Skip to main content
SpringerLink
Log in

Forced vibration analysis of cracked nanobeams

  • Technical Paper
  • Published:
Journal of the Brazilian Society of Mechanical Sciences and Engineering Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

Forced vibration responses of a cantilever nanobeam with crack are presented for modified couple stress theory with damping effect. The crack is modeled with a rotational spring. The Kelvin–Voigt model is considered in the damping effect. In solution of the dynamic problem, finite element method is used within Timoshenko beam theory in the time domain. Influences of the geometry, crack and material parameters on forced vibration responses of cracked nanobeams are examined and discussed. Also, different beam theories are compared in the forced vibration results.

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
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Eringen AC (1972) Nonlocal polar elastic continua. Int J Eng Sci 10:1–16

    Article  MathSciNet  MATH  Google Scholar 

  2. Toupin RA (1962) Elastic materials with couple stresses. Arch Ration Mech Anal 11:385–414

    Article  MathSciNet  MATH  Google Scholar 

  3. Lam DCC, Yang F, Chong ACM, Wang J, Tong P (2003) Experiments and theory in strain gradient elasticity. J Mech Phys Solids 51:1477–1508

    Article  MATH  Google Scholar 

  4. Mindlin RD, Tiersten HF (1962) Effects of couple-stresses in linear elasticity. Arch Ration Mech Anal 11:415–448

    Article  MathSciNet  MATH  Google Scholar 

  5. Mindlin RD (1963) Influence of couple-stresses on stress concentrations. Exp Mech 3:1–7

    Article  Google Scholar 

  6. Yang F, Chong A, Lam D, Tong P (2002) Couple stress based strain gradient theory for elasticity. Int J Solids Struct 39:2731–2743

    Article  MATH  Google Scholar 

  7. Park SK, Gao XL (2006) Bernoulli-Euler beam model based on a modified couple stress theory. J Micromech Microeng 16:2355–2359

    Article  Google Scholar 

  8. Şimsek M (2010) Dynamic analysis of an embedded microbeam carrying a moving microparticle based on the modified couple stress theory. Int J Eng Sci 48:1721–1732

    Article  MATH  Google Scholar 

  9. Wang CM, Xiang Y, Kitipornchai S (2009) Postbuckling of nano rods/tubes based on nonlocal beam theory. Int J Appl Mech 1:259–266

    Article  Google Scholar 

  10. Kahrobaiyan MH, Asghari M, Rahaeifard M, Ahmadian MT (2010) Investigation of the size dependent dynamic characteristics of atomic force microscope microcantilevers based on the modified couple stress theory. Int J Eng Sci 48:1985–1994

    Article  Google Scholar 

  11. Dos Santos JA, Reddy JN (2012) Free vibration and buckling analysis of beams with a modified couple-stress theory. Int J Appl Mech 4:1250026

    Article  Google Scholar 

  12. Akgöz B, Civalek Ö (2012) Longitudinal vibration analysis for microbars based on strain gradient elasticity theory. J Vib Control 20:606–616

    Article  MathSciNet  MATH  Google Scholar 

  13. Xia W, Wang L, Yin L (2010) Nonlinear non-classical microscale beams: static, bending, postbuckling and free vibration. Int J Eng Sci 48:2044–2053

    Article  MathSciNet  MATH  Google Scholar 

  14. Kocatürk T, Akbaş ŞD (2013) Wave propagation in a microbeam based on the modified couple stress theory. Struct Eng Mech 46:417–431

    Article  Google Scholar 

  15. Zhang J, Fu Y (2012) Pull-in analysis of electrically actuated viscoelastic microbeams based on a modified couple stress theory. Meccanica 47:1649–1658

    Article  MathSciNet  MATH  Google Scholar 

  16. Ansari R, Gholami R, Shojaei MF, Mohammadi V, Darabi MA (2016) Coupled longitudinal-transverse-rotational free vibration of post-buckled functionally graded first-order shear deformable micro-and nano-beams based on the Mindlin’s strain gradient theory. Appl Math Model 40:9872–9891

    Article  MathSciNet  Google Scholar 

  17. Tang M, Ni Q, Wang L, Luo Y, Wang Y (2014) Size-dependent vibration analysis of a microbeam in flow based on modified couple stress theory. Int J Eng Sci 85:20–30

    Article  Google Scholar 

  18. Sedighi HM, Changizian M, Noghrehabadi A (2014) Dynamic pull-in instability of geometrically nonlinear actuated micro-beams based on the modified couple stress theory. Latin Am J Solids Struct 11:810–825

    Article  Google Scholar 

  19. Ansari R, Gholami R, Norouzzadeh A, Darabi MA (2016) Wave characteristics of nanotubes conveying fluid based on the non-classical Timoshenko beam model incorporating surface energies. Arab J Sci Eng 41:4359–4369

    Article  MathSciNet  MATH  Google Scholar 

  20. Khorshidi MA, Shariati M (2016) Free vibration analysis of sigmoid functionally graded nanobeams based on a modified couple stress theory with general shear deformation theory. J Braz Soc Mech Sci Eng 38:2607–2619

