Smart Structures and Systems

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Mechanical behaviors of piezoelectric nonlocal nanobeam with cutouts

  • Eltaher, Mohamed A. (Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University) ;
  • Omar, Fatema-Alzahraa (Mechanical Design and Production Department, Faculty of Engineering, Zagazig University) ;
  • Abdraboh, Azza M. (Physics Department, Faculty of Science, Banha University) ;
  • Abdalla, Waleed S. (Mechanical Design and Production Department, Faculty of Engineering, Zagazig University) ;
  • Alshorbagy, Amal E. (Mechanical Design and Production Department, Faculty of Engineering, Zagazig University)
  • Received : 2019.07.09
  • Accepted : 2019.10.14
  • Published : 2020.02.25
⟨ Previous Next ⟩

Abstract

This work presents a modified continuum model to explore and investigate static and vibration behaviors of perforated piezoelectric NEMS structure. The perforated nanostructure is modeled as a thin perforated nanobeam element with Euler-Bernoulli kinematic assumptions. A size scale effect is considered by included a nonlocal constitutive equation of Eringen in differential form. Modifications of geometrical parameters of perforated nanobeams are presented in simplified forms. To satisfy the Maxwell's equation, the distribution of electric potential for the piezoelectric nanobeam model is assumed to be varied as a combination of a cosine and linear functions. Hamilton's principle is exploited to develop mathematical governing equations. Modified numerical finite model is adopted to solve the equation of motion and equilibrium equation. The proposed model is validated with previous respectable work. Numerical investigations are presented to illustrate effects of the number of perforated holes, perforation size, nonlocal parameter, boundary conditions, and external electric voltage on the electro-mechanical behaviors of piezoelectric nanobeams.

