449
Views
15
CrossRef citations to date
0
Altmetric
Original Articles

Thermomechanical vibration response of nanoplates with magneto-electro-elastic face layers and functionally graded porous core using nonlocal strain gradient elasticity

ORCID Icon, ORCID Icon & ORCID Icon
Pages 4477-4509 | Received 15 Mar 2023, Accepted 02 Apr 2023, Published online: 18 Apr 2023

References

  • Y.-F. Zhao, S.-Q. Zhang, X. Wang, S.-Y. Ma, G.-Z. Zhao, and Z. Kang, Nonlinear analysis of carbon nanotube reinforced functionally graded plates with magneto-electro-elastic multiphase matrix, Compos. Struct., vol. 297, pp. 115969, 2022. DOI: 10.1016/j.compstruct.2022.115969.
  • M. Vinyas, Computational analysis of smart magneto-electro-elastic materials and structures: review and classification, Arch. Comput. Methods Eng., vol. 28, no. 3, pp. 1205–1248, 2021. DOI: 10.1007/s11831-020-09406-4.
  • F. Zhang, C. Bai, and J. Wang, Study on dynamic stability of magneto-electro-thermo-elastic cylindrical nanoshells resting on Winkler–Pasternak elastic foundations using nonlocal strain gradient theory, J Braz. Soc. Mech. Sci. Eng., vol. 45, no. 1, pp. 23, 2023. DOI: 10.1007/s40430-022-03930-z.
  • A.I. Journal, I. Esen, and R. Özmen, Free and forced thermomechanical vibration and buckling responses of functionally graded magneto-electro-elastic porous nanoplates, Mech. Based Des. Struct. Mach., vol. 0, pp. 1–38, 2022. DOI: 10.1080/15397734.2022.2152045.
  • K. Madrahalli Chidanandamurthy, W. Wang, C. Fang, and S. Kattimani, Static, buckling, and free vibration characteristics of porous skew partially functionally graded magneto-electro-elastic plate, Mech. Based Des. Struct. Mach., pp. 1–36, 2021. DOI: 10.1080/15397734.2021.2008257.
  • V. Mahesh, and A.S. Mangalasseri, Agglomeration effects of CNTs on the energy harvesting performance of multifield interactive magneto-electro-elastic/nanocomposite unimorph smart beam, Mech. Based Des. Struct. Mach., pp. 1–27, 2022. DOI: 10.1080/15397734.2022.2144886.
  • S. Thai, V.X. Nguyen, and Q.X. Lieu, Bending and free vibration analyses of multi-directional functionally graded plates in thermal environment: A three-dimensional Isogeometric Analysis approach, Compos. Struct., vol. 295, pp. 115797, 2022. DOI: 10.1016/j.compstruct.2022.115797.
  • I. Khader, C. Koplin, C. Schröder, J. Stockmann, W. Beckert, W. Kunz, and A. Kailer, Characterization of a silicon nitride ceramic material for ceramic springs, J. Eur. Ceram. Soc., vol. 40, no. 10, pp. 3541–3554, 2020. DOI: 10.1016/j.jeurceramsoc.2020.03.046.
  • E. Schwarzer-Fischer, E. Zschippang, W. Kunz, C. Koplin, Y.M. Löw, U. Scheithauer, and A. Michaelis, CerAMfacturing of silicon nitride by using lithography-based ceramic vat photopolymerization (CerAM VPP), J. Eur. Ceram. Soc., vol. 43, no. 2, pp. 321–331, 2023. DOI: 10.1016/j.jeurceramsoc.2022.10.011.
  • Y. Yang, D, Cai, Z. Yang, X. Duan, P. He, D. Jia, and Y. Zhou, Rheology of organics-free aqueous ceramic suspensions for additive manufacturing of dense silicon nitride ceramics, Ceram. Int., vol. 48, no. 21, pp. 31941–31951, 2022. DOI: 10.1016/j.ceramint.2022.07.130.
  • K. Zhao, L. Dong, Y. Zheng, G. Deng, Z. Li, S. Qu, K. Chen, and J. Wu, Optimization of light-analyte interaction in Si3N4/polymer hybrid waveguide for sensitive sensing of pyridine vapor with ppb-level detection limit, Sensors Actuators B Chem., vol. 377, pp. 133104, 2023. DOI: 10.1016/j.snb.2022.133104.
