Browse > Article
http://dx.doi.org/10.12989/sem.2020.73.5.565

Thermo-electro-elastic nonlinear stability analysis of viscoelastic double-piezo nanoplates under magnetic field  

Ebrahimi, Farzad (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University)
Hosseini, S. Hamed S. (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University)
Selvamani, Rajendran (Department of mathematics, Karunya Institute of Technology and Sciences)
Publication Information
Structural Engineering and Mechanics / v.73, no.5, 2020 , pp. 565-584 More about this Journal
Abstract
The nonlinear thermo-electro-elastic buckling behavior of viscoelastic nanoplates under magnetic field is investigated based on nonlocal elasticity theory. Employing nonlinear strain-displacement relations, the geometrical nonlinearity is modeled while governing equations are derived through Hamilton's principle and they are solved applying semi-analytical generalized differential quadrature (GDQ) method. Eringen's nonlocal elasticity theory considers the effect of small size, which enables the present model to become effective in the analysis and design of nano-sensors and nano actuators. Based on Kelvin-Voigt model, the influence of the viscoelastic coefficient is also discussed. It is demonstrated that the GDQ method has high precision and computational efficiency in the buckling analysis of viscoelastic nanoplates. The good agreement between the results of this article and those available in literature validated the presented approach. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as electric voltage, small scale effects, elastomeric medium, magnetic field, temperature effects, the viscidity and aspect ratio of the nanoplate on its nonlinear buckling characteristics. It is explicitly shown that the thermo-electro-elastic nonlinear buckling behavior of viscoelastic nanoplates is significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of viscoelastic nanoplates as fundamental elements in nanoelectromechanical systems.
Keywords
small scale effect; nonlinear buckling; double nanoplate; viscoelastic; GDQ;
Citations & Related Records
Times Cited By KSCI : 25  (Citation Analysis)
연도 인용수 순위
1 Ansari, R., Rouhi, H. and Sahmani, S. (2011), "Thermal effect on axial buckling behavior of multi-walled carbon nanotubes based on nonlocal shell model", Physica E Low Dimensional Syst. Nanostruct., 44(2), 373-378. https://doi.org/10.1016/j.physe.2011.08.036.   DOI
2 Mohammadhassani, M., Nezamabadi-Pour, H., Suhatril, M. and Shariati, M. (2013), "Identification of a suitable ANN architecture in predicting strain in tie section of concrete deep beams", Struct. Eng. Mech, 46(6), 853-868. http://dx.doi.org/10.12989/sem.2013.46.6.853.   DOI
3 Moon, F. C. and Pao, Y. H. (1968), "Magnetoelastic buckling of a thin plate", J. Appl. Mech., 35(1), 53-58. https://doi.org/10.1115/1.3601173.   DOI
4 Murmu, T. and Pradhan, S. C. (2009), "Buckling of biaxially compressed orthotropic plates at small scales", Mech. Res. Communications, 36(8), 933-938.   DOI
5 Murmu, T., Sienz, J., Adhikari, S. and Arnold, C. (2013), "Nonlocal buckling of double-nanoplate-systems under biaxial compression", Compos. Part B Eng., 44(1), 84-94. https://doi.org/10.1016/j.compositesb.2012.07.053.   DOI
6 Pietrzakowski, M. (2008), "Piezoelectric control of composite plate vibration: Effect of electric potential distribution", Comput. Struct., 86(9), 948-954. https://doi.org/10.1016/j.compstruc.2007.04.023.   DOI
7 Pradhan, S. C. and Murmu, T. (2010), "Small scale effect on the buckling analysis of single-layered graphene sheet embedded in an elastic medium based on nonlocal plate theory", Physica E Low Dimensional Syst. Nanostruct., 42(5), 1293-1301. https://doi.org/10.1016/j.physe.2009.10.053.   DOI
8 Reddy, J. N. (2010), "Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates", J. Eng. Sci., 48(11), 1507-1518. https://doi.org/10.1016/j.ijengsci.2010.09.020.   DOI
9 Reddy, J. N. and Wang, C. M. (2004), "Dynamics of fluid-conveying beams: governing equations and finite element models", CORE Report No. 2004-03; Centre for Offshore Research and Engineering, Singapore.
