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1

Thermosensitive response of a functionally graded cylinder with fractional order derivative

Lamba Navneet Kumar

International Journal of Applied Mechanics and Engineering

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2022

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Vol. 27, no. 1

107--124

EN

The present paper deals with thermal behaviour analysis of an axisymmetric functionally graded thermosensitive hollow cylinder. The system of coordinates are expressed in cylindrical-polar form. The heat conduction equation is of time-fractional order02<α≤, subjected to the effect of internal heat generation. Convective boundary conditions are applied to inner and outer curved surfaces whereas heat dissipates following Newton’s law of cooling. The lower surface is subjected to heat flux, whereas the upper surface is thermally insulated. Kirchhoff’s transformation is used to remove the nonlinearity of the heat equation and further it is solved to find temperature and associated stresses by applying integral transformation method. For numerical analysis a ceramic-metal-based functionally graded material is considered and the obtained results of temperature distribution and associated stresses are presented graphically.

2

Nonlocal state-space strain gradient approach to the vibration of piezoelectric functionally graded nanobeam

Selvamani Rajendran, Loganathan Rubine, Ebrahimi Farzad

Engineering Transactions

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2022

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Vol. 70, iss. 4

319--338

EN

In this work, the state-space nonlocal strain gradient theory is used for the vibration analysis of piezoelectric functionally graded material (FGM) nanobeam. Power law relations are used to describe the computing analysis of FGM constituent properties. The refined higherorder beam theory and Hamilton’s principle are used to obtain the equations of motion of the piezoelectric nanobeam. Besides, the governing equations of the piezoelectric nanobeam are extracted by the developed nonlocal state-space theory, and the analytical wave dispersion method is used to solve wave propagation problems. The real and imaginary solutions for wave frequency, loss factor and wave number are obtained and presented in graphs.

3

Analytical and numerical investigation of the free vibration of functionally graded materials sandwich beams

Bakhy S.H., Al-Waily M., Al-Shammari M.A.

Archives of Materials Science and Engineering

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2021

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Vol. 110, nr 2

72--85

EN

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%.

4

Influence of gradient structure on wear characteristics of centrifugally cast functionally graded magnesium matrix composites for automotive applications

Saleh Bassiouny, Jiang Jinghua, Fathi Reham, Xu Qiong, Li Yuhua, Ma Aibin

Archives of Civil and Mechanical Engineering

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2021

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Vol. 21, no. 1

196--218

EN

In the past few years, the functionally graded materials (FGMs) have proved useful in many industrial applications such as aerospace, automotive, transportation and infrastructure because of their advantages like the ability to control mechanical properties, residual stresses, wear, and corrosion behavior through a smooth gradation of the elements in a particular direction of the products. In this current work, the microstructural and wear properties of AZ91 alloy reinforced with silicon carbide particles (SiCp) produced through the centrifugal casting method were investigated. Four weight fractions of SiCp with 10 µm average size were used to fabricate functionally graded (FG) tubes in the two mold rotational speeds of 1200 and 1500 rpm. Microstructural, microhardness, and wear tests were used for characterizing the developed FG tubes. From the results obtained, the gradient distribution of SiC particles inside the AZ91 matrix alloy substantially improved hardness and wear resistance for the FG tubes comparing to unreinforced alloy. Moreover, the mold rotational speed is the main factor in controlling the distribution of particles, thus determining the gradient properties of the manufactured FG tubes. These findings suggest that FG tubes are useful for aerospace and automotive applications that require more excellent surface resistance.

5

A homogenization procedure and a physical discrete model for geometrically nonlinear transverse vibrations of a clamped beam made of a functionally graded material

Rahmouni A., Benamar R.

Diagnostyka

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2017

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Vol. 18, No. 3

15--20

EN

Functionally graded materials are used in aircrafts, space vehicles and defence industries because of their good thermal resistance. Geometrically nonlinear free vibration of a functionally graded beam with clamped ends (FGCB) is modeled here by an N-dof discrete system presenting an equivalent isotropic beam, with effective bending and axial stiffness parameters obtained via a homogenization procedure. The discrete model is made of N masses placed at the ends of solid bars connected by rotational springs, presenting the flexural rigidity. Transverse displacements of the bar ends induce a variation in their lengths giving rise to axial forces modeled by longitudinal springs. The nonlinear semi-analytical model previously developed is used to reduce the vibration problem, via application of Hamilton’s principle and spectral analysis, to a nonlinear algebraic system involving the mass and rigidity tensors mij and kij and the nonlinearity tensor bijkl. The material properties of the (FGCB) examined is assumed to be graded according to a power rule of mixture in the thickness direction. The fundamental nonlinear frequency parameters found for the (FGCB) are in a good agreement with previously published results showing the validity of the present equivalent discrete model and its availability for further applications to non-uniform beam.

6

Study of dynamic buckling of FG plate due to heat flux pulse

Czechowski L.

International Journal of Applied Mechanics and Engineering

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2015

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Vol. 20, no. 1

19--31

EN

The paper deals with a FEM analysis of dynamic buckling of functionally graded clamped plates under heat flux loading with huge power. The materials of structures as well as their properties are varying in each layer across the plate thickness formulated by the power law distribution. The heat flux was applied evenly to the whole ceramic surface. The analysis was developed in the ANSYS 14.5 software. The duration of the heat flux loading equal to a period of natural fundamental flexural vibrations of given structures was taken into consideration. To implement large deflections of structures, the Green-Lagrange nonlinear-displacement equations and the incremental Newton-Raphson algorithm were applied. An evaluation of the dynamic response of structures was carried out on basis of the Budiansky-Hutchinson criterion. The studies were conducted for different volume fraction distributions and different shapes of the heat flux loading. The computation results of the heat flux versus maximal plate deflection are shown and discussed.

7

Coupled thermoelasticity of a functionally graded cracked layer under thermomechanical shocks

Rokhi M. M., Shariati M.

Archives of Mechanics

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2013

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Vol. 65, nr 2

71-96

EN

This paper investigates linear-elastic response of cracked functionally graded layers subjected to thermomechanical loading; classical coupled thermoelastic equations are used in the calculations. The coupled dynamical system of equations obtained from the extended finite element discretization is solved by the Newmark method in the time domain. Micromechanical models for conventional composites are used to estimate properties of functionally graded layer. The interaction integral is then employed to calculate the stress intensity factors at each time step. In addition, crack propagation phenomenon under thermomechanical shocks is investigated in this paper. We have used MATLAB software to implement the algorithm and related code of problem.