Higher order shear deformation bending results of a magnetoelectrothermoelastic functionally graded nanobeam in thermal, mechanical, electrical, and magnetic environments

References

• Arefi, M., G. H. Rahimi, M. J. Khoshgoftar. 2011. Optimized design of a cylinder under mechanical, magnetic and thermal loads as a sensor or actuator using a functionally graded piezomagnetic material. International Journal of Physical Sciences 6 (27):6315–6322. doi:10.5897/IJPS10.597.
   Google Scholar
• Ansari, R., R. Gholami, and H. Rouhi. 2015a. Size-dependent nonlinear forced vibration analysis of magneto-electro-thermo-elastic Timoshenko nanobeams based upon the nonlocal elasticity theory. Composite Structures 126:216–226. doi:10.1016/j.compstruct.2015.02.068.
   Web of Science ®Google Scholar
• Ansari, R., E. Hasrati, R. Gholami, and F. Sadeghi. 2015b. Nonlinear analysis of forced vibration of nonlocal third-order shear deformable beam model of magneto-electro-thermo elastic nanobeams. Composites Part B 83:226–241. doi:10.1016/j.compositesb.2015.08.038.
   Web of Science ®Google Scholar
• Ansari, R., and R. Gholami. 2016. Nonlocal free vibration in the pre and post buckled states of magneto-electro-thermo elastic rectangular nanoplates with various edge conditions. Smart Materials and Structures 25:095033 (17pp). doi:10.1088/0964-1726/25/9/095033.
   Web of Science ®Google Scholar
• Arefi, M. 2014. A complete set of equations for piezo-magnetoelastic analysis of a functionally graded thick shell of revolution. Latin American Journal of Solids and Structures 11 (11):2073–2092. doi:10.1590/S1679-78252014001100009.
   Web of Science ®Google Scholar
• Arefi, M. 2016. Analysis of wave in a functionally graded magneto-electroelasticnano-rod using nonlocal elasticity model subjected to electric and magnetic potentials. Acta Mechanica 228 (2):475–493. doi:10.1007/s00707-016-1584-7.
   Google Scholar
• Arefi, M. 2016a, Surface effect and non-local elasticity in wave propagation of functionally graded piezoelectric nano-rod excited to applied voltage. Applied Mathematics and Mechanics (English Edition) 37 (3):289–302.
   Google Scholar
• Arefi, M., and A. M. Zenkour. 2016. Free vibration, wave propagation and tension analyses of a sandwich micro/nano rod subjected to electric potential using strain gradient theory. Materials Research Express 3 (11):115704. doi:10.1088/2053-1591/3/11/115704.
   Web of Science ®Google Scholar
• Arefi, M., and Zenkour, A. M. 2017. Thermo-electro-magneto-mechanical bending behavior of size-dependent sandwich piezomagnetic nanoplates. Mechanics Research Communications 84:27–42. doi:10.1016/j.mechrescom.2017.06.002.
   Web of Science ®Google Scholar
• Arefi, M., and A. M. Zenkour. 2017a. Wave propagation analysis of a functionally graded magneto-electro-elastic nanobeam rest on visco-Pasternak foundation. Mechanics Research Communications 79:51–62. doi:10.1016/j.mechrescom.2017.01.004.
   Web of Science ®Google Scholar
• Arefi, M., and A. M. Zenkour. 2017b. Influence of micro-length-scale parameters and inhomogeneities on the bending, free vibration and wave propagation analyses of a FG Timoshenko’s sandwich piezoelectric microbeam. Journal of Sandwich Structures & Materials. doi:1099636217714181.
   Google Scholar
• Arefi, M., and A. M. Zenkour. 2017c. Effect of thermo-magneto-electro-mechanical fields on the bending behaviors of a three-layered nanoplate based on sinusoidal shear-deformation plate theory. Journal of Sandwich Structures & Materials. doi:1099636217697497.
   Google Scholar
• Arefi, M., and A. M. Zenkour. 2017d. Thermo-electro-mechanical bending behavior of sandwich nanoplate integrated with piezoelectric face-sheets based on trigonometric plate theory. Composite Structures 162:108–122. doi:10.1016/j.compstruct.2016.11.071.
   Web of Science ®Google Scholar
• Arefi, M., and A. M. Zenkour. 2017e. Sizedependent vibration and bending analyses of the piezomagnetic three-layer nanobeams. Applied Physics A, 123, 202.
   Web of Science ®Google Scholar
• Bhangale, R. K., and N. Ganesan. 2005. Free vibration studies of simply supported non-homogeneous functionally graded magneto-electro-elastic finite cylindrical shells. Journal of Sound and Vibration 288:412–422. doi:10.1016/j.jsv.2005.04.008.
