Free Vibration Analysis of Functionally Graded Cylindrical Shells Stiffened by Uniformly and Non-Uniformly Disturbuted Ring Stiffeners

2009 ◽  
Author(s):  
S. A. Moeini ◽  
M. Rahaeifard ◽  
M. T. Ahmadian ◽  
M. R. Movahhedy
Keyword(s):  
Free Vibration ◽  
Functionally Graded Materials ◽  
Vibration Analysis ◽  
Strain Energy ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Shear Stresses ◽  
Graded Materials ◽  
Energy Evaluation

Free vibration analysis of a transversely stiffened circular thin hollow cylinder made of functionally graded materials (FGMs) is analytically evaluated. Functionally graded materials are inhomogeneous composites which are usually made from a mixture of metal and ceramic. The gradient compositional variation of the constituents from one surface to the other provides an elegant solution to the problem of high transverse shear stresses induced when two dissimilar materials with large differences in material properties are bonded. In this paper, application of an FGM made of two different materials is investigated by applying Ritz method. While cylinder is assumed to be thin, strain energy evaluation is performed by Sander’s theorem. Stiffeners which are not necessarily in the same uniform shape are treated as discrete elements and can be placed on both sides of the cylinder or concentrate in the middle wall. Bending, stretching and wrapping effects of stiffeners are considered in calculation of strain energy. Evaluation of kinetic energy of stiffeners is performed by taking into account rotary and translational inertia. To apply Ritz method, polynomial functions are used and natural frequencies and mode shapes of ring stiffened thin cylinder are investigated. Results are compared and verified with previous theoretical and experimental studies of stiffened thin cylinders. Comparison indicates a good agreement between results.

scholarly journals Functionally Graded Materials: An Overview of Stability, Buckling, and Free Vibration Analysis

2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Ning Zhang ◽  
Tahir Khan ◽  
Haomin Guo ◽  
Shaoshuai Shi ◽  
Wei Zhong ◽  
...  
Keyword(s):  
Free Vibration ◽  
Functionally Graded Materials ◽  
Vibration Analysis ◽  
Single Point ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Graded Materials ◽  
The Past ◽  
Future Work ◽  
Advanced Development

Functionally graded materials (FGMs) are novel materials whose properties change gradually with respect to their dimensions. It is the advanced development of formerly used composite materials and consists of two or more materials in order to achieve the desired properties according to the application where an FGM is used. FGMs have obtained a great attention of researchers in the past decade due to their graded properties at every single point in various dimensions. The properties of an FGM are not identical to the materials that constitute it. This paper aims to present an overview of the existing literature on stability, buckling, and free vibration analysis of FGM carried out by numerous authors in the past decade. Moreover, the analyses of mathematical models adopted for the aforementioned analyses are not the core purpose of this paper. At the end, future work is also suggested in this review paper.

3-D Free Vibration Analysis of Functionally Graded Thick Circular and Annular Plates on Elastic Foundation

2010 ◽  
Author(s):  
Vahid Tajeddini ◽  
Abdolreza Ohadi ◽  
Mojtaba Sadighi
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Ritz Method ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Small Strain ◽  
Functionally Graded ◽  
Different Boundary Conditions ◽  
Fg Plates

This paper describes a study of three-dimensional free vibration analysis of thick circular and annular functionally graded (FG) plates resting on Pasternak foundation. The formulation is based on the linear, small strain and exact elasticity theory. Plates with different boundary conditions are considered and the material properties of the FG plate are assumed to vary continuously through the thickness according to power law. The kinematic and the potential energy of the plate-foundation system are formulated and the polynomial-Ritz method is used to solve the eigenvalue problem. Convergence and comparison studies are done to demonstrate the correctness and accuracy of the present method. With respect to geometric parameters, elastic coefficients of foundation and different boundary conditions some new results are reported which maybe used as a benchmark solution for future researches.

scholarly journals An exponential-trigonometric higher order shear deformation theory (HSDT) for bending, free vibration, and buckling analysis of functionally graded materials (FGMs) plates

2020 ◽  
Vol 29 ◽  
pp. 096369351987573 ◽  
Author(s):  
Yamna Belkhodja ◽  
Djamel Ouinas ◽  
Fatima Zohra Zaoui ◽  
Hamida Fekirini
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Functionally Graded Materials ◽  
Transverse Shear ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Shear Stresses ◽  
Graded Materials

Two assumptions have been made based on by this proposed theory, which come from recently developed exponential–trigonometric shape function for transverse shear deformation effect and a simple higher order shear deformation theory for plate, based on a constraint between two rotational displacements of axis parallel to the plate midplane, about the axes x, y Cartesian coordinates system, which caused fewer unknown number. For the application of this method, a displacement field extended as only bending membrane for transverse displacement is used, a governing equations of motion as a result are determined according to Hamilton’s principle, and simplified using Navier analytical solutions, as well as the transverse shear stresses effect that satisfied the stress-free boundary conditions on the simply supported plate free faces as a parabolic variation along the thickness are taken into account. A functionally graded materials plates are chosen for the parametric study, where the plates are functionally graded continuously in materials through the plate thickness as a function of power law or exponential form. The aim of this study is to analyze the bending, free vibration as well as the buckling mechanical behaviors, where the results are more focused on the investigation of different parameters such as the volume fraction index, geometric ratios, frequency modes, in-plane compressive load parameters and material properties effects on the deflection, stresses, natural frequencies, and critical buckling load, which are validated in terms of accuracy and efficiency with other plate theories results found in the literature.

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