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Analytical and numerical flexural properties of polymeric porous functionally graded (PFGM) sandwich beams

Njim E. K., Bakhy S. H., Al-Waily M.

Journal of Achievements in Materials and Manufacturing Engineering

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2022

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Vol. 110, nr 1

5--15

EN

Purpose: Materials with porosity gradient functionally gradient properties reflect changes in the material's position spatially in response to changes in porosity. One porous metal comprised the FGM core and had not previously been considered in bending analyses. Design/methodology/approach: Analytical formulations were derived based on the classical beam theory (CBT). According to the power-law scheme, the material properties of FG beams are supposed to vary along the thickness direction of the constituents. Findings: The results show that the porosity and power gradient parameters significantly influence flexural bending characteristics. It is found that there is a fair agreement between the analytical and numerical results, with a maximum error percentage not exceeding 5%. Research limitations/implications: The accuracy of analytical solutions is verified by employing the finite elements method (FEM) with commercial ANSYS 2021 R1 software. Practical implications: FGM beams' elastic properties with an even porosity distribution through-beam core and bonded with two thin solid skins at the upper and lower surfaces were carried out. Originality/value: This paper develops an analytical study to investigate the flexural problem of a functionally graded simply supported sandwich beam with porosities widely used in aircraft structures and biomedical engineering. The objective of the current work is to examine the effects of some key parameters, such as porous ratio, power-law index, and core metal type, on the flexural properties such as bending load, total deformation, and strain energy.

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Free vibration analysis of imperfect functionally graded sandwich plates: analytical and experimental investigation

Njim E.K., Bakhy S.H., Al-Waily M.

Archives of Materials Science and Engineering

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2021

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Vol. 111, nr 2

49--65

EN

Purpose: This paper develops a new analytical solution to conduct the free vibration analysis of porous functionally graded (FG) sandwich plates based on classical plate theory (CPT). The sandwich plate made of the FGM core consists of one porous metal that had not previously been taken into account in vibration analysis and two homogenous skins. Design/methodology/approach: The analytical formulations were generated based on the classical plate theory (CPT). According to the power law, the material properties of FG plates are expected to vary along the thickness direction of the constituents. Findings: The results show that the porosity parameter and the power gradient parameter significantly influence vibration characteristics. It is found that there is an acceptable error between the analytical and numerical solutions with a maximum discrepancy of 0.576 % at a slenderness ratio (a/h =100), while the maximum error percentage between the analytical and experimental results was found not exceeding 15%. Research limitations/implications: The accuracy of analytical solutions is verified by the adaptive finite elements method (FEM) with commercial ANSYS 2020 R2 software. Practical implications: Free vibration experiments on 3D-printed FGM plates bonded with two thin solid face sheets at the top and bottom surfaces were conducted. Originality/value: The novel sandwich plate consists of one porous polymer core and two homogenous skins which can be widely applied in various fields of aircraft structures, biomedical engineering, and defense technology. This paper presents an analytical and experimental study to investigate the free vibration problem of a functionally graded simply supported rectangular sandwich plate with porosities. The objective of the current work is to examine the effects of some key parameters, such as porous ratio, power-law index, and slenderness ratio, on the natural frequencies and damping characteristics.

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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%.

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Analytical and numerical free vibration analysis of porous functionally graded materials (FGPMs) sandwich plate using Rayleigh-Ritz method

Njim E.K., Bakhy S.H., Al-Waily M.

Archives of Materials Science and Engineering

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2021

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Vol. 110, nr 1

27--41

EN

Purpose: This study introduces a new approximated analytical solution of the free vibration analysis to evaluate the natural frequencies of functionally graded rectangular sandwich plates with porosities. Design/methodology/approach: The kinematic relations are developed based on the classical plate theory (CPT), and the governing differential equation is derived by employing the Rayleigh-Ritz approximate method. The FGM plate is assumed made of an isotropic material that has an even distribution of porosities. The materials properties varying smoothly in the thickness direction only according to the power-law scheme. Findings: The influences of changing the gradient index, porosity distribution, boundary conditions, and geometrical properties on the free vibration characteristics of functionally graded sandwich plates are analysed. Research limitations/implications: A detailed numerical investigation is carried out using the finite element method with the help of ANSYS 2020 R2 software to validate the results of the proposed analytical solution. Originality/value: The results with different boundary conditions show the influence of porosity distribution on the free vibration characteristics of FG sandwich plates. The results indicated a good agreement between the approximated method such as the Rayleigh-Ritz and the finite element method with an error percentage of no more than 5%.