Wave propagation analysis of magneto-electro-thermo-elastic nanobeams using sinusoidal shear deformation beam model and nonlocal strain gradient theory

Document Type : Invited by Davoud Younesian

Authors

1 School of Mechanical Engineering, Iran University of Science and Technology, Narmak, 16765-163, Tehran, Iran

2 Associate Professor, School of Mechanical Engineering, Iran University of Science and Technology, Narmak, 16765-163, Tehran, Iran

Abstract

The main goal of this research is to provide a more detailed investigation of the size-dependent response of magneto-electro-thermo-elastic (METE) nanobeams subjected to propagating wave, employing sinusoidal shear deformation beam theory (SSDBT). With the aim to consider the size influences of the structure, the nonlocal strain gradient theory (NSGT) is utilized. Hamilton’s principle within constitutive relations of METE materials is incorporated to derive the
governing equations. Utilizing Maxwell’s relation and magnet-electric boundary conditions, proper distributions for magnetic and electric potentials along the nanobeam are obtained. Thereafter an exact analysis is used to obtain the axial and flexural dispersion relations of METE nanobeams. In numerical results, detailed investigations of wave dispersion behavior related to three modes are addressed. In addition, a relation is introduced to determine the cut-off frequency of the system. Moreover, the effectiveness of various parameters
including length scale and nonlocal parameters, nanobeam thickness, and the
loadings due to imposed thermo-electro-magnetic field on the response of
propagating wave in METE nanobeams are examined.

Highlights

  • Details of wave propagation in METE nanobeams is studied using both SSDBT and NSGT.
  • Hamilton’s law and METE constitutive relations are used to extract the equations.
  • The effects of applied loadings on properties of wave dispersion are investigated.
  • Effect of applied potentials on the second flexural mode dispersion is found minor.
  • Temperature change shows no considerable influence on wave dispersion relation.
  • Magnetic/electric potential has decrease/increase effect on the cut-off wave number.

