Journal of Computational Applied Mechanics

Contribution study on factors impacting the vibration behavior of functionally graded nanoplates

Document Type : Research Paper

Authors

1 Faculty of Sciences & Technology, Civil Eng Department, University Abbes Laghrour, Khenchela 40000, Algeria

2 b Faculty of Sciences & Technology, Mechanic Eng Department, University Abbes Laghrour, Khenchela 40000, Algeria

3 Department of Mathematical Sciences, College of Applied Sciences, Umm Al-Qura University, Makkah, Saudi Arabia

4 Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

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

Abstract

This comprehensive study investigates the behavior of functionally graded (FG) nanoplates, providing insights into their characteristics and important design considerations. By examining factors such as homogenization models (Voigt Reuss, LRVE, and Tamura), volume fraction laws (power-law model, Viola-Tornabene four-parameter model, trigonometric model), eigenmode, aspect ratios, index material, and small-scale length parameters, the study evaluates their influence on the natural frequency response of simply supported nanoplates. A novel twisting function is introduced and its accuracy in predicting natural frequencies in FG square nanoplates is rigorously validated through numerical comparisons with existing literature. The findings obtained from this research offer valuable guidance for optimizing the design of FG nanoplates and significantly contribute to advancing our understanding of their dynamics and practical applications.

