Vibration and stability of laminated composite doubly curved shells by a higher order shear deformation theory

Abstract

The present study deals with a higher order shear deformation theory of laminated shells as suggested by Reddy and Liu. The theory is based on a displacement field in which the displacements of the middle surface are expanded as cubic functions of the thickness coordinate, and the transverse displacement is assumed to be constant through the thickness. This displacement field leads to the parabolic distribution of the transverse shear stresses (and zero transverse normal strain) and therefore no shear correction factors are used. The theory is also based on the assumption that the thickness to radius ratio of shell is small compared to unity and hence negligible.
The governing equations are derived in orthogonal curvilinear coordinates. These equations are then reduced to those of doubly curved shell. All the quantities are suitably non-dimensionalised. The Navier solution has been used which gives rise to a generalized eigenvalue problem in matrix formulation. The natural frequencies for vibration and buckling loads of laminated orthotropic doubly curved shells and panels with simply supported ends are obtained.
The eigenvalues, and hence the frequency parameters are calculated by using a standard computer program. To check the derivation and computer program, the frequencies in HZ for different layer are compares with earlier results.
The lowest value of frequency parameter and buckling load are computed for the laminated composite doubly curved shell. The effects of various parameters such as number of layers, aspect ratio, modular ratio, etc on the above are studied.
Frequency also increases as number of layers of the shell increases for symmetric cross-ply layout. But when there is unsymmetrical cross-ply layout, then frequency decreases. With the increasing of modular ratio, non-dimensional frequency is also increasing.