Advances in nano research

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Nonlinear and nonclassical vibration analysis of double walled piezoelectric cylindrical nanoshell

  • Kachapi, Sayyid H. Hashemi (Department of Mechanical Engineering, Babol Noshirvani University of Technology)
  • Received : 2020.03.03
  • Accepted : 2020.10.05
  • Published : 2020.11.25
⟨ Previous Next ⟩

Abstract

In current paper, nonlocal (NLT), nonlocal strain gradient (NSGT) and Gurtin-Murdoch surface/interface (GMSIT) theories with classical theory (CT) are utilized to investigate vibration and stability analysis of Double Walled Piezoelectric Nanosensor (DWPENS) based on cylindrical nanoshell. DWPENS simultaneously subjected to direct electrostatic voltage DC and harmonic excitations, structural damping, two piezoelectric layers and also nonlinear van der Waals force. For this purpose, Hamilton's principle, Galerkin technique, complex averaging and with arc-length continuation methods are used to analyze nonlinear behavior of DWPENS. For this work, three nonclassical theories compared with classical theory CT to investigate Dimensionless Natural Frequency (DNF), pull-in voltage, nonlinear frequency response and stability analysis of the DWPENS considering the nonlocal, material length scale, surface/interface (S/I) effects, electrostatic and harmonic excitation.

