Skip to main content
SpringerLink
Log in

On thermoelastic damping in axisymmetric vibrations of circular nanoplates: incorporation of size effect into structural and thermal areas

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

The paper at hand intends to evaluate thermoelastic damping (TED) in circular plates by incorporating nonlocal effect within the constitutive and heat conduction frameworks. To attain this purpose, nonclassical coupled thermoelastic equations are established on the basis of nonlocal elasticity theory and Guyer–Krumhansl (GK) heat conduction model. By considering symmetric time–harmonic vibrations, the size-dependent thermoelastic frequency equation is derived. By solving this nonclassical eigenvalue problem, real and imaginary parts of damped natural frequency are separated. According to the definition of TED in the framework of complex frequency approach, a closed-form expression characterizing TED in circular nanoplates is introduced. With the aim of surveying the nonlocal effect on TED, a comparison study is performed between the size-dependent outcomes and those extracted by way of classical continuum mechanics and heat conduction theories for simply supported and clamped circular nanoplates. When the dimensions of nanoplate become smaller, an obvious discrepancy between classical and nonclassical results is observed, which is irrefutable evidence of size effect on mechanical behavior of nanostructures.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. K. Ekinci, M. Roukes, Rev. Sci. Instrum. 76(6), 061101 (2005)

    Article  ADS  Google Scholar 

  2. Z. Lee, C. Ophus, L. Fischer, N. Nelson-Fitzpatrick, K. Westra, S. Evoy, V. Radmilovic, U. Dahmen, D. Mitlin, Nanotechnology 17(12), 3063 (2006)

    Article  Google Scholar 

  3. S. Song, Y. Qin, Y. He, Q. Huang, C. Fan, H.-Y. Chen, Chem. Soc. Rev. 39(11), 4234 (2010)

    Article  Google Scholar 

  4. M.S. Yao, X.J. Lv, Z.H. Fu, W.H. Li, W.H. Deng, G.D. Wu, G. Xu, Angew. Chem. 129(52), 16737 (2017)

    Article  Google Scholar 

  5. K. Jensen, K. Kim, A. Zettl, Nat. Nanotechnol. 3(9), 533 (2008)

    Article  ADS  Google Scholar 

  6. J. Chaste, A. Eichler, J. Moser, G. Ceballos, R. Rurali, A. Bachtold, Nat. Nanotechnol. 7(5), 301 (2012)

    Article  ADS  Google Scholar 

  7. C. Zhu, W. Guo, T. Yu, Nanotechnology 19(46), 465703 (2008)

    Article  ADS  Google Scholar 

  8. X. Shi, Y. Cheng, N.M. Pugno, H. Gao, Appl. Phys. Lett. 96(5), 053115 (2010)

    Article  ADS  Google Scholar 

  9. M. Ringler, A. Schwemer, M. Wunderlich, A. Nichtl, K. Kürzinger, T. Klar, J. Feldmann, Phys. Rev. Lett. 100(20), 203002 (2008)

    Article  ADS  Google Scholar 

  10. M. Sansa, E. Sage, E.C. Bullard, M. Gély, T. Alava, E. Colinet, A.K. Naik, L.G. Villanueva, L. Duraffourg, M.L. Roukes, Nat. Nanotechnol. 11(6), 552 (2016)

    Article  ADS  Google Scholar 

  11. N. Fleck, G. Muller, M.F. Ashby, J.W. Hutchinson, Acta Metall. Mater. 42(2), 475 (1994)

    Article  Google Scholar 

  12. J.S. Stölken, A. Evans, Acta Mater. 46(14), 5109 (1998)

    Article  ADS  Google Scholar 

  13. A.W. McFarland, J.S. Colton, J. Micromech. Microeng. 15(5), 1060 (2005)

    Article  ADS  Google Scholar 

  14. R.A. Toupin, Theories of Elasticity with Couple-Stress (1964)

  15. A.C. Eringen, Int. J. Eng. Sci. 10(5), 425 (1972)

    Article  Google Scholar 

  16. F. Yang, A. Chong, D.C.C. Lam, P. Tong, Int. J. Solids Struct. 39(10), 2731 (2002)

    Article  Google Scholar 

  17. D.C. Lam, F. Yang, A. Chong, J. Wang, P. Tong, J. Mech. Phys. Solids 51(8), 1477 (2003)

    Article  ADS  Google Scholar 

  18. C. Lim, G. Zhang, J. Reddy, J. Mech. Phys. Solids 78, 298 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  19. M. Gürses, B. Akgöz, Ö. Civalek, Appl. Math. Comput. 219(6), 3226 (2012)