  • L. Selvarajan, R. Rajavel, K. Venkataramanan, and V.P. Srinivasan, Experimental investigation on surface morphology and recasting layer of Si3N4-TiN composites machined by die-sinking and rotary EDM, Ceram. Int., vol. 49, no. 5, pp. 8487–8501, 2023. DOI: 10.1016/j.ceramint.2022.11.011.
  • B. Bai, R. Zhou, G. Yang, W. Zou, and W. Yuan, The constitutive behavior and dissociation effect of hydrate-bearing sediment within a granular thermodynamic framework, Ocean Eng., vol. 268, pp. 113408, 2023. DOI: 10.1016/j.oceaneng.2022.113408.
  • J. Lu, W. Liu, and Y. Zhao, Anisotropy in electrochemical jet texturing of rolled stainless steel SUS304, Mater. Des., vol. 215, pp. 110500, 2022. DOI: 10.1016/j.matdes.2022.110500.
  • T. Tang, Q. Shi, B. Lei, J. Zhou, Y. Gao, Y. Li, G. Zhang, and G. Chen, Transition of interfacial friction regime and its influence on thermal responses in rotary friction welding of SUS304 stainless steel: A fully coupled transient thermomechanical analysis, J. Manuf. Process., vol. 82, pp. 403–414, 2022. DOI: 10.1016/j.jmapro.2022.08.016.
  • H. He, W. Tian, J. Li, K. Shi, M. Sun, and J. Li, Failure analysis and finite element simulation on service conditions of SUS304 stainless steel, J. Mater. Eng. Perform., vol. 30, no. 8, pp. 5987–5999, 2021. DOI: 10.1007/s11665-021-05744-x.
  • Q. Zheng, X. Zhuang, and Z. Zhao, Flow behavior of SUS304 stainless steel under a wide range of forming temperatures and strain rates, Metal. Mater. Trans. A, vol. 52, no. 12, pp. 5200–5214, 2021. DOI: 10.1007/s11661-021-06447-7.
  • J. Sakamoto, N. Tada, and T. Uemori, Effect of resin lamination on tensile strength characteristics of SUS304 stainless steel thin film, Int. J. Adv. Manuf. Technol., vol. 116, no. 3–4, pp. 1081–1088, 2021. DOI: 10.1007/s00170-021-07510-8.
  • B. Cao, T. Iwamoto, and P.P. Bhattacharjee, An experimental study on strain-induced martensitic transformation behavior in SUS304 austenitic stainless steel during higher strain rate deformation by continuous evaluation of relative magnetic permeability, Mater. Sci. Eng. A, vol. 774, pp. 138927, 2020. DOI: 10.1016/j.msea.2020.138927.
  • D. Savastru, S. Miclos, R. Savastru, and I.I. Lancranjan, Analysis of mechanical vibrations applied on a LPGFS smart composite polymer material, Compos. Struct., vol. 226, pp. 111243, 2019. DOI: 10.1016/j.compstruct.2019.111243.
  • M.M. Shahzamanian, A. Partovi, and P.D. Wu, Finite element analysis of elastic–plastic and fracture behavior in functionally graded materials (FGMs), SN Appl. Sci., vol. 2, no. 12, pp. 2135, 2020. DOI: 10.1007/s42452-020-03901-w.
  • M. Bayat, I.M. Alarifi, A.A. Khalili, T.M.A.A. El-Bagory, H.M. Nguyen, and A. Asadi, Thermo-mechanical contact problems and elastic behaviour of single and double sides functionally graded brake disks with temperature-dependent material properties, Sci. Rep., vol. 9, no. 1, pp. 15317, 2019. DOI: 10.1038/s41598-019-51450-z.
  • D. Kumar, D. Kumar, A.M. Tigga, and D. Sagar, Synthesis of Al-B4C functionally graded materials by sound-wave-assisted vibrational casting methodology, J. Mater. Eng. Perform., 2022. DOI: 10.1007/s11665-022-07640-4.
  • L. Hadji, N. Zouatnia, and A. Kassoul, Wave propagation in functionally graded beams using various higher-order shear deformation beams theories, Struct. Eng. Mech., vol. 62, no. 2, pp. 143–149, 2017. DOI: 10.12989/sem.2017.62.2.143.