Keywords

References

  1. Aifantis, E.C. (1992), "On the role of gradients in the localization of deformation and fracture", Int. J. Eng. Sci., 30(10), 1279-1299. https://doi.org/10.1016/0020-7225(92)90141-3.
  2. Alizada, A.N. and Sofiyev, A.H. (2011), "Modified Young's moduli of nano-materials taking into account the scale effects and vacancies", Meccanica, 46, 915-920. https://doi.org/10.1007/s11012-010-9349-1.
  3. Alizada, A.N., Sofiyev, A H. and Kuruoglu, N. (2012), "The stress analysis of the substrate coated by nanomaterials with vacancies subjected to the uniform extension load", Acta Mech., 223, 1371-1383. https://doi.org/10.1007/s00707-012-0649-5.
  4. Amabili, M. (2008), Nonlinear Vibrations and Stability of Shells and Plates, Cambridge University Press, New York, USA.
  5. Arefi, M. (2018), "Analysis of a doubly curved piezoelectric nano shell: Nonlocal electro-elastic bending solution", Eur. J. Mech. A Solids., 70, 226-237. https://doi.org/10.1016/j.euromechsol.2018.02.012.
  6. Chatterjee, K., Sarkar, S., Rao K.J. and Paria, S. (2014), "Core/shell nanoparticles in biomedical applications", Adv. Colloid Interf. Sci., 209, 8-39. https://doi.org/10.1016/j.cis.2013.12.008.
  7. Chen, J., Guo, J. and Pan, E. (2017), "Wave propagation in magneto-electro-elastic multilayered plates with nonlocal effect", J. Sound Vib., 400, 550-563. https://doi.org/10.1016/j.jsv.2017.04.001.
  8. Donnell, L.H. (1976), Beam, Plates and Shells, McGraw-Hill, New York, USA.
  9. Duan, W.H., Wang, Q. and Quek, S.T. (2010), "Applications of piezoelectric materials in structural health monitoring and repair: Selected research examples", Materials, 3, 5169-5194. https://doi.org/10.3390/ma3125169.
  10. Ebrahimi, F., Dehghan, M. and Seyfi, A. (2019a), "Eringen's nonlocal elasticity theory for wave propagation analysis of magneto-electro-elastic nanotubes", Adv. Nano Res., Int. J., 7(1), 1-11. https://doi.org/10.12989/anr.2019.7.1.001.
  11. Ebrahimi, F. and Barati M.R. (2019b), "On static stability of electro-magnetically affected smart magneto-electro-elastic nanoplates", Adv. Nano Res., Int. J., 7(1), 63-75. https://doi.org/10.12989/anr.2019.7.1.063.
  12. Ebrahimi, F., Dabbagh, A., Rabczuk, T. and Tornabene F. (2019c), "Analysis of propagation characteristics of elastic waves in heterogeneous nanobeams employing a new two-step porosity-dependent homogenization scheme", Adv. Nano Res., Int. J., 7(2), 135-143. https://doi.org/10.12989/anr.2019.7.2.135.
  13. Ebrahimi, F., Karimiasl, M. and Mahesh, V. (2019d), "Vibration analysis of magneto-flexo-electrically actuated porous rotary nanobeams considering thermal effects via nonlocal strain gradient elasticity theory", Adv. Nano Res., Int. J., 7(4), 223-231. https://doi.org/10.12989/anr.2019.7.4.223.
  14. Ebrahimi, F., Seyfi, A. and Dabbagh, A. (2019e), "Dispersion of waves in FG porous nanoscale plates based on NSGT in thermal environment", Adv. Nano Res., Int. J., 7(5), 325-335. https://doi.org/10.12989/anr.2019.7.5.325.
  15. Eringen, A.C. (1972), "Nonlocal polar elastic continua", Int. J. Eng. Sci., 10, 1-16. https://doi.org/10.1016/0020-7225(72)90070-5.
  16. Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54, 4703-4710. https://doi.org/10.1063/1.332803.
  17. Eringen, A.C. (2002), Nonlocal Continuum Field Theories, Springer, New York, USA.
  18. Farokhi, H., Paidoussis, M.P. and Misra, A. (2016), "A new nonlinear model for analyzing the behaviour of carbon nanotube-based resonators", J. Sound Vib., 378, 56-75. https://doi.org/10.1016/j.jsv.2016.05.008.
  19. Ghorbani, K., Mohammadi, K., Rajabpour, A. and Ghadiri, M. (2019), "Surface and size-dependent effects on the free vibration analysis of cylindrical shell based on Gurtin-Murdoch and nonlocal strain gradient theories", J. Phys. Chem. Solids, 129, 140-150. https://doi.org/10.1016/j.jpcs.2018.12.038.