10 Arani, A. G. and Zarei, M. S. H. (2014), "Nonlinear nonlocal vibration of an embedded viscoelastic Y-SWCNT conveying viscous fluid under magnetic field using homotopy analysis method", J. Solid Mech., 6(2), 173-193.
11 Arani, A. G., Amir, S., Dashti, P. and Yousefi, M. (2014), "Flowinduced vibration of double bonded visco-CNTs under magnetic fields considering surface effect", Comput. Mater. Sci., 86, 144-154. https://doi.org/10.1016/j.commatsci.2014.01.047.   DOI
12 Arani, A. G., Kolahchi, R., Barzoki, A. A. M., Mozdianfard, M. R. and Farahani, S. M. N. (2013), "Elastic foundation effect on nonlinear thermo-vibration of embedded double-layered orthotropic graphene sheets using differential quadrature method", Proc. Institution of Mechanical Engineers, Part C J. Mech. Eng. Sci., 227(4), 862-879. https://doi.org/10.1177/0954406212453808.   DOI
13 Shahwan, K. W. and Waas, A. M. (1998), "Buckling of unilaterally constrained plates: applications to the study of delaminations in layered structures", J. Franklin Institute, 335(6), 1009-1039. https://doi.org/10.1016/S0016-0032(97)00053-7.   DOI
14 Armaghani, D. J., Mirzaei, F., Shariati, M., Trung, N. T., Shariat, M. and Trnavac, D. (2020), "Hybrid ANN-based techniques in predicting cohesion of sandy-soil combined with fiber", Geomech. Eng., 20(3), 175-189. https://doi.org/10.12989/gae.2020.20.3.175.   DOI
15 Chahnasir, E. S., Zandi, Y., Shariati, M., Dehghani, E., Toghroli, A., Mohamad, E. T., Shariati, A., Safa, M., Wakil, K. and Khorami, M. (2018), "Application of support vector machine with firefly algorithm for investigation of the factors affecting the shear strength of angle shear connectors", Smart Struct. Syst., 22(4), 413-424. https://doi.org/10.12989/sss.2018.22.4.413.   DOI
16 Chattopadhyay, A. and Gu, H. (1994), "New higher order plate theory in modeling delamination buckling of composite laminates", AIAA J., 32(8), 1709-1716. https://doi.org/10.2514/3.12163.   DOI
17 Sedghi, Y., Zandi, Y., Toghroli, A., Safa, M., Mohamad, E. T., Khorami, M. and Wakil, K. "Application of ANFIS technique on performance of C and L shaped angle shear connectors", Smart Struct. Syst., 22(3), 335-340. https://doi.org/10.12989/sss.2018.22.3.335.   DOI
18 Shahabi, S. E. M., Sulong, N. H., Shariati, M., Mohammadhassani, M. and Shah, S. N. R. (2016), "Numerical analysis of channel connectors under fire and a comparison of performance with different types of shear connectors subjected to fire", Steel Compos. Struct., 20(3), 651-669. https://doi.org/10.12989/scs.2016.20.3.651.   DOI
19 Shao, Z., Armaghani, D. J., Bejarbaneh, B. Y., Mu'azu, M. and Mohamad, E. T. (2019a), "Estimating the Friction Angle of Black Shale Core Specimens with Hybrid-ANN Approaches", Measurement, 145, https://doi.org/10.1016/j.measurement.2019.06.007.
