Dynamic stability of smart sandwich nanotubes based on modified couple stress theory using differential quadrature method (DQM). (English) Zbl 1525.74099
Summary: In this paper, dynamic stability of a smart sandwich nanotube is investigated. The core of the nanostructure is made from a single-walled carbon nanotube (SWCNT), which is coated with two ZnO piezoelectric layers. The inner piezoelectric layer is taken as a sensor and the outer layer as an actuator. The sandwich nanotube is embedded in an elastic visco-Pasternak medium. The modified couple stress theory is utilized to consider the small-scale effect, and the Kelvin-Voigt model is used to model the carbon nanotube and the ZnO layers. The surface tension is taken into account using the Gurtin-Murdoch theory. The nonlinear governing equations, derived by the Hamilton principle, are solved using differential quadrature method (DQM), to investigate dynamic stability range, and to calculate natural frequencies. The results of this study are compared against existing similar data in the literature, presented for some simpler cases. Then, the effect of various parameters, including the small scale parameter, the ratio of piezoelectric layer thickness to nanotube thickness, surface stresses, the visco-elastic foundation effect, the magnetic field effect, and the electrical polarity are scrutinized on the system dynamic stability range. The results indicate that consideration of the small scale can reduce the transverse displacement and frequency while increasing the thickness of the piezoelectric layer leads to a higher frequency. Moreover, incorporating the surface stresses into the model can increase the stability. Using the modified couple stress theory can be considered the main novelty of this paper.
MSC:
| 74H55 | Stability of dynamical problems in solid mechanics |
| 74H45 | Vibrations in dynamical problems in solid mechanics |
| 74K25 | Shells |
| 74E30 | Composite and mixture properties |
| 74F15 | Electromagnetic effects in solid mechanics |
| 74S99 | Numerical and other methods in solid mechanics |
Keywords:
piezoelectric layer; Kelvin-Voigt model; Gurtin-Murdoch surface tension theory; Hamilton principle; natural frequencyReferences:
| [1] | Dimiev, AM; Shukhina, K.; Behabtu, N.; Pasquali, M.; Tour, JM, Stage transitions in graphite intercalation compounds: role of the graphite structure, Phys. Chem. C, 123, 31, 19246-19253 (2019) |
| [2] | Kiani, K., Vibration analysis of two orthogonal slender single-walled carbon nanotubes with a new insight into continuum-based modeling of van der Waals forces, Compos. B Eng., 73, 72-81 (2015) |
| [3] | Zhen, YX; Fang, B., Nonlinear vibration of fluid-conveying single-walled carbon nanotubes under harmonic excitation, Int. J. Non-Linear Mech., 76, 48-55 (2015) |
| [4] | Posligua, V.; Bustamante, J.; Zambrano, CH; Harris, PJF; Grau-Crespo, R., The closed-edge structure of graphite and the effect of electrostatic charging, RSC Adv., 10, 13, 7994-8001 (2020) |
| [5] | Rao, CNR; Cheetham, AK, Science and technology of nanomaterials, current status and future prospects, J. Mater. Chem., 11, 2887-2894 (2001) |
| [6] | Toupin, RA, Elastic materials with couple stresses, Arch. Ration. Mech. Anal., 11, 385-414 (1962) · Zbl 0112.16805 |
| [7] | Mindlin, RD, Influence of couple-stresses on stress concentrations, Exp. Mech., 3, 1-7 (1963) |
| [8] | Mindlin, RD; Tiersten, HF, Effects of couple-stresses in linear elasticity, Arch. Ration. Mech. Anal., 11, 415-448 (1962) · Zbl 0112.38906 |
