On thickness shear deformation theories for the dynamic analysis of non-circular cylindrical shells

Abstract

This paper is concerned with the problem of free vibrations of homogeneous isotropic non-circular cylindrical shells, including the effects of thickness shear deformation and rotatory inertia. For this problem the equations of motion of two first approximation shell theories are derived. Both theories are transverse shear deformable analogues of the classical Love-type theory. The first theory involves thickness shear correction factors while the second one assumes a parabolic variation for thickness shear strains and stresses, with zero values at the inner and outer shell surfaces. The equations of both theories are solved, for the case of a simply supported non-circular cylindrical shell and, as an application, the free vibration problem of a simply supported oval cylindrical shell is considered. From comparisons made between corresponding numerical results based on both theories, as well as the classical Love-type theory, a superiority of the theory assuming parabolic variation of thickness shear is concluded.