  20. Ghorbanpour Arani, A., Kolahchi, R. and Hashemian, M. (2014), "Nonlocal surface piezoelasticity theory for dynamic stability of double-walled boron nitride nanotube conveying viscose fluid based on different theories", Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci., 228(17), 3258-3280. https://doi.org/10.1177/0954406214527270.
  21. Gurtin, M.E. and Murdoch, A.I. (1975), "A continuum theory of elastic material surface", Arch. Rat. Mech. Anal., 57, 291-323. https://doi.org/10.1007/BF00261375.
  22. Gurtin, M.E. and Murdoch, A.I. (1978), "Surface stress in solids", Int. J. Solids Struct., 14, 431-440. https://doi.org/10.1016/0020-7683(78)90008-2
  23. Hamdia, K.M., Ghasemi, H., Zhuang, X., Alajlan, N. and Rabczuk, T. (2018), "Sensitivity and uncertainty analysis for flexoelectric nanostructures", Comput. Mater. Contin., 337, 95-109. https://doi.org/10.1016/j.cma.2018.03.016.
  24. Hashemi Kachapi, S.H. (2020a), "Nonlinear vibration and stability analysis of piezo-harmo-electrostatic nanoresonator based on surface/interface and nonlocal strain gradient effects", J. Braz. Soc. Mech. Sci. Eng., 42(107), 107. https://doi.org/10.1007/s40430-020-2173-1.
  25. Hashemi Kachapi, S.H. (2020b), "Surface/interface approach in pull-in instability and nonlinear vibration analysis of fluid-conveying piezoelectric nanosensor", Mech. Based Des. Struct. Mach., 2020, 1-26. https://doi.org/10.1080/15397734.2020.1725566.
  26. Hashemi Kachapi, S.H., Dardel, M., Mohamadi Daniali, H. and Fathi, A. (2019a), "Effects of surface energy on vibration characteristics of double-walled piezo-viscoelastic cylindrical nanoshel", Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci., 233(15), 5264-5279. https://doi.org/10.1177/0954406219845019.
  27. Hashemi Kachapi, S.H., Dardel, M., Mohamadi Daniali, H. and Fathi, A. (2019b), "Pull-in instability and nonlinear vibration analysis of electrostatically piezoelectric nanoresonator with surface/interface effects", Thin-Wall. Struct., 143, 106210. https://doi.org/10.1016/j.tws.2019.106210.
  28. Hashemi Kachapi, S.H., Dardel, M., Mohamadi Daniali, H. and Fathi, A. (2019c), "Nonlinear dynamics and stability analysis of piezo-visco medium nanoshell resonator with electrostatic and harmonic actuation", Appl. Math. Model., 75, 279-309. https://doi.org/10.1016/j.apm.2019.05.035.
  29. Hashemi Kachapi, S.H., Dardel, M., Mohamadi Daniali, H. and Fathi, A. (2019d), "Nonlinear vibration and stability analysis of double-walled piezoelectric nanoresonator with nonlinear van der Waals and electrostatic excitation", J. Vib. Control, 6(9-10), 680-700. https://doi.org/10.1177/1077546319889858.
  30. Hashemi Kachapi, S.H., Mohamadi Daniali, H., Dardel, M. and Fathi, A. (2020), "The effects of nonlocal and surface/interface parameters on nonlinear vibrations of piezoelectric nanoresonator", J. Intell. Mater. Syst. Struct., 31(6), 818-842. https://doi.org/10.1177/1045389X19898756.
  31. Kosaka, P.M., Pini, V., Ruz, J.J., Da Silva, R.A., Gonzalez, M.U., Ramos, D., Calleja, M. and Tamayo, J. (2014), "Detection of cancer biomarkers in serum using a hybrid mechanical and optoplasmonic nanosensors", Nat. Nanotechnol., 9(12), 1047-1053. https://doi.org/10.1038/nnano.2014.250.
  32. Li, L. and Hu, Y. (2015), "Buckling analysis of size-dependent nonlinear beams based on a nonlocal strain gradient theory", Int. J. Eng. Sci., 97, 84-94. https://doi.org/10.1016/j.ijengsci.2015.08.013.
  33. Li, L., Hu, Y. and Li, X. (2016), "Longitudinal vibration of size-dependent rods via nonlocal strain gradient theory", Int. J. Mech. Sci., 115, 135-144. https://doi.org/10.1016/j.ijmecsci.2016.06.011.
  34. Lim C.W., Zhang, G. and Reddy, J.N. (2015), "A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation", J. Mech. Phys. Solids., 78, 298-313. https://doi.org/10.1016/j.jmps.2015.02.001.
  35. Managheb, S.A.M., Ziaei-Rad, S. and Tikani, R. (2018), "Energy harvesting from vibration of Timoshenko nanobeam under base excitation considering flexoelectric and elastic strain gradient effects", J. Sound Vib., 421, 166-189. https://doi.org/10.1016/j.jsv.2018.01.059.