  • S.A. Yahia, H.A. Atmane, M.S.A. Houari, and A. Tounsi, Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories, Struct. Eng. Mech., vol. 53, no. 6, pp. 1143–1165, 2015. DOI: 10.12989/sem.2015.53.6.1143.
  • L. Hadji, M. Avcar, and N. Zouatnia, Natural frequency analysis of imperfect FG sandwich plates resting on Winkler-Pasternak foundation, Mater. Today Proc., vol. 53, pp. 153–160, 2022. DOI: 10.1016/j.matpr.2021.12.485.
  • L. Sun, G. Grasselli, Q. Liu, and X. Tang, Thermal cracking simulation of functionally graded materials using the combined finite–discrete element method, Comp. Part. Mech., vol. 7, no. 5, pp. 903–917, 2020. DOI: 10.1007/s40571-019-00290-9.
  • T. Wu, Y. Hu, S. Wang, Y. Leng, and M. Wang, Effect of SiC content and interlayer difference on microstructural characterization and mechanical properties of functionally graded 6061Al/SiCp composites, Appl. Phys. A, vol. 126, no. 9, pp. 673, 2020. DOI: 10.1007/s00339-020-03848-0.
  • A. Ouldyerou, H. Mehboob, A. Merdji, L. Aminallah, A. Mehboob, and O.M. Mukdadi, Biomechanical analysis of printable functionally graded material (FGM) dental implants for different bone densities, Comput. Biol. Med., vol. 150, pp. 106111, 2022. DOI: 10.1016/j.compbiomed.2022.106111.
  • D.M. Sangeetha, D.T. Naveenkumar, V. Vınaykumar, and K.E. Prakash, Temperature stresses in Functionally graded (FGM) material plates using deformation theory – Analytical approach, Mater. Today Proc., vol. 49, pp. 1936–1941, 2022. DOI: 10.1016/j.matpr.2021.08.130.
  • A. Pasha, and R. B.m, Functionally graded materials (FGM) fabrication and its potential challenges & applications, Mater. Today Proc., vol. 52, pp. 413–418, 2022. DOI: 10.1016/j.matpr.2021.09.077.
  • M. Luginina, D. Angioni, S. Montinaro, R. Orrú, G. Cao, R. Sergi, D. Bellucci, and V. Cannillo, Hydroxyapatite/bioactive glass functionally graded materials (FGM) for bone tissue engineering, J. Eur. Ceram. Soc., vol. 40, no. 13, pp. 4623–4634, 2020. DOI: 10.1016/j.jeurceramsoc.2020.05.061.
  • Y. Sitli, K. Mhada, O. Bourihane, and H. Rhanim, Buckling and post-buckling analysis of a functionally graded material (FGM) plate by the Asymptotic Numerical Method, Structures, vol. 31, pp. 1031–1040, 2021. DOI: 10.1016/j.istruc.2021.01.100.
  • X.W. Chen, and Z.Q. Yue, Contact mechanics of two elastic spheres reinforced by functionally graded materials (FGM) thin coatings, Eng. Anal. Bound. Elem., vol. 109, pp. 57–69, 2019. DOI: 10.1016/j.enganabound.2019.09.009.
  • X. Xiao, Q. Zhang, J. Zheng, and Z. Li, Analytical model for the nonlinear buckling responses of the confined polyhedral FGP-GPLs lining subjected to crown point loading, Eng. Struct., vol. 282, pp. 115780, 2023. DOI: 10.1016/j.engstruct.2023.115780.
  • M. Avcar, and W.K.M. Mohammed, Free vibration of functionally graded beams resting on Winkler-Pasternak foundation, Arab. J. Geosci., vol. 11, no. 10, pp. 232, 2018. DOI: 10.1007/s12517-018-3579-2.
  • W.-Y. Jung, and S.-C. Han, Analysis of sigmoid functionally graded material (S-FGM) nanoscale plates using the nonlocal elasticity theory, Math. Probl. Eng., vol. 2013, pp. 1–10, 2013. () DOI: 10.1155/2013/476131.
  • M. Hosseini, M.R. Mofidi, A. Jamalpoor, and M. Safi Jahanshahi, Nanoscale mass nanosensor based on the vibration analysis of embedded magneto-electro-elastic nanoplate made of FGMs via nonlocal Mindlin plate theory, Microsyst. Technol., vol. 24, no. 5, pp. 2295–2316, 2018. DOI: 10.1007/s00542-017-3654-8.
