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

Buckling Behavior of Sandwich Cylindrical Shells Covered by Functionally Graded Coatings with Clamped Boundary Conditions under Hydrostatic Pressure

The buckling behavior of sandwich shells with functionally graded (FG) coatings operating under different external pressures was generally investigated under simply supported boundary conditions. Since it is very difficult to determine the approximation functions satisfying clamped boundary conditions and to solve the basic equations analytically within the framework of first order shear deformation theory (FOST), the number of publications on this subject is very limited. An analytical solution to the buckling problem of FG-coated cylindrical shells under clamped boundary conditions subjected to uniform hydrostatic pressure within the FOST framework is presented for the first time. By mathematical modeling of the FG coatings, the constitutive relations and basic equations of sandwich cylindrical shells within the FOST framework are obtained. Analytical solutions of the basic equations in the framework of the Donnell shell theory, obtained using the Galerkin method, is carried out using new approximation functions that satisfy clamped boundary conditions. Finally, the influences of FG models and volume fractions on the hydrostatic buckling pressure within the FOST and classical shell theory (CT) frameworks are investigated in detail

Buckling Behavior of FG-CNT Reinforced Composite Conical Shells Subjected to a Combined Loading

The buckling behavior of functionally graded carbon nanotube reinforced composite conical shells (FG-CNTRC-CSs) is here investigated by means of the first order shear deformation theory (FSDT), under a combined axial/lateral or axial/hydrostatic loading condition. Two types of CNTRC-CSs are considered herein, namely, a uniform distribution or a functionally graded (FG) distribution of reinforcement, with a linear variation of the mechanical properties throughout the thickness. The basic equations of the problem are here derived and solved in a closed form, using the Galerkin procedure, to determine the critical combined loading for the selected structure. First, we check for the reliability of the proposed formulation and the accuracy of results with respect to the available literature. It follows a systematic investigation aimed at checking the sensitivity of the structural response to the geometry, the proportional loading parameter, the type of distribution, and volume fraction of CNTs

The Application of the Modified Lindstedt–Poincaré Method to Solve the Nonlinear Vibration Problem of Exponentially Graded Laminated Plates on Elastic Foundations

The solution of the nonlinear (NL) vibration problem of the interaction of laminated plates made of exponentially graded orthotropic layers (EGOLs) with elastic foundations within the Kirchhoff–Love theory (KLT) is developed using the modified Lindstedt–Poincaré method for the first time. Young’s modulus and the material density of the orthotropic layers of laminated plates are assumed to vary exponentially in the direction of thickness, and Poisson’s ratio is assumed to be constant. The governing equations are derived as equations of motion and compatibility using the stress–strain relationship within the framework of KLT and von Karman-type nonlinear theory. NL partial differential equations are reduced to NL ordinary differential equations by the Galerkin method and solved by using the modified Lindstedt–Poincaré method to obtain unique amplitude-dependent expressions for the NL frequency. The proposed solution is validated by comparing the results for laminated plates consisting of exponentially graded orthotropic layers with the results for laminated homogeneous orthotropic plates. Finally, a series of examples are presented to illustrate numerical results on the nonlinear frequency of rectangular plates composed of homogeneous and exponentially graded layers. The effects of the exponential change in the material gradient in the layers, the arrangement and number of the layers, the elastic foundations, the plate aspect ratio and the nonlinearity of the frequency are investigated

Buckling of an orthotropic cylindrical thin shell with continuously varying thickness under a dynamic loading

365-370The buckling of an orthotropic composite cylindrical shell with variable thickness, subjected to a dynamic loading, is reported here. At first, the fundamental relations and Donnell type dynamic buckling equation of an orthotropic cylindrical shell with variable thickness have been obtained. Then, employing Galerkin's method, these equations have been reduced to a time dependent differential equation with variable coefficients. Finally, for different initial conditions and approximation functions, applying the Ritz type variational method, analytical expression has been found for the dynamic factor. Using these results, the effect of the variations of the power of time in the external pressure expression, the loading parameter and the ratios of the Young's moduli on the dynamic factor are studied numerically for the case when the thickness of the cylindrical shell varies as a power and exponential functions. It has been observed that these effects change the dynamic factor of the problem in the heading appreciably

Vibration analysis of shear deformable carbon nanotubes‐based functionally graded conical shells resting on elastic foundations

This article deals with the vibrational behavior of composite conical shells (CCSs) reinforced with carbon nanotubes (CNTs) resting on Winkler- and Pasternak-type foundations. A generalized version of the Ambartsumian's first-order shear deformation theory (FSDT) is here proposed to handle the vibration problems for CCSs reinforced with CNTs, resting on an elastic foundation, while considering a uniform and functionally graded (FG) distribution for the reinforcement phase throughout the shell thickness. The basic equations of the problem are determined and solved in closed form by means of the Galerkin procedure. First, we check for the reliability and accuracy of the proposed formulation with respect to the available literature. It follows a systematic investigation aimed at checking the sensitivity of the structural response to the geometry, the foundation stiffness, the type of distribution, and the volume fraction of CNTs

Stability of EG cylindrical shells with shear stresses on a Pasternak foundation

This article is the result of an investigation on the influence of a Pasternak elastic foundation on the stability of exponentially graded (EG) cylindrical shells under hydrostatic pressure, based on the first-order shear deformation theory (FOSDT) considering the shear stresses. The shear stresses shape function is distributed parabolic manner through the shell thickness. The governing equations of EG orthotropic cylindrical shells resting on the Pasternak elastic foundation on the basis of FOSDT are derived in the framework of Donnell-type shell theory. The novelty of present work is to achieve closed-form solutions for critical hydrostatic pressures of EG orthotropic cylindrical shells resting on Pasternak elastic foundation based on FOSDT. The expressions for critical hydrostatic pressures of EG orthotropic cylindrical shells with and without an elastic foundation based on CST are obtained, in special cases. Finally, the effects of Pasternak foundation, shear stresses, orthotropy and heterogeneity on critical hydrostatic pressures, based on FOSDT are investigated

Fonksiyonel Değişimli Malzemelerle Kaplı Seramik Silindirik Panelin Titreşim Analizi

In this study, the vibration of ceramic cylindrical panel covered by FGM coatings composed of zirconium oxide (ZrO2) and titanium-aloy (Ti6Al4V) is investigated. First, a sandwich cylindrical panel covered by FGM coatings is designed. After the derivation of basic equations are found expression for the frequency of ceramic cylindrical panels covered by FGM coatings. Discusses the influence of coatings profiles, sandwich shell characteristics, the radius-tothickness ratio and the core-to-coating thickness ratio on the dimensionless frequencies for FG and homogeneous sandwich cylindrical shell

Effects of shear stresses and rotary inertia on the stability and vibration of sandwich cylindrical shells with FGM core surrounded by elastic medium

The vibration and stability of axially loaded sandwich cylindrical shells with the functionally graded (FG) core with and without shear stresses and rotary inertia resting Pasternak foundation are investigated. The dynamic stability is derived based on the first order shear deformation theory (FSDT) including shear stresses. The axial load and dimensionless fundamental frequency for FG sandwich shell with shear stresses and rotary inertia and resting on the Pasternak foundation. Finally, the influences of variations of FG core, elastic foundations, shear stresses and rotary inertia on the fundamental frequencies and critical axial loads are investigated