    Article  Google Scholar 

  21. Cajić M, Karličić D, Lazarević M (2015) Nonlocal vibration of a fractional order viscoelastic nanobeam with attached nanoparticle. Theoret Appl Mech 42:167–190

    Article  MATH  Google Scholar 

  22. Ansari R, Shojaei MF, Gholami R (2016) Size-dependent nonlinear mechanical behavior of third-order shear deformable functionally graded microbeams using the variational differential quadrature method. Compos Struct 136:669–683

    Article  Google Scholar 

  23. Akbaş ŞD (2017) Static, Vibration, and Buckling Analysis of Nanobeams. In: Vakhrushev A (ed) Nanomechanics, InTech, https://doi.org/10.5772/67973

  24. Dai HL, Wang YK, Wang L (2015) Nonlinear dynamics of cantilevered microbeams based on modified couple stress theory. Int J Eng Sci 94:103–112

    Article  MathSciNet  Google Scholar 

  25. Ansari R, Oskouie MF, Gholami R (2016) Size-dependent geometrically nonlinear free vibration analysis of fractional viscoelastic nanobeams based on the nonlocal elasticity theory. Physica E 75:266–271

    Article  Google Scholar 

  26. Aissani K, Bouiadjra MB, Ahouel M, Tounsi A (2015) A new nonlocal hyperbolic shear deformation theory for nanobeams embedded in an elastic medium. Struct Eng Mech 55:743–763

    Article  Google Scholar 

  27. Ghayesh MH, Farokhi H, Hussain S (2016) Viscoelastically coupled size-dependent dynamics of microbeams. Int J Eng Sci 109:243–255

    Article  MathSciNet  Google Scholar 

  28. Hosseini SAH, Rahmani O (2016) Surface effects on buckling of double nanobeam system based on nonlocal Timoshenko model. Int J Struct Stab Dyn 16:1550077

    Article  MathSciNet  MATH  Google Scholar 

  29. Ansari R, Gholami R (2016) Nonlocal nonlinear first-order shear deformable beam model for post-buckling analysis of magneto-electro-thermo-elastic nanobeams. Scientia Iranica. Transaction F. Nanotechnology 23:3099

    Google Scholar 

  30. Akbaş ŞD (2016) Forced vibration analysis of viscoelastic nanobeams embedded in an elastic medium. Smart Struct Syst 18:1125–1143

    Article  Google Scholar 

  31. Ebrahimi F, Barati MR (2016) Buckling analysis of nonlocal third-order shear deformable functionally graded piezoelectric nanobeams embedded in elastic medium. J Braz Soc Mech Sci Eng 39:937–952

    Article  Google Scholar 

  32. Bedia WA, Benzair A, Semmah A, Tounsi A, Mahmoud SR (2015) On the thermal buckling characteristics of armchair single-walled carbon nanotube embedded in an elastic medium based on nonlocal continuum elasticity. Braz J Phys 45:225–233

    Article  Google Scholar 

  33. Chaht FL, Kaci A, Houari MSA, Tounsi A, Bég OA, Mahmoud SR (2015) Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect. Steel Compos Struct 18:425–442

    Article  Google Scholar 

  34. Bouafia K, Kaci A, Houari MSA, Benzair A, Tounsi A (2017) A nonlocal quasi-3D theory for bending and free flexural vibration behaviors of functionally graded nanobeams. Smart Struct Syst 19:115–126

    Article  Google Scholar 

  35. Ahouel M, Houari MSA, Bedia EA, Tounsi A (2016) Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept. Steel Compos Struct 20:963–981

    Article  Google Scholar 

  36. Ansari R, Gholami R (2016) Size-dependent nonlinear vibrations of first-order shear deformable magneto-electro-thermo elastic nanoplates based on the nonlocal elasticity theory. Int J Appl Mech 8:1650053

    Article  Google Scholar 

  37. Ansari R, Gholami R (2016) Surface effect on the large amplitude periodic forced vibration of first-order shear deformable rectangular nanoplates with various edge supports. Acta Astronaut 118:72–89

    Article  Google Scholar 

  38. Ansari R, Gholami R (2016) Size-dependent modeling of the free vibration characteristics of postbuckled third-order shear deformable rectangular nanoplates based on the surface stress elasticity theory. Compos B Eng 95:301–316

    Article  Google Scholar 

  39. Akbaş ŞD (2016) Static analysis of a nano plate by using generalized differential quadrature method. Int J Eng Appl Sci 8:30–39

    Google Scholar 

  40. Belkorissat I, Houari MSA, Tounsi A, Bedia EA, Mahmoud SR (2015) On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model. Steel Compos Struct 18:1063–1081

    Article  Google Scholar 

  41. Ansari R, Faghih Shojaei M, Mohammadi V, Gholami R, Darabi MA (2015) A nonlinear shear deformable nanoplate model including surface effects for large amplitude vibrations of rectangular nanoplates with various boundary conditions. Int J Appl Mech 7:1550076