   Web of Science ®Google Scholar
• Bhangale, R. K., and N. Ganesan. 2006. Static analysis of simply supported functionally graded and layered magneto-electro-elastic plates. International Journal of Solids and Structures 43:3230–3253. doi:10.1016/j.jsv.2005.12.030.
   Web of Science ®Google Scholar
• Bin, W., Y. Jiangong, and H. Cunfu. 2008. Wave propagation in non-homogeneous magneto-electro-elastic plates. Journal of Sound and Vibration 317:250–264. doi:10.1016/j.jsv.2008.03.008.
   Web of Science ®Google Scholar
• Cheng, L. 2017. Nonlocal thermo-electro-mechanical coupling vibrations of axially moving piezoelectric nanobeams. Mechanics Based Design of Structures and Machines 45 (4):463–478. doi:10.1080/15397734.2016.1242079.
   Web of Science ®Google Scholar
• Ebrahimi, F., and E. Salari. 2015. Thermal buckling and free vibration analysis of size dependent Timoshenko FG nanobeams in thermal environments. Composite Structures 128:363–380. doi:10.1016/j.compstruct.2015.03.023.
   Web of Science ®Google Scholar
• Ebrahimi, F., and M. R. Barati. 2017. Buckling analysis of smart size-dependent higher order magneto-electro-thermo-elastic functionally graded nanosize beams. Journal of Mechanics 33 (1):23–33. doi:10.1017/jmech.2016.46.
   Web of Science ®Google Scholar
• Eringen, A. C. 1972. Nonlocal polar elastic continua. International Journal of Engineering Science 10:1–16. doi:10.1016/0020-7225(72)90070-5.
   Web of Science ®Google Scholar
• Eringen, A. C. 1983. On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. Journal of Applied Physics 54:4703–4710. doi:10.1063/1.332803.
   Web of Science ®Google Scholar
• Eringen, A. C. 2002. Nonlocal continuum field theories. Springer Science & Business Media. Springer-Verlag New York.
   Google Scholar
• Ghadiri, M., and H. Safarpour. 2016. Free vibration analysis of embedded magneto-electro-thermoelastic cylindrical nanoshell based on the modified couple stress theory. Applied Physics A 122:833. doi:10.1007/s00339-016-0365-4.
   Web of Science ®Google Scholar
• Ghorbanpour Arani, A., M. Salari, H. Khademizadeh, and A. Arefmanesh. 2009. Magneto thermoelastic transient response of a functionally graded thick hollow sphere subjected to magnetic and thermoelastic fields. Archive of Applied Mechanics 79:481–497. doi:10.1007/s00419-008-0247-0.
   Web of Science ®Google Scholar
• Ghorbanpour Arani, A., E. Haghparast, Z. Khoddami Maraghi, and S. Amir. 2014. CNTRC cylinder under non-axisymmetric thermo-mechanical loads and uniform electromagnetic fields. Arabian Journal for Science & Engineering 39 (12):9057–9069. doi:10.1007/s13369-014-1419-6 (Springer Science & Business Media BV).
   Web of Science ®Google Scholar
• He, S.-R., and Q. Guan. 2006. Three dimensional analysis of piezoelectric/piezomagnetic and elastic media. Mechanics Based Design of Structures and Machines 34 (2):201–212. doi:10.1080/15397730600773973.
   Web of Science ®Google Scholar
• Huang, D. J., H. J. Ding, and W. Q. Chen. 2010. Static analysis of anisotropic functionally graded magneto-electro-elastic beams subjected to arbitrary loading. European Journal of Mechanics A/Solids 29:356–369. doi:10.1016/j.euromechsol.2009.12.002.
   Web of Science ®Google Scholar
• Jianguo, D., C. Liang, X. Libiao, and D. Guansuo. 2018. Nonlinear vibration analysis of functionally graded beams considering the influences of the rotary inertia of the cross section and neutral surface position. Mechanics Based Design of Structures and Machines 46 (2):225–237. doi:10.1080/15397734.2017.1329020.
   Web of Science ®Google Scholar
• Ke, L. L., and Y. S. Wang. 2014. Free vibration of size-dependent magneto-electro-elastic nanobeams based on the nonlocal theory. Physica E 63:52–61. doi:10.1007/s10409-014-0072-3.
   Google Scholar
• Ke, L. L., Y. S. Wang, J. Yang, and S. Kitipornchai. 2014a. Free vibration of size-dependent magneto-electro-elastic nanoplates based on the nonlocal theory. Acta Mechanica Sinica 30 (4):516–525. doi:10.1007/s10409-014-0072-3.