  36. Manbachi, A. and Cobbold, R.S.C. (2011), "Development and application of piezoelectric materials for ultrasound generation and detection", Ultrasound, 11, 187-196. https://doi.org/10.1258/ult.2011.011027.
  37. Manevitch, A.I. and Manevitch, L.I. (2005), The Mechanics of Nonlinear Systems with Internal Resonance, Imperial College Press, London, UK.
  38. Melancon, M.P., Lu, W., Zhong, M., Zhou, M., Liang, G., Elliott, A.M., Hazle, J.D., Myers, J.N., Li, C. and Stafford, R.J. (2011), "Targeted multifunctional gold-based nanoshells for magnetic resonance-guided laser ablation of head and neck cancer", Biomaterials, 32(30), 7600-7608. https://doi.org/10.1016/j.biomaterials.2011.06.039.
  39. Mousavi, S.M., Hashemi, S.A., Zarei, M., Amani, A.M. and Babapoor, A. (2018), "Nanosensors for chemical and biological and medical applications", Med. Chem., 8(8), 205-217. https://doi.org/10.4172/2161-0444.1000515.
  40. Rabczuk, T., Ren, H. and Zhuang, X. (2019), "A nonlocal operator method for partial differential equations with application to electromagnetic waveguide problem", Comput. Mater. Contin., 59, 31-55. https://doi.org/10.32604/cmc.2019.04567.
  41. Rahmanian, S. and Hosseini-Hashemi, S. (2019), "Size-dependent resonant response of a double-layered viscoelastic nanoresonator under electrostatic and piezoelectric actuations incorporating surface effects and Casimir regime", Int. J. Non Linear Mech., 109, 118-131. https://doi.org/10.1016/j.ijnonlinmec.2018.12.003.
  42. Rupitsch, S.J. (2019), Piezoelectric Sensors and Actuators: Fundamentals and Applications, New York, Springer.
  43. Sabzikar Boroujerdy, M. and Eslami, M.R. (2014), "Axisymmetric snap-through behavior of piezo-FGM shallow clamped spherical shells under thermo-electro-mechanical loading", Int. J. Press. Vessel Pip., 120-121, 19-26. https://doi.org/10.1016/j.ijpvp.2014.03.008.
  44. Samaniego, E., Anitescud, C., Goswami, S., Nguyen-Thanh, V.M., Guoe, H., Hamdia, K., Zhuang, X. and Rabczuk, T. (2020), "An energy approach to the solution of partial differential equations in computational mechanics via machine learning: Concepts, implementation and applications", Comput. Method Appl. M, 362, 112790. https://doi.org/10.1016/j.cma.2019.112790.
  45. Sofiyev, A.H., Tornabene, F., Dimitri, R. and Kuruoglu, N. (2020a), "Buckling behavior of FG-CNT reinforced composite conical shells subjected to a combined loading", Nanomaterials, 10(3), 1-19. https://doi.org/10.3390/nano10030419.
  46. Sofiyev, A.H., Mammadov, Z. Dimitri, R. and Tornabene, F. (2020b), "Vibration analysis of shear deformable CNT-based FG conical shells resting on elastic foundations", Math. Method Appl. Sci., 2020, 1-10. https://doi.org/10.1002/mma.6674.
  47. Sun, J., Wang, Z., Zhou, Z., Xu, X.G. and Lim, C.W. (2018), "Surface effects on the buckling behaviors of piezoelectric cylindrical nanoshells using nonlocal continuum model", Appl. Math. Model., 59, 341-356. https://doi.org/10.1016/j.apm.2018.01.032.
  48. Tzou, H. (2019), Piezoelectric Shells: Sensing, Energy Harvesting and Distributed Control, Springer, New York, USA.
  49. Vu-Bac, N., Lahmer, T., Zhuang, X., Nguyen-Thoi, T. and Rabczuk, T. (2016), "A software framework for probabilistic sensitivity analysis for computationally expensive models", Adv. Eng. Softw., 100, 19-31. https://doi.org/10.1016/j.advengsoft.2016.06.005.
  50. Zhang, H., Wang, C.M. and Challamel, N. (2018), "Modelling vibrating nano-strings by lattice, finite difference and Eringen's nonlocal models", J. Sound Vib., 425, 41-52. https://doi.org/10.1016/j.jsv.2018.04.001.
  51. Zhu, C.S., Fang, X.Q., Liu, J.X. and Li, H.Y. (2017), "Surface energy effect on nonlinear free vibration behavior of orthotropic piezoelectric cylindrical nano-shells", Eur. J. Mech. A Solids, 66, 423-432. https://doi.org/10.1016/j.euromechsol.2017.08.001.
  52. Zhu, C., Fang, X. and Liu, J. (2020), "A new approach for smart control of size-dependent nonlinear free vibration of viscoelastic orthotropic piezoelectric doubly-curved nanoshells", Appl. Math. Model., 77, 137-168. https://doi.org/10.1016/j.apm.2019.07.027.