Keywords

Acknowledgement

Supported by : King Abdulaziz University

References

  1. Abdalrahmaan, A.A., Eltaher, M.A., Kabeel, A.M., Abdraboh, A.M. and Hendi, A.A. (2019), "Free and forced analysis of perforated beams", Steel Compos. Struct., Int. J., 31(5), 489-502. https://doi.org/10.12989/scs.2019.31.5.489
  2. Akbas, S.D. (2017a), "Forced vibration analysis of functionally graded nanobeams", Int. J. Appl. Mech., 9(7), 1750100. https://doi.org/10.1142/S1758825117501009
  3. Akbas, S.D. (2017b), "Free vibration of edge cracked functionally graded microscale beams based on the modified couple stress theory", Int. J. Struct. Stabil. Dyn., 17(3), 1750033. https://doi.org/10.1142/S021945541750033X
  4. Akbas, S.D. (2018a), "Forced vibration analysis of cracked nanobeams", J. Brazil. Soc. Mech. Sci. Eng., 40(8), 392. https://doi.org/10.1007/s40430-018-1315-1
  5. Akbas, S.D. (2018b), "Forced vibration analysis of cracked functionally graded microbeams", Adv. Nano Res., Int. J., 6(1), 39-55. https://doi.org/10.12989/anr.2018.6.1.039
  6. Akbas, S.D. (2018c), "Bending of a cracked functionally graded nanobeam", Adv. Nano Res., Int. J., 6(3), 219-242. https://doi.org/10.12989/anr.2018.6.3.219
  7. Akbas, S.D. (2019), "Axially Forced Vibration Analysis of Cracked a Nanorod", J. Computat. Appl. Mech., 50(1), 63-68. https://doi.org/10.22059/jcamech.2019.281285.392
  8. Almitani, K.H., Abdalrahmaan, A.A. and Eltaher, M.A. (2019), "On forced and free vibrations of cutout squared beams", Steel Compos. Struct., Int. J., 32(5), 643-655. https://doi.org/10.12989/scs.2019.32.5.643
  9. Alshorbagy, A.E., Eltaher, M.A. and Mahmoud, F.F. (2011), "Free vibration characteristics of a functionally graded beam by finite element method", Appl. Mathe. Model., 35(1), 412-425. https://doi.org/10.1016/j.apm.2010.07.006
  10. Ansari, R., Gholami, R., Hosseini, K. and Sahmani, S. (2011), "A sixth-order compact finite difference method for vibrational analysis of nanobeams embedded in an elastic medium based on nonlocal beam theory", Mathe. Comput. Model., 54(11-12), 2577-2586. https://doi.org/10.1016/j.mcm.2011.06.030
  11. Ansari, R., Rouhi, S. and Ahmadi, M. (2018), "On the thermal conductivity of carbon nanotube/polypropylene nanocomposites by finite element method", J. Computat. Appl. Mech., 49(1), 70-85. 10.22059/JCAMECH.2017.243530.195
  12. Aydogdu, M. (2009), "A general nonlocal beam theory: its application to nanobeam bending, buckling and vibration", Physica E: Low-dimens. Syst. Nanostruct., 41(9), 1651-1655. https://doi.org/10.1016/j.physe.2009.05.014
  13. Chen, X. and Liew, K. (2004), "Buckling of rectangular functionally graded material plates subjected to nonlinearly distributed in-plane edge loads", Smart Mater. Struct., 13(6), 1430. https://doi.org/10.1088/0964-1726/13/6/014
  14. Eltaher, M., Alshorbagy, A.E. and Mahmoud, F. (2013a), "Vibration analysis of Euler-Bernoulli nanobeams by using finite element method", Appl. Mathe. Model., 37(7), 4787-4797. https://doi.org/10.1016/j.apm.2012.10.016
  15. Eltaher, M.A., Mahmoud, F.F., Assie, A.E. and Meletis, E.I. (2013b), "Coupling effects of nonlocal and surface energy on vibration analysis of nanobeams", Appl. Mathe. Computat., 224, 760-774. https://doi.org/10.1016/j.amc.2013.09.002
  16. Eltaher, M., Khairy, A., Sadoun, A. and Omar, F.-A. (2014), "Static and buckling analysis of functionally graded Timoshenko nanobeams", Appl. Mathe. Computat., 229, 283-295. https://doi.org/10.1016/j.amc.2013.12.072
  17. Eltaher, M.A., Khater, M.E., Park, S., Abdel-Rahman, E. and Yavuz, M. (2016), "On the static stability of nonlocal nanobeams using higher-order beam theories", Adv. Nano Res., Int. J., 4(1), 51-64. https://doi.org/10.12989/anr.2016.4.1.051
  18. Eltaher, M., Abdraboh, A. and Almitani, K. (2018a), "Resonance frequencies of size dependent perforated nonlocal nanobeam", Microsyst. Technol., 24, 3925-3937. https://doi.org/10.1007/s00542-018-3910-6
  19. Eltaher, M., Kabeel, A., Almitani, K. and Abdraboh, A. (2018b), "Static bending and buckling of perforated nonlocal sizedependent nanobeams", Microsyst. Technol., 24(12), 4881-4893. https://doi.org/10.1007/s00542-018-3905-3