20 Shao, Z., Gholamalizadeh, E., Boghosian, A., Askarian, B. and Liu, Z. (2019b). "The chiller's electricity consumption simulation by considering the demand response program in power system", Appl. Therm. Eng., 149, 1114-1124. https://doi.org/10.1016/j.applthermaleng.2018.12.121.   DOI
21 Shao, Z. and Vesel, A. (2015). "Modeling the packing coloring problem of graphs", Appl. Math. Model., 39(13), 3588-3595. https://doi.org/10.1016/j.apm.2014.11.060.   DOI
22 Dickinson, S. M. (1978), "The buckling and frequency of flexural vibration of rectangular isotropic and orthotropic plates using Rayleigh's method", J. Sound Vib., 61(1), 1-8. https://doi.org/10.1016/0022-460X(78)90036-6.   DOI
23 Chen, W., Shu, C., He, W. and Zhong, T. (2000), "The application of special matrix product to differential quadrature solution of geometrically nonlinear bending of orthotropic rectangular plates", Comput. Struct., 74(1), 65-76. https://doi.org/10.1016/S0045-7949(98)00320-4.   DOI
24 Chuanhua, X., Zhang, X., James H. Haido, Peyman Mehrabi, Ali Shariati, Edy Tonnizam Mohamad, Nguyen Hoang and Karzan Wakil, "Using genetic algorithms method for the paramount design of reinforced concrete structures", Struct. Eng. Mech., 71(5), 503-513. https://doi.org/10.12989/sem.2019.71.5.503.   DOI
25 Di Sciuva, M. (1986), "Bending, vibration and buckling of simply supported thick multilayered orthotropic plates: an evaluation of a new displacement model", J. Sound Vib., 105(3), 425-442. https://doi.org/10.1016/0022-460X(86)90169-0.   DOI
26 Eringen, A. C. (1972), "Nonlocal polar elastic continua", J. Eng. Sci., 10(1), 1-16. https://doi.org/10.1016/0020-7225(72)90070-5.   DOI
27 Jamalpoor, A. and Hosseini, M. (2015), "Biaxial buckling analysis of double-orthotropic microplate-systems including in-plane magnetic field based on strain gradient theory", Compos. Part B Eng., 75, 53-64. https://doi.org/10.1016/j.compositesb.2015.01.026.   DOI
28 Shao, Z., Wakil, K., Usak, M., Amin Heidari, M., Wang, B. and Simoes, R. (2018), "Kriging Empirical Mode Decomposition via support vector machine learning technique for autonomous operation diagnosing of CHP in microgrid", Appl. Thermal. Eng., 145, 58-70. https://doi.org/10.1016/j.applthermaleng.2018.09.028.   DOI
29 Eringen, A. C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54(9), 4703-4710. https://doi.org/10.1063/1.332803.   DOI
30 Findley, W. N., Lai, J. S. Y. and Onaran, K., (1976), Creep and Relaxation of Nonlinear Viscoelastic Materials, with an Introduction to Linear Viscoelasticity, Oxford, New York.
31 Javaheri, R. and Eslami, M. R. (2002), "Thermal buckling of functionally graded plates", AIAA J., 40(1), 162-169. https://doi.org/10.2514/2.1626.   DOI
32 Shariati, M., Mafipour, M. S., Mehrabi, P., Ahmadi, M., Wakil, K., Nguyen-Thoi, T. and Toghroli, A. (2020d), "Prediction of concrete strength in presence of furnace slag and fly ash using Hybrid ANN-GA (Artificial Neural Network-Genetic Algorithm)", Smart Struct. Syst., 25(2), 183-195. https://doi.org/10.12989/sss.2020.25.2.183.   DOI
33 Shariati, A., Ebrahimi, F., Karimiasl, M., Vinyas, M. and Toghroli, A. (2020a), "On transient hygrothermal vibration of embedded viscoelastic flexoelectric/piezoelectric nanobeams under magnetic loading", Adv. Nano. Res., 8(1), 49-58. https://doi.org/10.12989/anr.2020.8.1.049   DOI
34 Shariati, M., Ghorbani, M., Naghipour, M., Alinejad, N. and Toghroli, A. (2020b), "The effect of RBS connection on energy absorption in tall buildings with braced tube frame system", Steel Compos. Struct. 34(3), 393-407. https://doi.org/10.12989/scs.2020.34.3.393.   DOI
35 Shariati, M., Mafipour, M. S., Haido, J. H., Yousif, S. T., Toghroli, A., Trung, N. T. and Shariati, A. (2020c), "Identification of the most influencing parameters on the properties of corroded concrete beams using an Adaptive Neuro-Fuzzy Inference System (ANFIS)", Steel Compos. Struct. 34(1), 155. https://doi.org/10.12989/scs.2020.34.1.155.   DOI
36 Kapania, R. K. and Yang, T. Y. (1987), "Buckling, postbuckling, and nonlinear vibrations of imperfect plates", AIAA J., 25(10), 1338-1346. https://doi.org/10.2514/3.9788.   DOI
37 Jomehzadeh, E. and Saidi, A. R. (2011), "The small scale effect on nonlinear vibration of single layer graphene sheets", World Acad. Sci. Eng. Technol, 5, 235-239.