  • M.S.H. Al-Furjan, M.X. Xu, A. Farrokhian, G.S. Jafari, X. Shen, and R. Kolahchi, On wave propagation in piezoelectric-auxetic honeycomb-2D-FGM micro-sandwich beams based on modified couple stress and refined zigzag theories, Waves Random Complex Medium, pp. 1–25, 2022. DOI: 10.1080/17455030.2022.2030499.
  • A. Vahidi-Moghaddam, M.R. Hairi-Yazdi, and R. Vatankhah, Analytical solution for nonlinear forced vibrations of functionally graded micro resonators, Mech. Based Des. Struct. Mach., vol. 51, no. 3, pp. 1543–1562, 2023. DOI: 10.1080/15397734.2021.1873802.
  • Z.-Q. Lu, D.-H. Gu, H. Ding, W. Lacarbonara, and L.-Q. Chen, Nonlinear vibration isolation via a circular ring, Mech. Syst. Signal Process., vol. 136, pp. 106490, 2020. DOI: 10.1016/j.ymssp.2019.106490.
  • F. Ebrahimi, and M.R. Barati, Small-scale effects on hygro-thermo-mechanical vibration of temperature-dependent nonhomogeneous nanoscale beams, Mech. Adv. Mater. Struct., vol. 24, no. 11, pp. 924–936, 2017. DOI: 10.1080/15376494.2016.1196795.
  • F. Ebrahimi, and M.R. Barati, Vibration analysis of parabolic shear-deformable piezoelectrically actuated nanoscale beams incorporating thermal effects, Mech. Adv. Mater. Struct., vol. 25, no. 11, pp. 917–929, 2018. DOI: 10.1080/15376494.2017.1323141.
  • M. Lori Dehsaraji, A. Loghman, and M. Arefi, Three-dimensional thermo-electro-mechanical buckling analysis of functionally graded piezoelectric micro/nano-shells based on modified couple stress theory considering thickness stretching effect, Mech. Adv. Mater. Struct., vol. 28, no. 19, pp. 2030–2045, 2021. DOI: 10.1080/15376494.2020.1716419.
  • P. Wang, P. Yuan, S. Sahmani, and B. Safaei, Size-dependent nonlinear harmonically soft excited oscillations of nonlocal strain gradient FGM composite truncated conical microshells with magnetostrictive facesheets, Mech. Based Des. Struct. Mach., vol. 51, no. 1, pp. 1–27, 2023. DOI: 10.1080/15397734.2021.1903495.
  • M.F. Ahari, and M. Ghadiri, Resonator vibration of a magneto-electro-elastic nano-plate integrated with FGM layer subjected to the nano mass-Spring-damper system and a moving load, Waves Random Complex Medium, pp. 1–39, 2022. DOI: 10.1080/17455030.2022.2053233.
  • L. Guo, X. Xin, D. Shahsavari, and B. Karami, Dynamic response of porous E-FGM thick microplate resting on elastic foundation subjected to moving load with acceleration, Thin-Walled Struct., vol. 173, pp. 108981, 2022. DOI: 10.1016/j.tws.2022.108981.
  • M.W.T. Mak, and J.M. Lees, Carbon reduction and strength enhancement in functionally graded reinforced concrete beams, Eng. Struct., vol. 277, pp. 115358, 2023. DOI: 10.1016/j.engstruct.2022.115358.
  • H. Lazreg, B. Fabrice, M. Royal, A. Ali, and G.M. Hassan, Bending and buckling of porous multidirectional functionality graded sandwich plate, Struct. Eng. Mech., vol. 85, pp. 233–246, 2023. DOI: 10.12989/SEM.2023.85.2.233.
  • R. Elloumi, S. El-Borgi, M.A. Guler, and I. Kallel-Kamoun, The contact problem of a rigid stamp with friction on a functionally graded magneto-electro-elastic half-plane, Acta Mech., vol. 227, no. 4, pp. 1123–1156, 2016. DOI: 10.1007/s00707-015-1504-2.
  • V. Mahesh, and S.A. Ponnusami, Nonlinear damped transient response of sandwich auxetic plates with porous magneto-electro-elastic facesheets, Eur. Phys. J. Plus, vol. 137, no. 5, pp. 563, 2022. DOI: 10.1140/epjp/s13360-022-02756-x.