  20. Eltaher, M.A., Omar, F.A., Abdalla, W.S. and Gad, E.H. (2019a), "Bending and vibrational behaviors of piezoelectric nonlocal nanobeam including surface elasticity", Waves Random Complex Media, 29(2), 264-280. https://doi.org/10.1080/17455030.2018.1429693
  21. Eltaher, M.A., Mohamed, N., Mohamed, S. and Seddek, L.F. (2019b), "Postbuckling of curved carbon nanotubes using energy equivalent model", J. Nano Res., 57, 136-157. https://doi.org/10.4028/www.scientific.net/JNanoR.57.136
  22. Eltaher, M.A., Almalki, T.A., Ahmed, K.I.E. and Almitani, K.H. (2019c), "Characterization and behaviors of single walled carbon nanotube by equivalent-continuum mechanics approach", Adv. Nano Res., Int. J., 7(1), 39-49. https://doi.org/10.12989/anr.2019.7.1.039
  23. 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
  24. Eringen, A.C. (1984), "Plane waves in nonlocal micropolar elasticity", Int. J. Eng. Sci., 22(8-10), 1113-1121. https://doi.org/10.1016/0020-7225(84)90112-5
  25. Eringen, A.C. and Edelen, D. (1972), "On nonlocal elasticity", Int. J. Eng. Sci., 10(3), 233-248. https://doi.org/10.1016/0020-7225(72)90039-0
  26. Faraji-Oskouie, M., Norouzzadeh, A., Ansari, R. and Rouhi, H. (2019), "Bending of small-scale Timoshenko beams based on the integral/differential nonlocal-micropolar elasticity theory: a finite element approach", Appl. Mathe. Mech., 40(6), 767-782. https://doi.org/10.1007/s10483-019-2491-9
  27. Fernandez-Saez, J., Zaera, R., Loya, J. and Reddy, J. (2016), "Bending of Euler-Bernoulli beams using Eringen's integral formulation: a paradox resolved", Int. J. Eng. Sci., 99, 107-116. https://doi.org/10.1016/j.ijengsci.2015.10.013
  28. Gheshlaghi, B. and Hasheminejad, S.M. (2012), "Vibration analysis of piezoelectric nanowires with surface and small scale effects", Current Appl. Phys., 12(4), 1096-1099. https://doi.org/10.1016/j.cap.2012.01.014
  29. Hamed, M., Sadoun, A.M. and Eltaher, M.A. (2019), "Effects of porosity models on static behavior of size dependent functionally graded beam", Struct. Eng. Mech., Int. J., 71(1), 89-98. https://doi.org/10.12989/sem.2019.71.1.089
  30. Jandaghian, A.A. and Rahmani, O. (2015), "On the buckling behavior of piezoelectric nanobeams: An exact solution", J. Mech. Sci. Technol., 29(8), 3175-3182. https://doi.org/10.1007/s12206-015-0716-7
  31. Jandaghian, A. and Rahmani, O. (2016), "An analytical solution for free vibration of piezoelectric nanobeams based on a nonlocal elasticity theory", J. Mech., 32(2), 143-151. https://doi.org/10.1017/jmech.2015.53
  32. Juntarasaid, C., Pulngern, T. and Chucheepsakul, S. (2012), "Bending and buckling of nanowires including the effects of surface stress and nonlocal elasticity", Physica E: Low-dimens. Syst. Nanostruct., 46, 68-76. https://doi.org/10.1016/j.physe.2012.08.005
  33. Ke, L.-L., Liu, C. and Wang, Y.-S. (2015), "Free vibration of nonlocal piezoelectric nanoplates under various boundary conditions", Physica E: Low-dimens. Syst. Nanostruct., 66, 93-106. https://doi.org/10.1016/j.physe.2014.10.002
  34. Kheibari, F. and Beni, Y.T. (2017), "Size dependent electromechanical vibration of single-walled piezoelectric nanotubes using thin shell model", Mater. Des., 114, 572-583. https://doi.org/10.1016/j.matdes.2016.10.041
  35. Lazarus, A., Thomas, O. and Deu, J.-F. (2012), "Finite element reduced order models for nonlinear vibrations of piezoelectric layered beams with applications to NEMS", Finite Elem. Anal. Des., 49(1), 35-51. https://doi.org/10.1016/j.finel.2011.08.019
  36. Li, C., Lim, C.W. and Yu, J. (2010), "Dynamics and stability of transverse vibrations of nonlocal nanobeams with a variable axial load", Smart Mater. Struct., 20(1), 015023. https://doi.org/10.1088/0964-1726/20/1/015023
  37. Luschi, L. and Pieri, F. (2014), "An analytical model for the determination of resonance frequencies of perforated beams", J. Micromech. Microeng., 24(5), 055004. https://doi.org/10.1088/0960-1317/24/5/055004
