Affiliations: Department of Civil Engineering of Suleyman Demirel
University, Isparta, Turkey | Technical Sciences Department of Kasakh Branch of
Azerbaijan Teachers Institute, Kazakh, Azerbaijan
Note: [] Corresponding author: Assoc. Prof. Dr. Abdullah Sofiyev,
Department of Civil Engineering of Suleyman Demirel, University, Isparta,
Turkey. Tel: +90 246 2111243; Fax: +90 246 2370859; E-mail:
[email protected]
Abstract: In this paper an analytical procedure is given to study the free
vibration characteristics of laminated non-homogeneous orthotropic thin
circular cylindrical shells resting on elastic foundation, accounting for
Karman type geometric non-linearity. At first, the basic relations and modified
Donnell type stability equations, considering finite deformations, have been
obtained for laminated thin orthotropic circular cylindrical shells, the
Young's moduli of which varies piecewise continuously in the thickness
direction. Applying Galerkin method to the latter equations, a non-linear time
dependent differential equation is obtained for the displacement amplitude. The
frequency is obtained from this equation as a function of the shell
displacement amplitude. Finally, the effect of elastic foundation,
non-linearity, non-homogeneity, the number and ordering of layers on the
frequency is found for different mode numbers. These results are given in the
form of tables and figures. The present analysis is validated by comparing
results with those in the literature.
Keywords: elastic foundation, vibration, natural and nonlinear frequencies, cross-ply laminated cylindrical shells, orthotropic material
