Vibro-Electrical Behavior of a Viscoelastic Piezo-Nanowire in an Elastic Substrate Considering Stress Nonlocality and Microstructural Size-Dependent Effects

Year 2019, Volume: 11 Issue: 2, 369 - 386, 25.07.2019

Mohammad Malikan

https://doi.org/10.24107/ijeas.567435

Abstract

This research
deals with dynamics response of a Pol/BaTiO₃ nanowire including
viscosity influences. The wire is also impressed by a longitudinal electric
field. Hamilton's principle and Lagrangian strains are employed in conjunction
with a refined higher-order beam theory in order to derive equations of motion.
By combining nonlocality and small size effects of a unique model into the derived
equations, the couple relations which describe nanosize behavior in a small
scale are presented. By employing an analytical approach, the fundamental natural
frequencies are calculated numerically. The important results display that the
effect of internal viscosity and nonlocality whenever the nanowire is very
large are pointless.

Keywords

Dynamics response; Piezo-nanowires; Viscosity; Nonlocal strain gradient theory; Analytical approach

References

• Fu, Y., Zhang, P., 2010. Buckling and vibration of core–shell nanowires with weak interfaces. Mech. Res. Commun. 37, 622–626.
• Gongbai, C., Yunfei, Ch., Jiwei, J., Yuelin, W., 2007. Harmonic behavior of silicon nanowire by molecular dynamics. Mech. Res. Commun. 34, 503–507.
• Gheshlaghi, B., Hasheminejad, S. M., 2012. Vibration analysis of piezoelectric nanowires with surface and small scale effects. Curr. Appl. Phys. 12, 1096-1099.
• Hu, J., Odom, T. W., Lieber, C. M., 1999. Chemistry and Physics in One Dimension: Synthesis and Properties of Nanowires and Nanotubes. Acc. Chem. Res. 32, 435-445.
• Kiani, K., 2012. Magneto-elasto-dynamic analysis of an elastically confined conducting nanowire due to an axial magnetic shock. Phys. Lett. A. 376, 1679–1685.
• Kiani, K., 2014a. Surface effect on free transverse vibrations and dynamic instability of current-carrying nanowires in the presence of a longitudinal magnetic field. Phys. Lett. A. 378, 1834–1840.
• Kiani, K., 2014b. Forced vibrations of a current-carrying nanowire in a longitudinal magnetic field accounting for both surface energy and size effects. Phys. E: Low-Dim. Syst. Nanostruct, 63, 27-35.
• Kiani, K., 2015. Stability and vibrations of doubly parallel current-carrying nanowires immersed in a longitudinal magnetic field. Phys. Lett. A. 379, 348–360.
• Kiani, K., 2016. Dynamic interactions between double current-carrying nanowires immersed in a longitudinal magnetic field: Novel integro-surface energy-based models. Inter. J. Eng. Sci. 107, 98–133.
• Kiani, K., 2017. A refined integro-surface energy-based model for vibration of magnetically actuated doublenanowire- systems carrying electric current. Phys. E: Low-Dim. Syst. Nanostruct. 86. 225-236.
• Lupu, N., 2010. Nanowires Science and Technology. First Publishing, India, Intech.
• Li, X.-F., Wang, B.-L., Tang, G.-J., Lee, K.-Y., 2011. Size effect in transverse mechanical behavior of one-dimensional nanostructures. Phys. E. 44, 207–214.
• Lei, Y., Adhikari, S., Friswell, M. I., 2013. Vibration of nonlocal Kelvin–Voigt viscoelastic damped Timoshenko beams. Inter. J. Eng. Sci. 66–67, 1–13.
• Lim, C. W., Zhang, G., 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.
• Lu, L., Guo, X., Zhao, J., 2017. Size-dependent vibration analysis of nanobeams based on the nonlocal strain gradient theory, Inter. J. Eng. Sci. 116, 12–24.
• Malikan, M., Nguyen, V. B., Tornabene, F., 2018. Damped forced vibration analysis of single-walled carbon nanotubes resting on viscoelastic foundation in thermal environment using nonlocal strain gradient theory. Eng. Sci. Tech., Inter. J. 21, 778-786.
• Malikan, M., Nguyen, V. B., 2018. Buckling analysis of piezo-magnetoelectric nanoplates in hygrothermal environment based on a novel one variable plate theory combining with higher-order nonlocal strain gradient theory. Phys. E: Low-Dim. Syst. Nanostruct. 102, 8-28.
• Malikan, M., 2017. Electro-mechanical shear buckling of piezoelectric nanoplate using modified couple stress theory based on simplified first order shear deformation theory. Appl. Math. Modell. 48, 196-207.
• Malikan, M., 2018. Temperature influences on shear stability of a nanosize plate with piezoelectricity effect. Multidiscip. Model. Mater. Struct., 14, 125-142.
• Malikan, M., 2019. Electro-thermal buckling of elastically supported double-layered piezoelectric nanoplates affected by an external electric voltage. Multidiscip. Model. Mater. Struct. 15, 50-78.
• Pishkenari, H.N., Afsharmanesh, B., Tajaddodianfar, F., 2016. Continuum models calibrated with atomistic simulations for the transverse vibrations of silicon nanowires. Inter. J. Eng. Sci. 100, 8–24.
• Rao, C. N. R., Govindaraj, A., 2005. Nanotubes and Nanowires. First Publishing, UK, R. S. C. Publication.
• She, G. L., Yuan, F. G., Ren, Y. R., 2017. Thermal buckling and post-buckling analysis of functionally graded beams based on a general higher-order shear deformation theory. Appl. Math. Modell. 47, 340-357.
• She, G. L., Yuan, F. G., Ren, Y. R., Liu, H. B., Xiao, W. S., 2018. Nonlinear bending and vibration analysis of functionally graded porous tubes via a nonlocal strain gradient theory. Comp. Struct. 203, 614-623.
• Su, G.-Y., Li, Y.-X., Li, X.-Y., Muller, R., 2018. Free and forced vibrations of nanowires on elastic substrates. Inter. J. Mech. Sci. 138-139, 62-73.
• Thai, H. T., 2012. A nonlocal beam theory for bending, buckling, and vibration of nanobeams, Inter. J. of Eng. Sci. 52, 56–64.Tourki Samaei, A., Gheshlaghi, B., Wang, G.-F., 2013. Frequency analysis of piezoelectric nanowires with surface effects. Curr. Appl. Phys. 13, 2098-2102.
• Wang, Z. L., 2006. Nanowires and Nanobelts: Materials Properties and Devices, Nanowires and Nanobelts of Functional Materials. First printing, USA, Springer. 2.
• Zhoua, J., Wanga, Zh., Grotsb, A., Heb, X., 2007. Electric field drives the nonlinear resonance of a piezoelectric nanowire. Solid State Commun. 144, 118–123.
• Zhang, Y. Q., Pang, M., Chen, W. Q., 2015. Transverse vibrations of embedded nanowires under axial compression with high-order surface stress effects. Phys. E. 66, 238–244.