    MathSciNet  Google Scholar 

  20. M. Fazlali, S.A. Faghidian, M. Asghari, H.M. Shodja, Eur. Phys. J. Plus 135(8), 1 (2020)

    Article  Google Scholar 

  21. M.H. Ghayesh, Appl. Phys. A 117(3), 1393 (2014)

    Article  Google Scholar 

  22. O. Rahmani, M. Shokrnia, H. Golmohammadi, S. Hosseini, Eur. Phys. J. Plus 133(2), 1 (2018)

    Article  Google Scholar 

  23. F. Ebrahimi, M. Habibi, H. Safarpour, Eng Comput. 35(4), 1375 (2019)

    Article  Google Scholar 

  24. A. Zenkour, Eur. Phys. J. Plus 133(5), 196 (2018)

    Article  Google Scholar 

  25. F. Ebrahimi, M.R. Barati, Ö. Civalek, Eng. Comput. 36 (2019)

  26. V. Borjalilou, E. Taati, M.T. Ahmadian, SN Appl. Sci. 1(11), 1323 (2019)

    Article  Google Scholar 

  27. Ö. Civalek, B. Uzun, M.Ö. Yaylı, B. Akgöz, Eur. Phys. J. Plus 135(4), 381 (2020)

    Article  Google Scholar 

  28. E. Taati, V. Borjalilou, A. Fallah, Famida, M.T. Ahmadian, Mech. Based Des. Struct. Mach. 48 (2020)

  29. M. Arefi, O. Civalek, Arch. Civ. Mech. Eng. 20(1), 1 (2020)

    Article  Google Scholar 

  30. M.H. Ghayesh, Int. J. Eng. Sci. 135, 75 (2019)

    Article  MathSciNet  Google Scholar 

  31. H. SafarPour, K. Mohammadi, M. Ghadiri, A. Rajabpour, Eur. Phys. J. Plus 132(6), 281 (2017)

    Article  Google Scholar 

  32. M.H. Ghayesh, Compos. Struct. 225, 110974 (2019)

    Article  Google Scholar 

  33. F. Zheng, Y. Lu, A. Ebrahimi-Mamaghani, Waves Random Complex Media 30 (2020)

  34. M.H. Ghayesh, H. Farokhi, A. Farajpour, Thin-Walled Struct. 150, 106117 (2020)

    Article  Google Scholar 

  35. B. Alibeigi, Y.T. Beni, F. Mehralian, Eur. Phys. J. Plus 133(3), 1 (2018)

    Article  Google Scholar 

  36. M.H. Ghayesh, Appl. Math. Model. 59, 583 (2018)

    Article  MathSciNet  Google Scholar 

  37. A.E. Abouelregal, M. Marin, Symmetry 12(8), 1276 (2020)

    Article  Google Scholar 

  38. A. Amiri, M. Mohammadimehr, M. Anvari, Appl. Math. Mech. 41(7), 1027 (2020)

    Article  Google Scholar 

  39. M.H. Ghayesh, Eur. J. Mech. A/Solids 73, 492 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  40. B. Akgöz, Ö. Civalek, Acta Mech. 224(9), 2185 (2013)