Keywords

Main Subjects

[1]          F. Yang, A. C. M. Chong, D. C. C. Lam, P. Tong, Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures, Vol. 39, pp. 2731-2743, 05/01, 2002.
[2]          E. C. Aifantis, Strain gradient interpretation of size effects, International Journal of Fracture, Vol. 95, No. 1, pp. 299-314, 1999/01/01, 1999.
[3]          H. Moosavi, M. Mohammadi, A. Farajpour, S. Shahidi, Vibration analysis of nanorings using nonlocal continuum mechanics and shear deformable ring theory, Physica E: Low-dimensional Systems and Nanostructures, Vol. 44, No. 1, pp. 135-140, 2011.
[4]          M. Khorasani, Z. Soleimani Javid, E. Arshid, L. Lampani, Ö. Civalek, Thermo-elastic buckling of honeycomb micro plates integrated with FG-GNPs reinforced Epoxy skins with stretching effect, Composite Structures, Vol. 258, pp. 113430, 02/01, 2021.
[5]          B. Akgöz, Ö. Civalek, Buckling Analysis of Functionally Graded Tapered Microbeams via Rayleigh–Ritz Method, Mathematics, Vol. 10, pp. 4429, 11/24, 2022.
[6]          B. Akgöz, Ö. Civalek, Application of strain gradient elasticity theory for buckling analysis of protein microtubules, Current Applied Physics, Vol. 11, No. 5, pp. 1133-1138, 2011.
[7]          P. Lu, L. He, H. Lee, C. Lu, Thin plate theory including surface effects, International Journal of Solids and Structures - INT J SOLIDS STRUCT, Vol. 43, pp. 4631-4647, 08/01, 2006.
[8]          M. Sobhy, A comprehensive study on FGM nanoplates embedded in an elastic medium, Composite Structures, Vol. 134, 09/01, 2015.
[9]          M. Sobhy, A. Radwan, A New Quasi 3D Nonlocal Plate Theory for Vibration and Buckling of FGM Nanoplates, International Journal of Applied Mechanics, Vol. 09, pp. 1750008, 02/08, 2017.
[10]        A. Zenkour, A novel mixed nonlocal elasticity theory for thermoelastic vibration of nanoplates, Composite Structures, Vol. 185, 11/01, 2017.
[11]        A. Abdelrahman, M. A. Eltaher, On bending and buckling responses of perforated nanobeams including surface energy for different beams theories, Engineering with Computers, Vol. 38, pp. 1-27, 06/01, 2022.
[12]        Q.-H. Pham, T. T. Tran, V. K. Tran, P.-C. Nguyen, T. Nguyen-Thoi, A. M. Zenkour, Bending and hygro-thermo-mechanical vibration analysis of a functionally graded porous sandwich nanoshell resting on elastic foundation, Mechanics of Advanced Materials and Structures, Vol. 29, No. 27, pp. 5885-5905, 2022.
[13]        A. Garg, H. D. Chalak, A. Zenkour, M.-O. Belarbi, M. S. A. Houari, A Review of Available Theories and Methodologies for the Analysis of Nano Isotropic, Nano Functionally Graded, and CNT Reinforced Nanocomposite Structures, Archives of Computational Methods in Engineering, 10/04, 2021.
[14]        P. Phung-Van, C. H. Thai, A novel size-dependent nonlocal strain gradient isogeometric model for functionally graded carbon nanotube-reinforced composite nanoplates, Engineering with Computers, pp. 1-14, 2021.
[15]        A. Zenkour, R. Alghanmi, A refined quasi-3D theory for the bending of functionally graded porous sandwich plates resting on elastic foundations, Thin-Walled Structures, Vol. 181, pp. 110047, 12/01, 2022.
[16]        M. Arefi, S. Firouzeh, E. Mohammad-Rezaei Bidgoli, Ö. Civalek, Analysis of Porous Micro-plates Reinforced with FG-GNPs Based on Reddy plate Theory, Composite Structures, Vol. 247, pp. 112391, 04/01, 2020.
[17]        A. Garg, H. D. Chalak, A. Zenkour, M.-O. Belarbi, R. Sahoo, Bending and free vibration analysis of symmetric and unsymmetric functionally graded CNT reinforced sandwich beams containing softcore, Thin-Walled Structures, Vol. 170, pp. 108626, 01/01, 2022.
[18]        İ. Esen, A. Abdelrahman, M. A. Eltaher, Free vibration and buckling stability of FG nanobeams exposed to magnetic and thermal fields, Engineering with Computers, Vol. 38, 08/01, 2022.
[19]        L. Hoa, P. Vinh, N. Duc, T. Nguyen-Thoi, L. Son, D. Thom, Bending and free vibration analyses of functionally graded material nanoplates via a novel nonlocal single variable shear deformation plate theory, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 235, pp. 095440622096452, 10/15, 2020.
[20]        Ş. Akbaş, Modal analysis of viscoelastic nanorods under an axially harmonic load, Advances in nano research, Vol. 8, pp. 277-282, 05/27, 2020.
[21]        E. E. Ghandourh, A. M. Abdraboh, Dynamic analysis of functionally graded nonlocal nanobeam with different porosity models, Steel and Composite Structures, An International Journal, Vol. 36, No. 3, pp. 293-305, 2020.
[22]        S. Natarajan, S. Chakraborty, M. Thangavel, S. Bordas, T. Rabczuk, Size-dependent free flexural vibration behavior of functionally graded nanoplates, Computational Materials Science, Vol. 65, pp. 74-80, 2012.
