Free Vibration of Laminated Composite Cross-Ply Spherical Panels

Abstract

The use of laminated composite curved panels is common in many engineering fields; the study of vibration problems arising in spherical shells/panels has become increasingly important. Free vibration frequencies and mode shapes are essential for the analysis of resonant response and flutter. Due to its significance in structural mechanics, many researchers have worked on the vibration characteristics of spherical shells/panels.
Composite structures have extensive use in aerospace, civil, marine and other engineering applications. Laminated composites are becoming key components in many of them. Their high performance places them at the top of the list of engineering materials needed for advanced design applications. This is because controlling the lamination angle and the stacking sequence can alter their structural properties leading to an optimal design. The higher specific modulus and specific strength of these composites means that the weight of certain components can be reduced. The increasingly wider application to other fields of engineering has necessitated the evolution of adequate analytical tools for the better understanding of the structural behavior and efficient utilization of the materials.
Composites have the specific advantage that their structural characteristics can be tailored to suit the design requirements. Hence they are finding increased use in primary and secondary structures in aerospace projects. The composites, like most structural materials, are fabricatedwith appropriate quality control. The control works under finite limits due to practical and economic considerations. This results in variation in material properties, making them random.
In this thesis work, an analytical solution of frequency characteristics for the free vibration of laminated composite thin spherical panels has been obtained by using the first order shear deformation theory as well as a higher order shear deformation theory. Compared with classical theory and higher order theory, the “first order shear deformation theory” combines higher accuracy and lower calculation efforts. The higher order shear deformation 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 parabolic distribution of the transverse shear stresses and zero transverse normal strain and hence no shear correction factors are used.
The objective of this study is to examine the effect of various shell parameters on the frequency characteristics of laminated composite cross-ply thin spherical panels. For reasons of simplicity, the simply supported boundary conditions are assumed for the panels. The formulation is general. Frequency envelopes for different lamination schemes for the panels have been plotted. The results obtained by both the shear deformation theories have also been compared. From the results, the influence of radius to length ratio on natural frequency of the spherical shell is larger than that of length to thickness ratio. Also there is not much difference in the results by the first and higher order shear deformation theory.