory for thin shells and the characteristic beam functions as approximate axial modal functions. Applying the Ritz procedure to the Lagrangian energy expression yields a system of Mathieu–Hill equations the stability of which is analyzed using Bolotin’s method. The present study examines the effects of different boundary conditions on the parametric response of homogeneous isotropic cylindrical shells for various transverse modes and length parameters.

Highlights

The dynamic stability of cylindrical shells has received much attention over the years
A literature search showed that a study on the effects of boundary conditions on the dynamic stability of circular cylindrical shells, with the inclusion of free edge conditions into the comparisons, is not available
The F-F case exhibited the highest point of origin and largest unstable region size for any particular mode while the SS-SS case always had the lowest point of origin

Summary

Introduction

The dynamic stability of cylindrical shells has received much attention over the years. Yao [16] was the first to investigate dynamic stability in cylindrical shells and the loading used in this work considered both radial and axial directions. The boundary conditions considered were for a shell clamped at both ends. Bert and Birman [4], in the parametric instability study of thick orthotropic cylindrical shells considered simplysupported end conditions. A literature search showed that a study on the effects of boundary conditions on the dynamic stability of circular cylindrical shells, with the inclusion of free edge conditions into the comparisons, is not available. To the authors’ knowledge, no results are available for the dynamic stability of shells with free end conditions. A comprehensive study as such would be interesting as it would shed light on the effects of boundary conditions on the instability regions

Theory and formulation

Stability analysis

Axial modal functions and boundary conditions

Conclusion