38 Jung, W. Y., Han, S. C. and Park, W. T. (2014), "A modified couple stress theory for buckling analysis of S-FGM nanoplates embedded in Pasternak elastic medium", Compos. Part B Eng., 60, 746-756. https://doi.org/10.1016/j.compositesb.2013.12.058.   DOI
39 Kane, C. L. and Mele, E. J. (1997), "Size, shape, and low energy electronic structure of carbon nanotubes", Phys. Rev. Lett., 78(10), 1932. https://doi.org/10.1103/PhysRevLett.78.1932.   DOI
40 Katebi, J., Shoaei-parchin, M., Shariati, M., Trung, N. T., & Khorami, M. (2019), "Developed comparative analysis of metaheuristic optimization algorithms for optimal active control of structures", Eng. Comput., 1-20. https://doi.org/10.1007/s00366-019-00780-7.
41 Shariati, M., Trung, N. T., Wakil, K., Mehrabi, P., Safa, M. and Khorami, M. (2019), "Moment-rotation estimation of steel rack connection using extreme learning machine", Steel. Compos. Struct., 31(5), 427-435. https://doi.org/10.12989/sem.2019.70.5.639.   DOI
42 Shariati, M., Mafipour, M. S., Mehrabi, P., Bahadori, A., Zandi, Y., Salih, M. N. A., Nguyen, H., Dou, J., Song, X. and Poi-Ngian, S. (2019a), "Application of a Hybrid Artificial Neural Network-Particle Swarm Optimization (ANN-PSO) Model in Behavior Prediction of Channel Shear Connectors Embedded in Normal and High-Strength Concrete", Appl. Sci., 9(24), 5534.   DOI
43 Shariati, M., Mafipour, M.S., Mehrabi, P., Shariati, A., Toghroli, A., Trung, N.T. and Salih, M.N.A. (2020e), "A novel approach to predict shear strength of tilted angle connectors using artificial intelligence techniques", Eng. Comput., 1-21. https://doi.org/10.1007/s00366-019-00930-x.
