Electro-magnetic potential effects on free vibration of rotating circular cylindrical shells of functionally graded materials with laminated composite core and piezo electro-magnetic two face sheets

Purpose: In this study, the free vibration analysis of functionally graded materials (FGMs) sandwich beams having different core metals and thicknesses is considered. The variation of material through the thickness of functionally graded beams follows the power-law distribution. The displacement field is based on the classical beam theory. The wide applications of functionally graded materials (FGMs) sandwich structures in automotive, marine construction, transportation, and aerospace industries have attracted much attention, because of its excellent bending rigidity, low specific weight, and distinguished vibration characteristics. Design/methodology/approach: A mathematical formulation for a sandwich beam comprised of FG core with two layers of ceramic and metal, while the face sheets are made of homogenous material has been derived based on the Euler–Bernoulli beam theory. Findings: The main objective of this work is to obtain the natural frequencies of the FG sandwich beam considering different parameters. Research limitations/implications: The important parameters are the gradient index, slenderness ratio, core metal type, and end support conditions. The finite element analysis (FEA), combined with commercial Ansys software 2021 R1, is used to verify the accuracy of the obtained analytical solution results. Practical implications: It was found that the natural frequency parameters, the mode shapes, and the dynamic response are considerably affected by the index of volume fraction, the ratio as well as face FGM core constituents. Finally, the beam thickness was dividing into frequent numbers of layers to examine the impact of many layers' effect on the obtained results. Originality/value: It is concluded, that the increase in the number of layers prompts an increment within the frequency parameter results' accuracy for the selected models. Numerical results are compared to those obtained from the analytical solution. It is found that the dimensionless fundamental frequency decreases as the material gradient index increases, and there is a good agreement between two solutions with a maximum error percentage of no more than 5%.

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

Advances in Materials Science and Engineering ◽

10.1155/2019/1354150 ◽

2019 ◽

Vol 2019 ◽

pp. 1-18 ◽

Cited By ~ 5

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.

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Vibration Characteristics of Ring-Stiffened Functionally Graded Circular Cylindrical Shells

ISRN Mechanical Engineering ◽

10.5402/2012/232498 ◽

2012 ◽

Vol 2012 ◽

pp. 1-13 ◽

Cited By ~ 2

Author(s):

Muhmmad Nawaz Naeem ◽

Shazia Kanwal ◽

Abdul Ghafar Shah ◽

Shahid Hussain Arshad ◽

Tahir Mahmood

Keyword(s):

Circular Cylindrical Shell ◽

Cylindrical Shells ◽

Vibration Characteristics ◽

Functionally Graded ◽

Lagrangian Function ◽

Dynamical Equations ◽

Graded Materials ◽

Present Technique ◽

Circular Cylindrical Shells ◽

Stiffened Cylindrical Shells

The vibration characteristics of ring stiffened cylindrical shells are analyzed. These shells are assumed to be structured from functionally graded materials (FGM) and are stiffened with isotropic rings. The problem is formulated by coupling the expressions for strain and kinetic energies of a circular cylindrical shell with those for rings. The Lagrangian function is framed by taking difference of strain and kinetic energies. The Rayleigh-Ritz approach is employed to obtain shell dynamical equations. The axial model dependence is approximated by characteristic beam functions that satisfy the boundary conditions. The validity and efficiency of the present technique are verified by comparisons of present results with the previous ones determined by other researchers.

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A semi-analytical finite element model for the analysis of cylindrical shells made of functionally graded materials

Composite Structures ◽

10.1016/j.compstruct.2009.04.008 ◽

2009 ◽

Vol 91 (4) ◽

pp. 427-432 ◽

Cited By ~ 46

Author(s):

H. Santos ◽

Cristóvão M. Mota Soares ◽

Carlos A. Mota Soares ◽

J.N. Reddy

Keyword(s):

Finite Element ◽

Finite Element Model ◽

Functionally Graded Materials ◽

Cylindrical Shells ◽

Element Model ◽

Functionally Graded ◽

Graded Materials

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Thermoelastic Fracture Mechanics for Nonhomogeneous Material Subjected to Unsteady Thermal Load

Journal of Applied Mechanics ◽

10.1115/1.321153 ◽

1999 ◽

Vol 67 (1) ◽

pp. 87-95 ◽

Cited By ~ 26

Author(s):

B. L. Wang ◽

J. C. Han ◽

S. Y. Du

Keyword(s):

Functionally Graded Materials ◽

Material Properties ◽

Crack Problem ◽

Laminated Composite ◽

Functionally Graded ◽

Comprehensive Treatment ◽

Numerical Illustration ◽

Graded Materials ◽

Nonhomogeneous Material ◽

Crack Problems

This article provides a comprehensive treatment of cracks in nonhomogeneous structural materials such as functionally graded materials. It is assumed that the material properties depend only on the coordinate perpendicular to the crack surfaces and vary continuously along the crack faces. By using a laminated composite plate model to simulate the material nonhomogeneity, we present an algorithm for solving the system based on the Laplace transform and Fourier transform techniques. Unlike earlier studies that considered certain assumed property distributions and a single crack problem, the current investigation studies multiple crack problems in the functionally graded materials with arbitrarily varying material properties. The algorithm can be applied to steady state or transient thermoelastic fracture problem with the inertial terms taken into account. As a numerical illustration, transient thermal stress intensity factors for a metal-ceramic joint specimen with a functionally graded interlayer subjected to sudden heating on its boundary are presented. The results obtained demonstrate that the present model is an efficient tool in the fracture analysis of nonhomogeneous material with properties varying in the thickness direction. [S0021-8936(00)01601-9]

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