Journal of Applied and Computational Mechanics

Even and Uneven Porosities on Rotating Functionally Graded ‎Variable-thickness Annular Disks with Magneto-electro-thermo-‎mechanical Loadings

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Science, Damietta University, P.O. Box 34517, Egypt‎

2 Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh 33516, Egypt‎

Abstract

This paper investigates the porosity effect on rotating functionally graded piezoelectric (FGP) variable-thickness annular disk. Even and uneven porosity distributions for the disk are approximated. The porous annular disk is subjected to the influence of electromagnetic, thermal, and mechanical loadings. Material coefficients are graded and described as a power law in the radial direction of the annular rotating disk. The resulting differential equation with boundary conditions is solved using the semi-analytical technique. Two cases are studied for the porous annular disk, circular disk, and mounted disk. The effectiveness of the porosity factor and grading index on the temperature, stresses, and displacement are reported. Comparisons between non-porous and porous annular disks for even and uneven porosity are executed and discussed. The obtained results are presented to conclude the important role of porosity on the rotating variable-thickness annular disk for the purpose of engineering mechanical design.

Keywords

Main Subjects

Publisher’s Note Shahid Chamran University of Ahvaz remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

[1] Abazid, M.A., Zenkour, A.M., Sobhy, M., Wave propagation in FG porous GPLs-reinforced nanoplates under in-plane mechanical load and Lorentz magnetic force via a new quasi 3D plate theory, Mechanics Based Design of Structures and Machines, 50(5), 2022, 1831-1850.
[2] Ebrahimi, F., Jafari, A., Barati, M.R., Vibration analysis of magneto-electro-elastic heterogeneous porous material plates resting on elastic foundations, Thin-Walled Structures, 119, 2017, 33–46.
[3] Arefi, M., Firouzeh, S., Rezaei Bidgoli, E.M., Civalek, O., Analysis of porous micro-plates reinforced with FG-GNPs based on Reddy plate theory, Composite Structures, 247, 2020, 112391.
[4] Barati, M.R., Shahverdi, H., Aero-hygro-thermal stability analysis of higher-order refined supersonic FGM panels with even and uneven porosity distributions, Journal of Fluids and Structures, 73, 2017, 125–136.
[5] Sobhy, M., Zenkour, A.M., Wave propagation in magnetoporosity FG bi-layer nanoplates based on a novel quasi-3D refined plate theory, Waves in Random and Complex Media, 31(5), 2021, 921-941.
[6] Vaka, V., Sathujoda, P., Bhalla, N. A., Kumar, Y.V.S., Steady-state and transient vibration analysis of a thermally loaded power law-based functionally graded rotor system with induced porosities, Forces in Mechanics, 9, 2022, 100123.
[7] Kumar, R., Panchal, M., Elastodynamic response of vibrations in a magneto-micropolar porous medium possessing cubic symmetry, Chemical Engineering Communications, 197, 2010, 1500–1514.
[8] Kumar, R., Sharma, P., Variational principle, uniqueness and reciprocity theorems in porous magneto-piezothermoelastic medium, Cogent Mathematics, 3, 2016, 1231947.
[9] Karami, B., Shahsavari, D., Li, L., Temperature-dependent flexural wave propagation in nanoplatetype porous heterogenous material subjected to in-plane magnetic field, Journal of Thermal Stresses, 41(4), 2018, 483–499.
[10] Kiran, M.C., Kattimani, S.C., Vinyas, M., Porosity influence on structural behaviour of skew functionally graded magneto-electro-elastic plate, Composite Structures, 191, 2018, 36–77.
[11] Wattanasakulpong, N., Ungbhakorn, V., Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities, Aerospace Science and Technology, 32 (1), 2014, 111–120.
[12] Akbas, S., Thermal Effects on the Vibration of Functionally Graded Deep Beams with Porosity, International Journal of Applied Mechanics, 9(5), 2017, 1750076.
[13] Chen, D., Kitipornchai, S., Yang, J., Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core, Thin-Walled Structures, 107, 2016, 39-48.
[14] Ebrahimi, F., Jafari, A., A higher-order thermomechanical vibration analysis of temperature-dependent FGM beams with porosities, Journal of Engineering, 2016, 2016, 9561504.