    Article  MathSciNet  Google Scholar 

  41. V. Borjalilou, M. Asghari, Int. J. Appl. Mech. 11(01), 1950007 (2019)

    Article  Google Scholar 

  42. Y. Gholami, R. Ansari, R. Gholami, H. Rouhi, Eur. Phys. J. Plus 134(4), 167 (2019)

    Article  Google Scholar 

  43. B. Akgöz, Ö. Civalek, J. Vib. Control 20(4), 606 (2014)

    Article  MathSciNet  Google Scholar 

  44. M.H. Ghayesh, M. Amabili, H. Farokhi, Int. J. Eng. Sci. 63, 52 (2013)

    Article  Google Scholar 

  45. V. Borjalilou, M. Asghari, J. Therm. Stress. 43(4), 401 (2020)

    Article  Google Scholar 

  46. S. Esfahani, S.E. Khadem, A.E. Mamaghani, Int. J. Mech. Mater. Des. 15(3), 489 (2019)

    Article  Google Scholar 

  47. M. Mahinzare, H. Akhavan, M. Ghadiri, J. Intell. Mater. Syst. Struct. 31(12), 1511 (2020)

    Article  Google Scholar 

  48. M. Şimşek, Int. J. Eng. Sci. 105, 12 (2016)

    Article  Google Scholar 

  49. R. Barretta, S. Ali Faghidian, F.M. de Sciarra, F.P. Pinnola, Mech. Adv. Mater. Struct. 26 (2019)

  50. M. Forsat, S. Badnava, S.S. Mirjavadi, M.R. Barati, A. Hamouda, Eur. Phys. J. Plus 135(1), 81 (2020)

    Article  Google Scholar 

  51. A. Gholipour, M.H. Ghayesh, S. Hussain, Eng. Comput. 36 (2020)

  52. X. Zhu, Z. Lu, Z. Wang, L. Xue, A. Ebrahimi-Mamaghani, Eng. Comput. 36 (2020)

  53. J. Ignaczak, M. Ostoja-Starzewski, Thermoelasticity with Finite Wave Speeds (OUP, Oxford, 2009)

    Book  MATH  Google Scholar 

  54. M. Xu, X. Li, Int. J. Heat Mass Transf. 55(7–8), 1905 (2012)

    Article  Google Scholar 

  55. H.W. Lord, Y. Shulman, J. Mech. Phys. Solids 15(5), 299 (1967)

    Article  ADS  Google Scholar 

  56. D.Y. Tzou, Macro-to Microscale Heat Transfer: The Lagging Behavior (Wiley, Hoboken, 2014)

    Book  Google Scholar 

  57. R.A. Guyer, J. Krumhansl, Phys. Rev. 148(2), 766 (1966)

    Article  ADS  Google Scholar 

  58. T.V. Roszhart, Presented at the IEEE 4th Technical Digest on Solid-State Sensor and Actuator Workshop (1990) (unpublished)

  59. C. Zener, Phys. Rev. 52(3), 230 (1937)

    Article  ADS  Google Scholar 

  60. R. Lifshitz, M.L. Roukes, Phys. Rev. B 61(8), 5600 (2000)

    Article  ADS  Google Scholar 

  61. E. Taati, M.M. Najafabadi, J. Reddy, Compos. Struct. 116, 595 (2014)

    Article  Google Scholar 

  62. E.K. Kakhki, S.M. Hosseini, M. Tahani, Appl. Math. Model. 40(4), 3164 (2016)

    Article  MathSciNet  Google Scholar 

  63. G. Rezazadeh, M. Sheikhlou, R. Shabani, Meccanica 50(12), 2963 (2015)

    Article  MathSciNet  Google Scholar 

  64. H. Zhang, T. Kim, G. Choi, H.H. Cho, Int. J. Heat Mass Transf. 103, 783 (2016)

    Article  Google Scholar 

  65. Y.J. Yu, X.-G. Tian, J. Liu, Acta Mech. 228(4), 1287 (2017)

    Article  MathSciNet  Google Scholar 

  66. V. Borjalilou, M. Asghari, Acta Mech. 229(9), 3869 (2018)

    Article  MathSciNet  Google Scholar 

  67. W. Deng, L. Li, Y. Hu, X. Wang, X. Li, J. Therm. Stress. 41(9), 1182 (2018)

    Article  Google Scholar 

  68. S. Rashahmadi, S. Meguid, Acta Mech. 230(3), 771 (2019)

    Article  MathSciNet  Google Scholar 

  69. V. Borjalilou, M. Asghari, Mech. Adv. Mater. Struct. 26 (2019)

  70. H. Kumar, S. Mukhopadhyay, Int. J. Heat Mass Transf. 148, 118997 (2020)

    Article  Google Scholar 

  71. V. Borjalilou, M. Asghari, E. Taati, J. Vib. Control 26(11–12), 1042 (2020)

    Article  MathSciNet  Google Scholar 

  72. J.N. Reddy, Theory and Analysis of Elastic Plates and Shells (CRC Press, Boca Raton, 1999)

    Google Scholar 

  73. P. Li, Y. Fang, R. Hu, J. Sound Vib. 331(3), 721 (2012)

    Article  ADS  Google Scholar 

  74. F. Guo, W. Jiao, G. Wang, Z. Chen, J. Therm. Stress. 39(3), 360 (2016)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Electrical Engineering, Henan Polytechnic, Zhengzhou, Henan, 450046, China

    Feigao Li

  2. Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran

    Shahab Esmaeili

Authors
  1. Feigao Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shahab Esmaeili
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Feigao Li.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, F., Esmaeili, S. On thermoelastic damping in axisymmetric vibrations of circular nanoplates: incorporation of size effect into structural and thermal areas. Eur. Phys. J. Plus 136, 194 (2021). https://doi.org/10.1140/epjp/s13360-021-01084-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-021-01084-w

Search

Navigation