| [9] | Yang, F.; Chong, ACM; Lam, DCC; Tong, P., Couple stress based strain gradient theory for elasticity, Int. J. Solids. Struct., 39, 2731-2743 (2002) · Zbl 1037.74006 |
| [10] | Asghari, M.; Kahrobaiyan, MH; Ahmadian, MT, A nonlinear Timoshenko beam formulation based on the modified couple stress theory, Int. J. Eng. Sci., 48, 1749-1761 (2010) · Zbl 1231.74258 |
| [11] | Wang, B.; Zhao, J.; Zhou, S., A micro scale Timoshenko beam model based on strain gradient elasticity theory, Eur. J. Mech. A/Solids, 29, 591-599 (2010) · Zbl 1480.74194 |
| [12] | Xia, W.; Wang, L.; Yin, L., Nonlinear non-classical microscale beams: Static bending, postbuckling and free vibration, Int. J. Eng. Sci., 48, 2044-2053 (2010) · Zbl 1231.74277 |
| [13] | Ke, LL; Wang, YS, Size effect on dynamic stability of functionally graded microbeams based on a modified couple stress theory, Compos. Struct., 93, 342-350 (2011) |
| [14] | Reddy, JN, Microstructure-dependent couple stress theories of functionally graded beams, J. Mech. Phys. Sol., 59, 2382-2399 (2011) · Zbl 1270.74114 |
| [15] | Ke, LL; Wang, YS; Yang, J.; Kitipornchai, S., Nonlinear free vibration of size-dependent functionally graded microbeams, Int. J. Eng. Sci., 50, 256-267 (2012) · Zbl 1423.74395 |
| [16] | Wang, LH; Hu, ZD; Zhong, Z., Dynamic analysis of an axially translating viscoelastic beam with an arbitrarily varying length, Acta Mech., 214, 225-244 (2010) · Zbl 1375.74058 |
| [17] | Wang, L.; Hu, Z.; Zhong, Z., Dynamic analysis of an axially translating plate with time-variant length, Acta Mech., 215, 9-23 (2010) · Zbl 1398.74158 |
| [18] | Moslemi, A.; Khadem, SE; Khazaee, M., Nonlinear vibration and dynamic stability analysis of an axially moving beam with a nonlinear energy sink, Nonlinear Dyn., 104, 1955-1972 (2021) |
| [19] | Ghorbanpour Arani, A.; Atabakhshian, V.; Loghman, A.; Shajari, AR; Amir, S., Nonlinear vibration of embedded SWBNNTs based on nonlocal Timoshenko beam theory using DQ method, Phys. B, 407, 2549-2555 (2012) |
| [20] | Sedighi, HM; Bozorgmehri, A., Dynamic instability analysis of doubly clamped cylindrical nanowires in the presence of Casimir attraction and surface effects using modified couple stress theory, Acta Mech., 227, 1575-1591 (2016) · Zbl 1341.74132 |
| [21] | Shanab, RA; Mohamed, SA; Mohamed, NA, Comprehensive investigation of vibration of sigmoid and power law FG nanobeams based on surface elasticity and modified couple stress theories, Acta Mech., 231, 1977-2010 (2020) · Zbl 1440.74189 |
| [22] | Nešić, N.; Cajić, M.; Karličić, D.; Obradović, A.; Simonović, J., Nonlinear vibration of a nonlocal functionally graded beam on fractional visco-Pasternak foundation, Nonlinear Dyn., 107, 2003-2026 (2022) |
| [23] | Wang, L.; Liu, Y.; Zhou, Y.; Yang, F., Static and dynamic analysis of thin functionally graded shell with in-plane material inhomogeneity, Int. J. Mech. Sci., 193, 106165 (2021) |
| [24] | Kolahchi, R.; Cheraghbak, A., Agglomeration effects on the dynamic buckling of viscoelastic microplates reinforced with SWCNTs using Bolotin method, Nonlinear Dyn., 90, 479-492 (2017) · Zbl 1390.74097 |
| [25] | Mohamed, N.; Mohamed, SA; Eltaher, MA, Buckling and post-buckling behaviors of higher order carbon nanotubes using energy-equivalent model, Eng. Comput., 37, 4, 1-14 (2021) |
| [26] | Gao, M.; Lichun, B.; Liang, X., Analysis for thermal properties and some influence parameters on carbon nanotubes by an energy method, Appl. Math. Model, 89, 73-88 (2021) · Zbl 1481.74134 |
| [27] | Farrokhian, A.; Salmani-Tehrani, M., Vibration and damping analysis of smart sandwich nanotubes using surface-visco-piezo-elasticity theory for various boundary conditions, Eng. Anal. Bound. Elem., 135, 337-358 (2022) · Zbl 1521.74082 |