[15] Tantawy, R., Zenkour, A.M. Effect of Porosity and Hygrothermal Environment on FGP Hollow Spheres under Electromechanical Loads, Journal of Applied and Computational Mechanics, 8(2), 2022, 710–722.
[16] Zenkour, A.M., Quasi-3D refined theory for functionally graded porous plates: displacements and stresses, Physical Mesomechanics, 23(1), 2020, 22-35.
[17] Mashat, D.S., Zenkour, A.M., Radwan, A.F., Aquasi – 3D higher order plate theory for bending of FG plates resting on elastic foundations under hygro-thermo-mechanical loads with porosity, European Journal of Mechanics/ A Solids, 82, 2020, 103985.
[18] Qing, H., Wei, L., Linear and nonlinear free vibration analysis of functionally graded porous nanobeam using stress-driven nonlocal integral model, Communications in Nonlinear Science and Numerical Simulation, 109, 2022, 106300.
[19] Tang, Y., Qing, H., Size-dependent nonlinear post-buckling analysis of functionally graded porous Timoshenko microbeam with nonlocal integral models, Communications in Nonlinear Science and Numerical Simulation, 116, 2023, 106808.
[20] Zhao, Y., Zhang, S., Wang, X., Ma, S., Zhao, G., Kang, Z., Nonlinear analysis of carbon nanotube reinforced functionally graded plates with magneto-electro-elastic multiphase matrix, Composite Structures, 297, 2022, 115969.
[21] Zhang, S., Zhao, Y., Wang, X., Chen, M., Schmidt, R., Static and dynamic analysis of functionally graded magneto-electro-elastic plates and shells, Composite Structures, 281, 2022, 114950.
[22] Zhang, S., Huang, Z., Zhao, Y., Ying, S., Ma, S., Static and dynamic analyses of FGPM cylindrical shells with quadratic thermal gradient distribution, Composite Structures, 277, 2021, 114658.
[23] Wei, L., Qing, H., Bending, buckling and vibration analysis of Bi-directional functionally graded circulary annular microplate based on MCST, Composite Structures, 292, 2022, 115633.
[24] Shariati, M., Shishehsaz, M., Mosalmani, R., Roknizadeh, S.A.S., Size effect on the axisymmetric vibrational response of functionally graded circular nano-plate based on the nonlocal stress-Driven method, Journal of Applied and Computational Mechanics, 8(3), 2022, 962-980.
[25] Ootao, Y., Tanigawa, Y., Transient piezothermoelastic analysis for a functionally graded thermopiezoelectric hollow sphere, Composite Structures, 81, 2007, 540–549.
[26] Arani, A.G., Kolahchi, R., Mosallaie Barzoki, A.A., Loghman, A., Electro-thermo-mechanical behaviors of FGPM spheres using analytical method and ANSYS software, Applied Mathematical Modelling, 36, 2012, 139–157.
[27] Bayat, M., Saleem, M., Sahari, B.B., Hamouda, A.M.S., and Mahdi, E., Mechanical and thermal stresses in a functionally graded rotating disk with variable thickness due to radially symmetry loads, International Journal of Pressure Vessels and Piping, 86, 2009, 357-372.
[28] Allam, M.N.M., Tantawy, R., Zenkour, A., Thermoelastic stresses in functionally graded rotating annular disks with variable thickness, Journal of Theoretical and Applied Mechanics, 56(4), 2018, 1029-1041.
[29] Bayat, M., Rahimi, M., Saleem, M., Mohazzab, A.H., Wudtke, I., Talebi, H., One dimensional analysis for magneto-thermo-mechanical response in a functionally graded annular variable-thickness rotating disk, Applied Mathematical Modelling, 38(19), 2014, 4625-4639.
[30] Paria, G., Magneto-elasticity and magneto-thermo-elasticity, Advances in Applied Mechanics, 10(1), 1967, 73-112.
[31] Dai, T., Dai, H.L., Analysis of a rotating FGMEE circular disk with variable thickness under thermal environment, Applied Mathematical Modelling, 45, 2017, 900-924.
[32] Dai, H.L., Jiang, H.J., Analytical study for electromagnetothermoelastic behavior of a functionally graded piezoelectric solid cylinder, Mechanics of Advanced Materials and Structures, 20(10), 2013, 800-811.
[33] Dai, H.L., Dai, T., Yang, L., Free vibration of a FGPM circular plate placed in a uniform magnetic field, Meccanica, 48(10), 2013, 2339-2347.
[34] Ezzat, M.A., Generation of generalized thermomagnetoelastic waves by thermal shock in a perfectly conducting half-space, Journal of Thermal Stresses, 20, 1997, 633-917.
[35] Kraus, J.D., Electromagnetic, McGraw Hill, USA, 1984.
[36] Dai, H.L., Wang, X., Dynamic responses of piezoelectric hollow cylinders in an axial magnetic field, International Journal of Solids and Structures, 41, 2004, 5231-5246.
Journal of Applied and Computational Mechanics
Volume 9, Issue 3
July 2023
Pages 695-711