Effects of Elastic Foundation on the Vibration of Laminated Non-Homogeneous Orthotropic Circular Cylindrical Shells

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

Effects of Elastic Foundation on the Vibration of Laminated Non-Homogeneous Orthotropic Circular Cylindrical Shells

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

Free vibrations of cross-ply laminated non-homogeneous composite truncated conical shells

7th International Conference on Vibration Problems (ICOVP 2005) -- SEP 05-09, 2005 -- Isik Univ, Sile Campus, Istanbul, TURKEYWOS: 000246655700005In this study, the free vibration of cross-ply laminated non-homogeneous orthotropic truncated conical shells is studied. At first, the basic relations have been obtained for cross-ply laminated orthotropic truncated conical shells, the Young's moduli and density of which vary piecewise continuously in the thickness direction. Applying Galerkin method to the foregoing equations, the frequency of vibration is obtained. Finally, the effect of non-homogeneity, the number and ordering of layers on the frequency is found for different mode numbers, and the results are presented in tables and compared with other works

The nonlinear dynamic buckling response of functionally graded truncated conical shells

In this study, the nonlinear dynamic buckling of functionally graded (FG) truncated conical shells subjected to axial compressive load varying as a linear function of time is investigated. The material properties of the FG truncated shell are assumed to vary continuously through the thickness of the shell. The nonlinear pre-buckling deformations of the FG truncated conical shell are taken into account. The fundamental relations and modified Donnell type nonlinear dynamic stability and compatibility equations of the FG truncated conical shell are derived and solved by using the Superposition principle, Galerkin and Runge-Kutta methods. The values of the dimensionless nonlinear critical time parameter have been found numerically. Finally, carrying out some computations, the effects of the compositional profiles, the variation of the truncated conical shell geometric parameters and the axial loading speed on the dimensionless linear and nonlinear critical time parameters have been studied. Comparing the results of this study with those in the literature validates the present analysis. © 2012 Elsevier Ltd. All rights reserved

Stability analysis of clamped nonhomogeneous shells on the elastic foundation

In the present study a theoretical analysis is presented for determining the stability characteristics of clamped non-homogeneous shells on the elastic foundation subjected to the lateral pressure. The basic equations have been derived for the shell, the Young modulus of which varies exponentially in the thickness direction and rests on the elastic foundation. By applying the Galerkin method to the basic equations, the expressions for the critical lateral pressure of the non-homogeneous shell with or without an elastic foundation are obtained. Finally, the effects of the non-homogeneity, elastic foundation and shell characteristics on the critical lateral pressure have been studied

Modeling and Solution of Large Amplitude Vibration Problem of Construction Elements Made of Nanocomposites Using Shear Deformation Theory

The main purpose of the study is to investigate the vibration behaviors of carbon nanotube (CNT) patterned double-curved construction elements using the shear deformation theory (SDT). After the visual and mathematical models of CNT patterned double-curved construction elements are created, the large amplitude stress–strain relationships and basic dynamic equations are derived using the first order shear deformation theory (FSDT). Then, using the Galerkin method, the problem is reduced to the nonlinear vibration of nanocomposite continuous systems with quadratic and cubic nonlinearities. Applying the Grigolyuk method to the obtained nonlinear differential equation, large-amplitude frequency-amplitude dependence is obtained. The expressions for nonlinear frequencies of homogenous and inhomogeneous nanocomposite construction members such as plates, panels, spherical and hyperbolic-paraboloid (hypar) shells in the framework of FSDT are found in special cases. The accuracy of the results of the current study has been confirmed by comparing them with the reliable results reported in the literature. Original analyses are carried out to examine the effects of nonlinearity, CNT patterns and volume fraction changes on frequencies in the framework of shear deformation and classical shell theories

Effects of the non-homogeneity and elastic medium on the critical torsional load of the orthotropic cylindrical shell

In this study, the torsional stability problem of non-homogeneous orthotropic composite cylindrical shells in the elastic medium, using the Galerkin method was investigated. The Winkler model is used to describe the reaction of the elastic medium on the cylindrical shell. Mixed boundary conditions are considered. The effects of variations of shell parameters, non-homogeneity, orthotropy and foundation stiffness on the critical torsional load are examined

Stability analysis of FGM layered shells in the surrounding medium

In this study, the stability analysis of three-layered shells containing a functionally graded material layer in the surrounding medium and subjected to the uniform lateral pressure is investigated. The surrounding elastic medium is modeled as a Pasternak foundation. The dimensionless critical lateral pressures of three-layered functionally graded material shells with and without elastic foundations are obtained. Effects of compositional profiles and elastic foundation on the dimensionless critical lateral pressures have been studied