| [28] | Tessler, A.; Sciuva, MD; Gherlone, MA, A consistent refinement of first-order shear deformation theory for laminated composite and sandwich plates using improved zigzag kinematics, J. Mech. Mat. Struct., 5, 341-367 (2010) |
| [29] | Di Sciuva, M., First-order displacement-based zigzag theories for composite laminates and sandwich structures, VII Eur. Congr. Comput. Methods Appl. Sci. Eng., 3, 4528-4552 (2016) · doi:10.7712/100016 |
| [30] | Ghorbanpour Arani, A.; Kolahchi, R.; Jamali, M.; Mosayyebi, M.; Alinaghian, I., Dynamic instability of visco-SWCNTs conveying pulsating fluid based on sinusoidal surface couple stress theory, J. Solid Mech., 9, 2, 225-238 (2017) |
| [31] | Mohammad Abadi, M.; Daneshmehr, AR, An investigation of modified couple stress theory in buckling analysis of micro composite laminated Euler-Bernoulli and Timoshenko beams, Int. J. Eng. Sci., 75, 40-53 (2014) · Zbl 1423.74346 |
| [32] | Hosseini Hashemi, Sh; Es’haghi, M.; Karimi, M., Closed-form vibration analysis of thick annular functionally graded plates with integrated piezoelectric layers, Int. J. Mech. Sci., 52, 410-428 (2010) |
| [33] | Ansari, R.; Mohammadi, V.; Faghih Shojaei, M.; Gholami, R.; Rouhi, H., Nonlinear vibration analysis of Timoshenko nanobeams based on surface stress elasticity theory, Eur. J. Mech. A/Solids, 45, 143-152 (2014) · Zbl 1406.74279 |
| [34] | Ansari, R.; Sahmani, S., Surface stress effects on the free vibration behavior of nanoplates, Int. J. Eng. Sci., 49, 1204-1215 (2011) · Zbl 1423.74532 |
| [35] | Arda, M., Torsional vibration analysis of carbon nanotubes using Maxwell and Kelvin-Voigt type viscoelastic material models, Eur. Mech. Sci., 4, 3, 90-95 (2020) |
| [36] | Kutlu, A.; Gurlu, B.; Omurtag, MH; Ergin, A., Dynamic response of Mindlin plates resting on arbitrarily orthotropic Pasternak foundation and partially in contact with fluid, Ocean Eng., 42, 112-125 (2012) |
| [37] | Ghorbanpour Arani, A.; Kolahchi, R.; Zarei, MS, Visco-surface-nonlocal piezoelasticity effects on nonlinear dynamic stability of graphene sheets integrated with ZnO sensors and actuators using refined zigzag theory, Compos. Struct., 132, 506-526 (2015) |
| [38] | Bellman, R.; Casti, J., Differential quadrature and long-term integration, J. Math. Anal. Appl., 34, 235-238 (1971) · Zbl 0236.65020 |
| [39] | Patel, SN; Datta, PK; Sheikh, AH, Buckling and dynamic instability analysis of stiffened shell panels, Thin-Walled Struct., 44, 321-333 (2006) |
| [40] | Wang, L.; Ni, Q., On vibration and instability of carbon nanotubes conveying fluid, Comput. Mater. Sci., 43, 399-402 (2008) |
| [41] | Ghorbanpour Arani, A.; Kolahchi, R.; MosallaieBarzoki, AA; Mozdianfard, MR; Noudeh Farahani, SM, Elastic foundation effect on nonlinear thermo vibration of embedded double-layered orthotropic graphene sheets using differential quadrature Method, J. Mech. Eng. Sci., 227, 4, 862-879 (2012) |
| [42] | Gao, Y.; Wang, ZhL, Electrostatic potential in a bent piezoelectric nanowire, the fundamental theory of nanogenerator and nanopiezotronics, Nano Lett., 7, 2488-2505 (2007) |
| [43] | Hoang, MT; Yvonnet, J.; Mitrushchenkov, A.; Chambaud, G., First-principles based multiscale model of piezoelectric nanowires with surface effects, J. Appl. Phy., 113, 014309 (2013) |
| [44] | Simsek, M.; Reddy, JN, Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory, Int. J. Eng. Sci., 64, 37-53 (2013) · Zbl 1423.74517 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
