The vibrations of non-circular cylindrical shells with initial stresses

Abstract

The differential equations which govern the vibrations with initial stresses of thin non-circular cylinders of arbitrary curvature are obtained by a variational approach. The initial stresses which are considered are stresses produced by axial loads, torsion, and normal pressure. The solution procedure is presented and numerical results are presented for the free vibrations of freely supported oval cylinders without initial stress. Frequency factors of oval cylinders are compared with those of circular cylinders as the length, thickness, and non-circularity are varied. The equivalence of the solutions for the free vibrations with and without initial axial stress is also established.