    Article  Google Scholar 

  42. Ansari R, Norouzzadeh A, Gholami R, Shojaei MF, Darabi MA (2016) Geometrically nonlinear free vibration and instability of fluid-conveying nanoscale pipes including surface stress effects. Microfluid Nanofluid 20:28

    Article  Google Scholar 

  43. Ansari R, Ramezannezhad H, Gholami R (2012) Nonlocal beam theory for nonlinear vibrations of embedded multiwalled carbon nanotubes in thermal environment. Nonlinear Dyn 67:2241–2254

    Article  MathSciNet  MATH  Google Scholar 

  44. Ansari R, Pourashraf T, Gholami R (2015) An exact solution for the nonlinear forced vibration of functionally graded nanobeams in thermal environment based on surface elasticity theory. Thin-Walled Struct 93:169–176

    Article  Google Scholar 

  45. Ansari R, Gholami R, Rouhi H (2015) Size-dependent nonlinear forced vibration analysis of magneto-electro-thermo-elastic Timoshenko nanobeams based upon the nonlocal elasticity theory. Compos Struct 126:216–226

    Article  Google Scholar 

  46. Bounouara F, Benrahou KH, Belkorissat I, Tounsi A (2016) A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation. Steel Compos Struct 20:227–249

    Article  Google Scholar 

  47. Fang T-H, Chang W-J, Liao S-C (2003) Simulated nanojet ejection process by spreading droplets on a solid surface. J Phys Condens Matter 15:8263–8271

    Article  Google Scholar 

  48. Fang T-H, Chang W-J (2003) Sensitivity analysis of scanning near-field optical microscope probe. Opt Laser Technol 35:267–271

    Article  Google Scholar 

  49. Loya J, López-Puente J, Zaera R, Fernández-Sáez J (2009) Free transverse vibrations of cracked nanobeams using a nonlocal elasticity model. J Appl Phys 105:044309

    Article  Google Scholar 

  50. Hasheminejad BSM, Gheshlaghi B, Mirzaei Y, Abbasion S (2011) Free transverse vibrations of cracked nanobeams with surface effects. Thin Solid Films 519:2477–2482

    Article  Google Scholar 

  51. Torabi K, Nafar Dastgerdi J (2012) An analytical method for free vibration analysis of Timoshenko beam theory applied to cracked nanobeams using a nonlocal elasticity model. Thin Solid Films 520:6595–6602

    Article  Google Scholar 

  52. Liu SJ, Qi SH, Zhang WM (2013) Vibration behavior of a cracked micro-cantilever beam under electrostatic excitation. Zhendong yu Chongji/J Vib Shock 32:41–45

    Google Scholar 

  53. Roostai H, Haghpanahi M (2014) Vibration of nanobeams of different boundary conditions with multiple cracks based on nonlocal elasticity theory. Appl Math Model 38:1159–1169

    Article  MathSciNet  Google Scholar 

  54. Yaylı MO, Çerçevik AE (2015) Axial vibration analysis of cracked nanorods with arbitrary boundary conditions. J Vibroeng 17:2907–2921

    Google Scholar 

  55. Tadi Beni Y, Jafari A, Razavi H (2015) Size effect on free transverse vibration of cracked nano-beams using couple stress theory. Int J Eng 28:296–304

    Google Scholar 

  56. Wang K, Wang B (2015) Timoshenko beam model for the vibration analysis of a cracked nanobeam with surface energy. J Vib Control. https://doi.org/10.1177/1077546313513054

    MathSciNet  Google Scholar 

  57. Stamenković M, Karličić D, Goran J, Kozić P (2016) Nonlocal forced vibration of a double single-walled carbon nanotube system under the influence of an axial magnetic field. J Mech Mater Struct 11:279–307

    Article  MathSciNet  Google Scholar 

  58. Peng X-L, Li X-F, Tang G-J, Shen Z-B (2015) Effect of scale parameter on the deflection of a nonlocal beam and application to energy release rate of a crack. ZAMM—J Appl Math Mech 95:1428–1438

    Article  MathSciNet  MATH  Google Scholar 

  59. Akbaş ŞD (2016) Analytical solutions for static bending of edge cracked micro beams. Struct Eng Mech 59:579–599

    Article  Google Scholar 

  60. Akbaş ŞD (2017) Free vibration of edge cracked functionally graded microscale beams based on the modified couple stress theory. Int J Struct Stab Dyn 17:1750033

    Article  MathSciNet  Google Scholar 

  61. Chakraborty A, Mahapatra DR, Gopalakrishnan S (2002) Finite element analysis of free vibration and wave propagation in asymmetric composite beams with structural discontinuities. Compos Struct 55:23–36

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Civil Engineering, Bursa Technical University, Bursa, Turkey

    Şeref D. Akbaş

Authors
  1. Şeref D. Akbaş
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Şeref D. Akbaş.

Additional information

Technical Editor: Kátia Lucchesi Cavalca Dedini.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Akbaş, Ş.D. Forced vibration analysis of cracked nanobeams. J Braz. Soc. Mech. Sci. Eng. 40, 392 (2018). https://doi.org/10.1007/s40430-018-1315-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40430-018-1315-1

Keywords

Search

Navigation