44 Ke, L. L. and Wang, Y. S. (2012), "Thermoelectric-mechanical vibration of piezoelectric nanobeams based on the nonlocal theory", Smart Mater. Struct., 21(2), 025018. https://doi.org/10.1088/0964-1726/21/2/025018.   DOI
45 Knightly, G. H. and Sather, D. (1974), "Nonlinear buckled states of rectangular plates", Arch. Rational Mech. Anal., 54(4), 356-372. https://doi.org/10.1007/BF00249196.   DOI
46 Kolahchi, R., Bidgoli, M. R., Beygipoor, G. and Fakhar, M. H. (2015), "A nonlocal nonlinear analysis for buckling in embedded FG-SWCNT-reinforced microplates subjected to magnetic field", J. Mech. Sci. Technol., 29(9), 3669-3677. https://doi.org/10.1007/s12206-015-0811-9.   DOI
47 Shariati, M., Mafipour, M. S., Mehrabi, P., Zandi, Y., Dehghani, D., Bahadori, A., Shariati, A., Trung, N.T., Salih, M.N.A. and Poi-Ngian, S. (2019), "Application of Extreme Learning Machine (ELM) and Genetic Programming (GP) to design steel-concrete composite floor systems at elevated temperatures", Steel Compos. Struct., 33(3), 319-332. https://doi.org/10.12989/scs.2019.33.3.319.   DOI
48 Shariati, M., Naghipour, M., Yousofizinsaz, G., Toghroli, A. and Pahlavannejad Tabarestani, N. (2020f), "Numerical study on the axial compressive behavior of built-up CFT columns considering different welding lines", Steel Compos. Struct. 34(3), 377-391.https://doi.org/10.12989/scs.2020.34.3.377.   DOI
49 Lakes, R., (2009), Viscoelastic Materials, Cambridge, New York.
50 Kutlu, A. and Omurtag, M. H. (2012), "Large deflection bending analysis of elliptic plates on orthotropic elastic foundation with mixed finite element method", J. Mech. Sci., 65(1), 64-74. https://doi.org/10.1016/j.ijmecsci.2012.09.004.   DOI
51 Lancaster, P. and Tismenetsky, M. (1985), The Theory of Matrices: with Applications, Elsevier, Germany.
52 Lei, Z. X., Liew, K. M. and Yu, J. L. (2013), "Buckling analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method", Compos. Struct., 98, 160-168. https://doi.org/10.1016/j.compstruct.2012.11.006.   DOI
53 Li, S. R., Zhou, Y. H. and Song, X. (2002), "Non-linear vibration and thermal buckling of an orthotropic annular plate with a centric rigid mass", J. Sound Vib., 251(1), 141-152. https://doi.org/10.1006/jsvi.2001.3987.   DOI
54 Li, Y. S., Cai, Z. Y. and Shi, S. Y. (2014), "Buckling and free vibration of magnetoelectroelastic nanoplate based on nonlocal theory", Compos. Struct., 111, 522-529. https://doi.org/10.1016/j.compstruct.2014.01.033.   DOI
55 Shen, H. S. (2009), "Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments", Compos. Struct., 91(1), 9-19. https://doi.org/10.1016/j.compstruct.2009.04.026.   DOI
56 Shi, X., Hassanzadeh-Aghdam, M. and Ansari, R. (2019a), "Viscoelastic analysis of silica nanoparticle-polymer nanocomposites", Compos. Part B Eng., 158, 169-178. https://doi.org/10.1016/j.compositesb.2018.09.084.   DOI
57 Shi, X., Jaryani, P., Amiri, A., Rahimi, A. and Malekshah, E. H. (2019b), "Heat transfer and nanofluid flow of free convection in a quarter cylinder channel considering nanoparticle shape effect", Powder Technol., 346, 160-170. https://doi.org/10.1016/j.powtec.2018.12.071.   DOI
58 Shen, H. S. (2000), "Nonlinear bending of shear deformable laminated plates under transverse and in-plane loads and resting on elastic foundations", Compos. Struct., 50(2), 131-142. https://doi.org/10.1016/S0263-8223(00)00088-X.   DOI