   Web of Science ®Google Scholar
• Ke, L. L., Y. S. Wang, and J. N. Reddy. 2014. Thermo-electro-mechanical vibration of size dependent piezoelectric cylindrical nanoshells under various boundary conditions. Composite Structures 116:626–636. doi:10.1016/j.compstruct.2014.05.048.
   Web of Science ®Google Scholar
• Ke, L. L., Y. S. Wang, J. Yang, and S. Kitipornchai. 2014b. The size dependent vibration of embedded magneto-electro-elastic cylindrical nanoshells. Smart Materials and Structures 23:125036 (17pp). doi:10.1088/0964-1726/23/12/125036.
   Web of Science ®Google Scholar
• Kim, J., and J. N. Reddy. 2013. Analytical solutions for bending, vibration, and buckling of FGM plates using a couple stress-based third-order theory. Composite Structures 03:86–98. doi:10.1016/j.compstruct.2013.03.007.
   Google Scholar
• Kumaravel, A., N. Ganesan, and S. Swarnamani. 2007a. Free vibration behavior of multiphase and layered magneto-electro-elastic beam. Journal of Sound and Vibration 299:44–63. doi:10.1016/j.jsv.2006.06.044.
   Web of Science ®Google Scholar
• Kumaravel, A., N. Ganesan, and R. Sethuraman. 2007b. Buckling and vibration analysis of layered and multiphase magneto-electro-elastic beam under thermal environment. Multidiscipline Modeling in Materials and Structures 3 (4):461–476. doi:10.1163/157361107782106401.
   Google Scholar
• Lang, Z., and L. Xuewu. 2013. Buckling and vibration analysis of functionally graded magneto-electro-thermo-elastic circular cylindrical shells. Applied Mathematical Modelling 37:2279–2292. doi:10.1016/j.apm.2012.05.023.
   Web of Science ®Google Scholar
• Larbi, L. O., A. Kaci, M. S. A. Houari, and A. Tounsi. 2013. An efficient shear deformation beam theory based on neutral surface position for bending and free vibration of functionally graded beams. Mechanics Based Design of Structures and Machines 41 (4):421–433. doi:10.1080/15397734.2013.763713.
   Web of Science ®Google Scholar
• Li, Y. S., Z. Y. Cai, and S. Y. Shi. 2014. Buckling and free vibration of magneto electro elastic nanoplate based on nonlocal theory. Composite Structures 111:522–529. doi:10.1016/j.compstruct.2014.01.033.
   Web of Science ®Google Scholar
• Li, Y. S., P. Ma, and W. Wang. 2015. Bending, buckling, and free vibration of magneto electro elastic nanobeam based on nonlocal theory. Journal of Intelligent Material Systems and Structures 27 (9):1139–1149. doi:10.1177/1045389x15585899.
   Web of Science ®Google Scholar
• Liu, C., L. L. Ke, Y. S. Wang, J. Yang, and S. Kitipornchai. 2013. Thermo-electro-mechanical vibration of piezoelectric nanoplates based on the nonlocal theory. Composite Structures 106:167–174. doi:10.1016/j.compstruct.2013.05.031.
   Web of Science ®Google Scholar
• Lotey, G. S., and N. Verma. 2013. Magnetoelectric coupling in multiferroic BiFeOU nanowires. Chemical Physics Letters 579:78–84. doi:10.1080/00150193.2012.675272.
   Web of Science ®Google Scholar
• Mohammadimehr, M., S. V. Okhravi, and S. M. AkhavanAlavi. 2016. Free vibration analysis of magneto-electro-elastic cylindrical composite panel reinforced by various distributions of CNTs with considering open and closed circuits boundary conditions based on FSDT. Journal of Vibration and Control 288:412–422. doi:10.1177/1077546316664022.
   Google Scholar
• Pan, E. 2001. Exact solution for simply supported and multilayered magneto-electro elastic plates. Journal of Applied Mechanics 68:608–618. doi:10.1115/1.1380385.
   Web of Science ®Google Scholar
• Pan, E., and F. Han. 2005. Exact solution for functionally graded and layered magneto-electro-elastic plates. International Journal of Engineering Science 43:321–339. doi:10.1016/j.ijengsci.2004.09.006.
   Web of Science ®Google Scholar
• Pan, E., and N. Waksmanski. 2016. Deformation of a layered magnetoelectroelastic simply-supported plate with nonlocal effect, an analytical three-dimensional solution. Smart Materials and Structures 25:095013 (17pp). doi:10.1088/0964-1726/25/9/095013.