  • H. Gao, X. Huang, X. Ma, X. Li, L. Guo, and H. Yang, An ultra-wideband coding polarizer for beam control and RCS reduction, Front. Phys., vol. 18, no. 4, pp. 42301, 2023. DOI: 10.1007/s11467-022-1252-4.
  • M.C. Kiran, and S. Kattimani, Assessment of vibrational frequencies and static characteristics of multilayered skew magneto-electro-elastic plates: a finite element study, Iran J. Sci. Technol. Trans. Mech. Eng., vol. 44, no. 1, pp. 61–82, 2020. DOI: 10.1007/s40997-018-0250-1.
  • S.Q. Zhang, Y.F. Zhao, X. Wang, M. Chen, and R. Schmidt, Static and dynamic analysis of functionally graded magneto-electro-elastic plates and shells, Compos. Struct., vol. 281, pp. 114950, 2022. DOI: 10.1016/j.compstruct.2021.114950.
  • I. Esen, and R. Özmen, Thermal vibration and buckling of magneto-electro-elastic functionally graded porous nanoplates using nonlocal strain gradient elasticity, Compos. Struct., vol. 296, pp. 115878, 2022. DOI: 10.1016/j.compstruct.2022.115878.
  • X. Yu, X. Fan, and X. Bi, Size-dependent frequency analysis of the magneto-electro-elastic rotary microdisk by incorporating modified couple stress and higher-order shear deformation theories, Mech. Based Des. Struct. Mach., vol. 51, no. 4, pp. 1822–1841, 2023. DOI: 10.1080/15397734.2021.1878904.
  • D.T.D. Nguyen, F. Javidan, M. Attar, S. Natarajan, Z. Yang, E.H. Ooi, C. Song, and E.T. Ooi, Fracture analysis of cracked magneto-electro-elastic functionally graded materials using scaled boundary finite element method, Theor. Appl. Fract. Mech., vol. 118, pp. 103228, 2022. DOI: 10.1016/j.tafmec.2021.103228.
  • Z. Li, Q. Wang, B. Qin, R. Zhong, and H. Yu, Vibration and acoustic radiation of magneto-electro-thermo-elastic functionally graded porous plates in the multi-physics fields, Int. J. Mech. Sci., vol. 185, pp. 105850, 2020. DOI: 10.1016/j.ijmecsci.2020.105850.
  • A. Sharma, Effect of porosity on active vibration control of smart structure using porous functionally graded piezoelectric material, Compos. Struct., vol. 280, pp. 114815, 2022. DOI: 10.1016/j.compstruct.2021.114815.
  • Y. Gogotsi, Nanomaterials Handbook. Advanced Materials and Technologies Series, 2nd edition. CRC Press, Boca Raton, 2017. DOI: 10.1201/9781315371795.
  • K. Gao, Q. Huang, S. Kitipornchai, and J. Yang, Nonlinear dynamic buckling of functionally graded porous beams, Mech. Adv. Mater. Struct., vol. 28, no. 4, pp. 418–429, 2021. DOI: 10.1080/15376494.2019.1567888.
  • N. Wattanasakulpong, and V. Ungbhakorn, Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities, Aerosp. Sci. Technol., vol. 32, no. 1, pp. 111–120, 2014. DOI: 10.1016/j.ast.2013.12.002.
  • F. Ebrahimi, F. Ghasemi, and E. Salari, Investigating thermal effects on vibration behavior of temperature-dependent compositionally graded Euler beams with porosities, Meccanica, vol. 51, no. 1, pp. 223–249, 2016. DOI: 10.1007/s11012-015-0208-y.
  • K. Li, D. Wu, X. Chen, J. Cheng, Z. Liu, W. Gao, and M. Liu, Isogeometric Analysis of functionally graded porous plates reinforced by graphene platelets, Compos. Struct., vol. 204, pp. 114–130, 2018. DOI: 10.1016/j.compstruct.2018.07.059.
  • Y.S. Touloukian, Thermophysical Properties of High Temperature Solid Materials. Macmillan, New York, 1967.
  • Y.S. Touloukian, Thermophysical Properties of High Temperature Solid Materials. Volume 4. Oxides and Their Solutions and Mixtures. Part 1, vol 1. Macmillan, New York, 1966.
  • Y. Kiani, and M.R. Eslami, An exact solution for thermal buckling of annular FGM plates on an elastic medium, Compos. Part B Eng., vol. 45, no. 1, pp. 101–110, 2013. DOI: 10.1016/j.compositesb.2012.09.034.