59 Swaminathan, K. and Ragounadin, D. (2004), "Analytical solutions using a higher-order refined theory for the static analysis of antisymmetric angle-ply composite and sandwich plates", Compos. Struct., 64(3-4), 405-417. https://doi.org/10.1016/j.compstruct.2003.09.042.   DOI
60 Liu, C., Ke, L. L., Wang, Y. S., Yang, J. and Kitipornchai, S. (2013), "Thermo-electro-mechanical vibration of piezoelectric nanoplates based on the nonlocal theory", Compos. Struct., 106, 167-174. https://doi.org/10.1016/j.compstruct.2013.05.031.   DOI
61 Suhatril, M., Osman, N., Sari, P. A., Shariati, M. and Marto, A. (2019), "Significance of Surface Eco-Protection Techniques for Cohesive Soils Slope in Selangor, Malaysia", Geotech. Geological Eng., 37(3), 2007-2014. https://doi.org/10.1007/s10706-018-0740-3.   DOI
62 Mansouri, I., Shariati, M., Safa, M., Ibrahim, Z., Tahir, M. M. and Petkovic, D. (2019), "Analysis of influential factors for predicting the shear strength of a V-shaped angle shear connector in composite beams using an adaptive neuro-fuzzy technique", J. Intelligent Manufact., 30(3), 1247-1257. https://doi.org/10.1007/s10845-017-1306-6.   DOI
63 Luo, Z., Sinaei, H., Ibrahim, Z., Shariati, M., Jumaat, Z., Wakil, Pham, Binh Thai, Mohamad, E.T. and Khorami, M. (2019) "Computational and experimental analysis of beam to column joints reinforced with CFRP plates", Steel Compos. Struct., 30(3), 271-280. https://doi.org/10.12989/scs.2019.30.3.271.   DOI
64 Ma, L. S. and Wang, T. J. (2003), "Nonlinear bending and post-buckling of a functionally graded circular plate under mechanical and thermal loadings", J. Solids Struct., 40(13-14), 3311-3330. https://doi.org/10.1016/S0020-7683(03)00118-5.   DOI
65 Maiti, A., Svizhenko, A. and Anantram, M. P. (2002), "Electronic transport through carbon nanotubes: Effects of structural deformation and tube chirality", Phys. Review Lett., 88(12), 126805. https://doi.org/10.1103/PhysRevLett.88.126805.   DOI
66 Milovancevic, M., Marinovic, J. S., Nikolic, J., Kitic, A., Shariati, M., Trung, N. T., Wakil, K. and Khorami, M. (2019). "UML diagrams for dynamical monitoring of rail vehicles", Physica A Statistical Mech. Appl., 53, 121169. https://doi.org/10.1016/j.physa.2019.121169.
67 Mohammadhassani, M., Saleh, A., Suhatril, M. and Safa, M. (2015), "Fuzzy modelling approach for shear strength prediction of RC deep beams", Smart Struct. Syst., 16(3), 497-519. https://doi.org/10.12989/sss.2015.16.3.497.   DOI
68 Zhang, J., Wang, C. and Chen, W. (2014), "Surface and piezoelectric effects on the buckling of piezoelectric nanofilms due to mechanical loads", Meccanica, 49(1), 181-189. https://doi.org/10.1007/s11012-013-9784-x.   DOI
69 Trung, N. T., Shahgoli, A. F., Zandi, Y., Shariati, M., Wakil, K., Safa, M. and Khorami, M. (2019), "Moment-rotation prediction of precast beam-to-column connections using extreme learning machine", Struct. Eng. Mech., 70(5), 639-647. https://doi.org/10.12989/sem.2019.70.5.639.   DOI
70 Wang, Q. (2002), "Axi-symmetric wave propagation in a cylinder coated with a piezoelectric layer", J. Solids Struct., 39(11), 3023-3037. https://doi.org/10.1016/S0020-7683(02)00233-0.   DOI
71 Zhao, M., Qian, C., Lee, S. W. R., Tong, P., Suemasu, H. and Zhang, T. Y. (2007), "Electro-elastic analysis of piezoelectric laminated plates", Adv. Compos. Mater., 16(1), 63-81. https://doi.org/10.1163/156855107779755273.   DOI
72 Ziliukas, A. (2008), "Plate buckling under complex loading", Mechanics, 74(6), 17-20.
73 Zong, Z. and Zhang, Y. (2009), Advanced Differential Quadrature Methods, Chapman and Hall/CRC Press, Florida, U.S.A.