   Web of Science ®Google Scholar
• Rahimi, G. H., M. Arefi, and M. J. Khoshgoftar. 2012. Electro elastic analysis of a pressurized thick-walled functionally graded piezoelectric cylinder using the first order shear deformation theory and energy method. Mechanika 18 (3):292–300. doi:10.5755/j01.mech.18.3.1875.
   Google Scholar
• Ramirez, F., P. R. Heyliger, and E. Pan. 2006. Free vibration response of two-dimensional magneto-electro-elastic laminated plates. Journal of Sound and Vibration 292:626–644. doi:10.1016/j.jsv.2005.08.004.
   Web of Science ®Google Scholar
• Reddy, J. N. 2007. Nonlocal theories for bending, buckling and vibration of beams. International Journal of Engineering Science 45:288–307. doi:10.1016/j.ijengsci.2007.04.004.
   Web of Science ®Google Scholar
• Şimşek, M., and H. H. Yurtcu. 2013. Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory. Composite Structures 97:378–386. doi:10.1016/j.compstruct.2012.10.038.
   Web of Science ®Google Scholar
• Sladek, J., V. Sladek, P. Solek, and Ch. Zhang. 2010. Fracture analysis in continuously nonhomogeneous magneto-electro-elastic solids under a thermal load by the MLPG. International Journal of Solids and Structures 47:1381–1391. doi:10.1016/j.ijsolstr.2010.01.025.
   Web of Science ®Google Scholar
• Sofiyev, A., H. Hui, A. Valiyev, F. Kadioglu, S. Turkaslan, G. Q. Yuan, V. Kalpakci, and A. Özdemir. 2015. Effects of shear stresses and rotary inertia on the stability and vibration of sandwich cylindrical shells with FGM core surrounded by elastic medium. Mechanics Based Design of Structures and Machines 44 (4):384–404. doi:10.1080/15397734.2015.1083870.
   Web of Science ®Google Scholar
• Sharma, S., R. Vig, and N. Kumar. 2016. Finite element modeling of smart piezo structure: Considering dependence of piezoelectric coefficients on electric field. Mechanics Based Design of Structures and Machines 44 (4):372–383. doi:10.1080/15397734.2015.1076728.
   Web of Science ®Google Scholar
• Tong, Z. H., S. H. Lo, C. P. Jiang, and Y. K. Cheung. 2008. An exact solution for the three-phase thermo-electro-magneto-elastic cylinder model and its application to piezoelectric–magnetic fiber composites. International Journal of Solids and Structures 45:5205–5219. doi:10.1016/j.ijsolstr.2008.04.003.
   Web of Science ®Google Scholar
• Tufekci, E., U. Eroglu, and A. Serhan. 2016. Exact solution for in-plane static problems of circular beams made of functionally graded materials. Mechanics Based Design of Structures and Machines 44 (4):476–494. doi:10.1080/15397734.2015.1121398.
   Web of Science ®Google Scholar
• Vaezi, M., M. Moory Shirbani, and A. Hajnayeb. 2016. Free vibration analysis of magneto-electro-elastic microbeams subjected to magneto-electric loads. Physica E 75:280–286. doi:10.1016/j.physe.2015.09.019.
   Google Scholar
• Wu, C. P., and Y. H. Tsai. 2007. Static behavior of functionally graded magneto-electro-elastic shells under electric displacement and magnetic flux. International Journal of Engineering Science 45:744–769. doi:10.1016/j.ijengsci.2007.05.002.
   Web of Science ®Google Scholar
• Wang, X., X. Liang, and Ch. Jin. 2016. Accurate dynamic analysis of functionally graded beams under a moving point load. Mechanics Based Design of Structures and Machines 45 (1):76–91. doi:10.1080/15397734.2016.1145060.
   Web of Science ®Google Scholar
• Xin, L., and Z. Hu. 2015. Free vibration of layered magneto-electro-elastic beams by SS-DSC approach. Composite Structures 125:96–103. doi:10.1016/j.compstruct.2015.01.048.
   Web of Science ®Google Scholar
• Yuda, H., and Z. Xiaoguang. 2011. Parametric vibrations and stability of a functionally graded plate. Mechanics Based Design of Structures and Machines 39 (3):367–377. doi:10.1080/15397734.2011.557970.
   Web of Science ®Google Scholar
• Zenkour, A. M., and M. Arefi. 2017. Nonlocal transient electrothermomechanical vibration and bending analysis of a functionally graded piezoelectric single-layered nanosheet rest on visco-Pasternak foundation. Journal of Thermal Stresses 40 (2):167–184. doi:10.1080/01495739.2016.1229146.
   Web of Science ®Google Scholar