[23]        M. Koizumi, FGM activities in Japan, Composites Part B: Engineering, Vol. 28, No. 1, pp. 1-4, 1997/01/01/, 1997.
[24]        H.-T. Thai, T. P. Vo, A nonlocal sinusoidal shear deformation beam theory with application to bending, buckling, and vibration of nanobeams, International Journal of Engineering Science, Vol. 54, pp. 58-66, 2012.
[25]        F. Ebrahimi, M. Barati, A. Zenkour, Vibration Analysis of Smart Embedded Shear Deformable Nonhomogeneous Piezoelectric Nanoscale Beams based on Nonlocal Elasticity Theory, International Journal of Aeronautical and Space Sciences, Vol. 18, pp. 255-269, 06/01, 2017.
[26]        A. Shariati, D. w. Jung, H. Mohammad-Sedighi, K. K. Żur, M. Habibi, M. Safa, On the Vibrations and Stability of Moving Viscoelastic Axially Functionally Graded Nanobeams, Materials, Vol. 13, No. 7, pp. 1707, 2020.
[27]        J. Reddy, Nonlocal theories for bending, buckling and vibration of beams, International Journal of Engineering Science, Vol. 45, pp. 288-307, 02/01, 2007.
[28]        J. Reddy, S. Pang, Nonlocal continuum theories of beams for the analysis of carbon nanotubes, Journal of Applied Physics, Vol. 103, pp. 023511-023511, 02/01, 2008.
[29]        M. A. Eltaher, S. Emam, F. Ibrahim, Free vibration analysis of functionally graded size-dependent nanobeams, Applied Mathematics and Computation, Vol. 218, pp. 7406-7420, 03/01, 2012.
[30]        R. Nazemnezhad, S. Hosseini-Hashemi, Nonlocal nonlinear free vibration of functionally graded nanobeams, Composite Structures, Vol. 110, pp. 192-199, 04/01, 2014.
[31]        F. Ebrahimi, M. Barati, Ö. Civalek, Application of Chebyshev–Ritz method for static stability and vibration analysis of nonlocal microstructure-dependent nanostructures, Engineering with Computers, Vol. 36, 07/01, 2020.
[32]        L. Hadji, M. Avcar, Nonlocal free vibration analysis of porous FG nanobeams using hyperbolic shear deformation beam theory, Advances in Nano Research, Vol. 10, pp. 281-293, 03/16, 2021.
[33]        Y. Gafour, A. Hamidi, A. Benahmed, M. Zidour, T. Bensattalah, Porosity-dependent free vibration analysis of FG nanobeam using non-local shear deformation and energy principle, Advances in nano research, Vol. 8, No. 1, pp. 37-47, 2020.
[34]        A. C. Eringen, Theory of micropolar plates, Zeitschrift für angewandte Mathematik und Physik ZAMP, Vol. 18, pp. 12-30, 1967.
[35]        A. C. Eringen, Nonlocal polar elastic continua, International journal of engineering science, Vol. 10, No. 1, pp. 1-16, 1972.
[36]        A. C. Eringen, D. Edelen, On nonlocal elasticity, International journal of engineering science, Vol. 10, No. 3, pp. 233-248, 1972.
[37]        A. C. Eringen, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of applied physics, Vol. 54, No. 9, pp. 4703-4710, 1983.
[38]        B. Farshi, A. Assadi, A. Alinia-ziazi, Frequency analysis of nanotubes with consideration of surface effects, Applied Physics Letters, Vol. 96, pp. 093105-093105, 03/02, 2010.
[39]        R. Billel, Contribution to study the effect of (Reuss, LRVE, Tamura) models on the axial and shear stress of sandwich FGM plate (Ti–6A1–4V/ZrO2) subjected on linear and nonlinear thermal loads, AIMS Materials Science, Vol. 10, No. 1, pp. 26-39, 2023.
[40]        B. Rebai, K. Mansouri, M. Chitour, A. Berkia, T. Messas, F. Khadraoui, B. Litouche, Effect of idealization models on deflection of functionally graded material (FGM) plate, Journal of Nano-and Electronic Physics, Vol. 15, No. 1, 2023.
[41]        W. Voigt, Ueber die Beziehung zwischen den beiden Elasticitätsconstanten isotroper Körper, Annalen der physik, Vol. 274, No. 12, pp. 573-587, 1889.
[42]        A. Reuß, Berechnung der fließgrenze von mischkristallen auf grund der plastizitätsbedingung für einkristalle, ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 9, No. 1, pp. 49-58, 1929.
[43]        M. M. Gasik, R. R. Lilius, Evaluation of properties of W Cu functional gradient materials by micromechanical model, Computational materials science, Vol. 3, No. 1, pp. 41-49, 1994.
[44]        J. R. Zuiker, Functionally graded materials: choice of micromechanics model and limitations in property variation, Composites Engineering, Vol. 5, No. 7, pp. 807-819, 1995.
[45]        I. Tamura, Strength and ductility of Fe-Ni-C alloys composed of austenite and martensite with various strength, in Proceeding of, Cambridge, Institute of Metals, pp. 611-615.
[46]        T. Mori, K. Tanaka, Average stress in matrix and average elastic energy of materials with misfitting inclusions, Acta metallurgica, Vol. 21, No. 5, pp. 571-574, 1973.
Journal of Computational Applied Mechanics
Volume 55, Issue 3
July 2024
Pages 369-380
  • Receive Date: 06 April 2024
  • Revise Date: 23 April 2024
  • Accept Date: 24 April 2024