Keywords

Main Subjects

References

[1] J. Chen, P. Heyliger, E. Pan, Free vibration of three-dimensional multilayered magneto-electro-elastic plates under combined clamped/free boundary conditions, Journal of Sound and Vibration, 333 (2014) 4017-4029.
[2] M. Fakhari, N. Saeedi, A. Amiri, Size-dependent vibration and instability of magneto-electro-elastic nano-scale pipes containing an internal flow with slip boundary condition, International Journal of Engineering, 29 (2016) 995-1004.
[3] A. Daga, N. Ganesan, K. Shankar, Behaviour of magneto-electro-elastic sensors under transient mechanical loading, Sensors and Actuators A: Physical, 150 (2009) 46-55.
[4] M.-F. Liu, An exact deformation analysis for the magneto-electro-elastic fiber-reinforced thin plate, Applied Mathematical Modelling, 35 (2011) 2443-2461.
[5] A. Amiri, I. Pournaki, E. Jafarzadeh, R. Shabani, G. Rezazadeh, Vibration and instability of fluid-conveyed smart micro-tubes based on magneto-electro-elasticity beam model, Microfluidics and Nanofluidics, 20 (2016) 38.
[6] A. Jandaghian, O. Rahmani, Free vibration analysis of magneto-electro-thermo-elastic nanobeams resting on a Pasternak foundation, Smart Materials and Structures, 25 (2016) 035023.
[7] L.-H. Ma, L.-L. Ke, Y.-Z. Wang, Y.-S. Wang, Wave propagation in magneto-electro-elastic nanobeams via two nonlocal beam models, Physica E: Low-dimensional Systems and Nanostructures, 86 (2017) 253-261.
[8] A. Amiri, R. Shabani, G. Rezazadeh, Coupled vibrations of a magneto-electro-elastic micro-diaphragm in micro-pumps, Microfluidics and Nanofluidics, 20 (2016) 18.
[9] A. Milazzo, An equivalent single-layer model for magnetoelectroelastic multilayered plate dynamics, Composite Structures, 94 (2012) 2078-2086.
[10] M. Arefi, A.H. Soltan Arani, Higher order shear deformation bending results of a magnetoelectrothermoelastic functionally graded nanobeam in thermal, mechanical, electrical, and magnetic environments, Mechanics Based Design of Structures and Machines, 46 (2018) 669-692.
[11] F. Ebrahimi, A. Dabbagh, On flexural wave propagation responses of smart FG magneto-electro-elastic nanoplates via nonlocal strain gradient theory, Composite Structures, 162 (2017) 281-293.
[12] N. Sina, H. Moosavi, H. Aghaei, M. Afrand, S. Wongwises, Wave dispersion of carbon nanotubes conveying fluid supported on linear viscoelastic two-parameter foundation including thermal and small-scale effects, Physica E: Low-dimensional Systems and Nanostructures, 85 (2017) 109-116.
[13] J. Chen, J. Guo, E. Pan, Wave propagation in magneto-electro-elastic multilayered plates with nonlocal effect, Journal of Sound and Vibration, 400 (2017) 550-563.
[14] H. Liu, Z. Lv, Q. Li, Flexural wave propagation in fluid-conveying carbon nanotubes with system uncertainties, Microfluidics and Nanofluidics, 21 (2017) 140.
[15] L. Li, H. Tang, Y. Hu, The effect of thickness on the mechanics of nanobeams, International Journal of Engineering Science, 123 (2018) 81-91.
[16] H. Tang, L. Li, Y. Hu, Coupling effect of thickness and shear deformation on size-dependent bending of micro/nano-scale porous beams, Applied Mathematical Modelling, 66 (2019) 527-547.
[17] H. Tang, L. Li, Y. Hu, W. Meng, K. Duan, Vibration of nonlocal strain gradient beams incorporating Poisson's ratio and thickness effects, Thin-Walled Structures, 137 (2019) 377-391.
[18] F. Ebrahimi, M.R. Barati, Magnetic field effects on nonlocal wave dispersion characteristics of size-dependent nanobeams, Applied Physics A, 123 (2017) 81.
[19] J. Zang, B. Fang, Y.-W. Zhang, T.-Z. Yang, D.-H. Li, Longitudinal wave propagation in a piezoelectric nanoplate considering surface effects and nonlocal elasticity theory, Physica E: Low-dimensional Systems and Nanostructures, 63 (2014) 147-150.
[20] Q. Wang, Wave propagation in carbon nanotubes via nonlocal continuum mechanics, Journal of Applied Physics, 98 (2005) 124301.
[21] L. Li, Y. Hu, L. Ling, Wave propagation in viscoelastic single-walled carbon nanotubes with surface effect under magnetic field based on nonlocal strain gradient theory, Physica E: Low-dimensional Systems and Nanostructures, 75 (2016) 118-124.
[22] L. Li, Y. Hu, L. Ling, Flexural wave propagation in small-scaled functionally graded beams via a nonlocal strain gradient theory, Composite Structures, 133 (2015) 1079-1092.
[23] F. Ebrahimi, M.R. Barati, A. Dabbagh, A nonlocal strain gradient theory for wave propagation analysis in temperature-dependent inhomogeneous nanoplates, International Journal of Engineering Science, 107 (2016) 169-182.
[24] W. Xiao, L. Li, M. Wang, Propagation of in-plane wave in viscoelastic monolayer graphene via nonlocal strain gradient theory, Applied Physics A, 123 (2017) 388.
[25] G.-L. She, K.-M. Yan, Y.-L. Zhang, H.-B. Liu, Y.-R. Ren, Wave propagation of functionally graded porous nanobeams based on non-local strain gradient theory, The European Physical Journal Plus, 133 (2018) 368.
[26] B. Karami, D. Shahsavari, M. Janghorban, Wave propagation analysis in functionally graded (FG) nanoplates under in-plane magnetic field based on nonlocal strain gradient theory and four variable refined plate theory, Mechanics of Advanced Materials and Structures, 25 (2018) 1047-1057.
[27] A. Ghorbanpour Arani, M. Jamali, M. Mosayyebi, R. Kolahchi, Analytical modeling of wave propagation in viscoelastic functionally graded carbon nanotubes reinforced piezoelectric microplate under electro-magnetic field, Proceedings of the Institution of Mechanical Engineers, Part N: Journal of Nanomaterials, Nanoengineering and Nanosystems, 231 (2017) 17-33.
[28] H. Zeighampour, Y.T. Beni, I. Karimipour, Wave propagation in double-walled carbon nanotube conveying fluid considering slip boundary condition and shell model based on nonlocal strain gradient theory, Microfluidics and Nanofluidics, 21 (2017) 85.
[29] L. Li, Y. Hu, Wave propagation in fluid-conveying viscoelastic carbon nanotubes based on nonlocal strain gradient theory, Computational Materials Science, 112 (2016) 282-288.
[30] F. Kaviani, H.R. Mirdamadi, Wave propagation analysis of carbon nano-tube conveying fluid including slip boundary condition and strain/inertial gradient theory, Computers & Structures, 116 (2013) 75-87.
[31] Y.-X. Zhen, Wave propagation in fluid-conveying viscoelastic single-walled carbon nanotubes with surface and nonlocal effects, Physica E: Low-dimensional Systems and Nanostructures, 86 (2017) 275-279.
[32] L. Wang, Wave propagation of fluid-conveying single-walled carbon nanotubes via gradient elasticity theory, Computational Materials Science, 49 (2010) 761-766.
[33] A.G. Arani, M. Roudbari, S. Amir, Longitudinal magnetic field effect on wave propagation of fluid-conveyed SWCNT using Knudsen number and surface considerations, Applied Mathematical Modelling, 40 (2016) 2025-2038.
[34] F. Ebrahimi, M.R. Barati, Wave propagation analysis of quasi-3D FG nanobeams in thermal environment based on nonlocal strain gradient theory, Applied Physics A, 122 (2016) 843.
[35] A. Amiri, R. Talebitooti, L. Li, Wave propagation in viscous-fluid-conveying piezoelectric nanotubes considering surface stress effects and Knudsen number based on nonlocal strain gradient theory, The European Physical Journal Plus, 133 (2018) 252.
[36] A. Masoumi, A. Amiri, R. Talebitooti, Flexoelectric effects on wave propagation responses of piezoelectric nanobeams via nonlocal strain gradient higher order beam model, Materials Research Express, 6 (2019) 1050d1055.
[37] F. Ebrahimi, M.R. Barati, A. Dabbagh, Wave dispersion characteristics of axially loaded magneto-electro-elastic nanobeams, Applied Physics A, 122 (2016) 949.
[38] M. Arefi, Analysis of wave in a functionally graded magneto-electro-elastic nano-rod using nonlocal elasticity model subjected to electric and magnetic potentials, Acta Mechanica, 227 (2016) 2529-2542.
[39] L.-L. Ke, Y.-S. Wang, Free vibration of size-dependent magneto-electro-elastic nanobeams based on the nonlocal theory, Physica E: Low-Dimensional Systems and Nanostructures, 63 (2014) 52-61.
Journal of Theoretical and Applied Vibration and Acoustics
Volume 5, Issue 2
July 2019
Pages 153-176

Files

Share

How to cite

Statistics