  • D.G. Zhang, Thermal post-buckling and nonlinear vibration analysis of FGM beams based on physical neutral surface and high order shear deformation theory, Meccanica, vol. 49, no. 2, pp. 283–293, 2014. DOI: 10.1007/s11012-013-9793-9.
  • A.C. Eringen, Theories of nonlocal plasticity, Int. J. Eng. Sci., vol. 21, no. 7, pp. 741–751, 1983. DOI: 10.1016/0020-7225(83)90058-7.
  • C.W. Lim, G. Zhang, and J.N. Reddy, A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation, J. Mech. Phys. Solids., vol. 78, pp. 298–313, 2015. DOI: 10.1016/j.jmps.2015.02.001.
  • L. Li, X. Li, and Y. Hu, Free vibration analysis of nonlocal strain gradient beams made of functionally graded material, Int. J. Eng. Sci., vol. 102, pp. 77–92, 2016. DOI: 10.1016/j.ijengsci.2016.02.010.
  • A. Farajpour, and A. Rastgoo, Influence of carbon nanotubes on the buckling of microtubule bundles in viscoelastic cytoplasm using nonlocal strain gradient theory, Results Phys., vol. 7, pp. 1367–1375, 2017. DOI: 10.1016/j.rinp.2017.03.038.
  • A.C. Eringen, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, J. Appl. Phys., vol. 54, no. 9, pp. 4703–4710, 1983. DOI: 10.1063/1.332803.
  • K.K. Żur, M. Arefi, J. Kim, and J.N. Reddy, Free vibration and buckling analyses of magneto-electro-elastic FGM nanoplates based on nonlocal modified higher-order sinusoidal shear deformation theory, Compos. Part B Eng., vol. 182, pp. 107601, 2020. DOI: 10.1016/j.compositesb.2019.107601.
  • J.N. Reddy, C.M. Wang, and S. Kitipornchai, Axisymmetric bending of functionally graded circular and annular plates, Eur. J. Mech. A/Solids, vol. 18, no. 2, pp. 185–199, 1999. DOI: 10.1016/S0997-7538(99)80011-4.
  • E. Pan, and P.R. Heyliger, Free vibrations of simply supported and multilayered magneto-electro-elastic plates, J. Sound Vib., vol. 252, no. 3, pp. 429–442, 2002. DOI: 10.1006/jsvi.2001.3693.
  • M. Arefi, and A.M. Zenkour, A simplified shear and normal deformations nonlocal theory for bending of functionally graded piezomagnetic sandwich nanobeams in magneto-thermo-electric environment, J. Sandwich Struct. Mater., vol. 18, no. 5, pp. 624–651, 2016. DOI: 10.1177/1099636216652581.
  • M. Arefi, and A.M. Zenkour, Free vibration analysis of a three-layered microbeam based on strain gradient theory and three-unknown shear and normal deformation theory, Steel Compos. Struct., vol. 26, pp. 421–437, 2018. DOI: 10.12989/scs.2018.26.4.421.
  • J.N. Reddy, Energy principles and variational methods. In: Theory and Analysis of Elastic Plates and Shells, CRC Press, Boca Raton, 2020. DOI: 10.1201/9780849384165-6.
  • G.T. Monaco, N. Fantuzzi, F. Fabbrocino, and R. Luciano, Critical temperatures for vibrations and buckling of magneto-electro-elastic nonlocal strain gradient plates, Nanomaterials, vol. 11, pp. 1–18, 2021. DOI: 10.3390/nano11010087.
  • F. Ramirez, P.R. Heyliger, and E. Pan, Discrete layer solution to free vibrations of functionally graded magneto-electro-elastic plates, Mech. Adv. Mater. Struct., vol. 13, no. 3, pp. 249–266, 2006. DOI: 10.1080/15376490600582750.
  • R. Aghababaei, and J.N. Reddy, Nonlocal third-order shear deformation plate theory with application to bending and vibration of plates, J. Sound Vib., vol. 326, no. 1–2, pp. 277–289, 2009. DOI: 10.1016/j.jsv.2009.04.044.
  • J.N. Reddy, and C.D. Chin, Thermomechanical analysis of functionally graded cylinders and plates, J. Thermal Stress., vol. 21, no. 6, pp. 593–626, 1998. DOI: 10.1080/01495739808956165.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.