  38. Luschi, L. and Pieri, F. (2016), "An analytical model for the resonance frequency of square perforated Lame-mode resonators", Sensors Actuators B: Chem., 222, 1233-1239. https://doi.org/10.1016/j.snb.2015.07.085
  39. Mahinzare, M., Ranjbarpur, H. and Ghadiri, M. (2018), "Free vibration analysis of a rotary smart two directional functionally graded piezoelectric material in axial symmetry circular nanoplate", Mech. Syst. Signal Process., 100, 188-207. https://doi.org/10.1016/j.ymssp.2017.07.041
  40. Mohamed, N., Eltaher, M.A., Mohamed, S. and Seddek, L.F. (2019), "Energy equivalent model in analysis of postbuckling of imperfect carbon nanotubes resting on nonlinear elastic foundation", Struct. Eng. Mech., Int. J., 70(6), 737-750. https://doi.org/10.12989/sem.2019.70.6.737
  41. Murmu, T. and Adhikari, S. (2012), "Nonlocal frequency analysis of nanoscale biosensors", Sensors Actuators A: Phys., 173(1), 41-48. https://doi.org/10.1016/j.sna.2011.10.012
  42. Pei, J., Tian, F. and Thundat, T. (2004), "Glucose biosensor based on the microcantilever", Anal. Chem., 76(2), 292-297. https://doi.org/10.1021/ac035048k
  43. Reddy, J. (2007), "Nonlocal theories for bending, buckling and vibration of beams", Int. J. Eng. Sci., 45(2-8), 288-307. https://doi.org/10.1016/j.ijengsci.2007.04.004
  44. She, G.L., Yan, K.M., Zhang, Y.L., Liu, H.B. and Ren, Y.R. (2018a), "Wave propagation of functionally graded porous nanobeams based on non-local strain gradient theory", Eur. Phys. J. Plus, 133(9), 368. https://doi.org/10.1140/epjp/i2018-12196-5
  45. She, G.L., Yuan, F.G. and Ren, Y.R. (2018b), "On wave propagation of porous nanotubes", Int. J. Eng. Sci., 130, 62-74. https://doi.org/10.1016/j.ijengsci.2018.05.002
  46. She, G.L., Ren, Y.R. and Yan, K.M. (2019), "On snap-buckling of porous FG curved nanobeams", Acta Astronautica, 161, 475-484. https://doi.org/10.1016/j.actaastro.2019.04.010
  47. Tanner, S.M., Gray, J.M., Rogers, C., Bertness, K.A. and Sanford, N.A. (2007), "High-Q GaN nanowire resonators and oscillators", Appl. Phys. Lett., 91(20), 203117. https://doi.org/10.1063/1.2815747
  48. Thai, S., Thai, H.-T., Vo, T.P. and Lee, S. (2018), "Postbuckling analysis of functionally graded nanoplates based on nonlocal theory and isogeometric analysis", Compos. Struct., 201, 13-20. https://doi.org/10.1016/j.compstruct.2018.05.116
  49. Wang, Z.-l., Liu, J., Zheng, D.-c., Zhang, A.-b., Hu, K.-x. and Wang, J. (2019), "Vibration Analysis of Laminated Plates in a Piezoelectric Inkjet Printhead", Proceedings of 2019 Symposium on Piezoelectrcity, Acoustic Waves and Device Applications (SPAWDA), Harbin, China, January.
  50. Yan, Z. and Jiang, L.Y. (2011), "The vibrational and buckling behaviors of piezoelectric nanobeams with surface effects", Nanotechnol., 22(24), 245703. https://doi.org/10.1088/0957-4484/22/24/245703
  51. Zakeri, M., Attarnejad, R. and Ershadbakhsh, A.M. (2016), "Analysis of Euler-Bernoulli nanobeams: A mechanical-based solution", J. Computat. Appl. Mech., 47(2), 159-180. https://doi.org/10.22059/JCAMECH.2017.140165.97
  52. Zand, M.M. and Ahmadian, M. (2009), "Vibrational analysis of electrostatically actuated microstructures considering nonlinear effects", Commun. Nonlinear Sci. Numer. Simul., 14(4), 1664-1678. https://doi.org/10.1016/j.cnsns.2008.05.009

Cited by

  1. Bending behavior of squared cutout nanobeams incorporating surface stress effects vol.36, pp.2, 2020, https://doi.org/10.12989/scs.2020.36.2.143
  2. On bending analysis of perforated microbeams including the microstructure effects vol.76, pp.6, 2020, https://doi.org/10.12989/sem.2020.76.6.765
  3. Nonlinear nonlocal-surface energy-based vibrations of a bidirectionally excited nanobeam at its supports vol.96, pp.2, 2021, https://doi.org/10.1088/1402-4896/abcdc4
  4. Static analysis of cutout microstructures incorporating the microstructure and surface effects vol.38, pp.5, 2020, https://doi.org/10.12989/scs.2021.38.5.583
  5. Finite element based stress and vibration analysis of axially functionally graded rotating beams vol.79, pp.1, 2020, https://doi.org/10.12989/sem.2021.79.1.023