240
Views
6
CrossRef citations to date
0
Altmetric
Original Articles

An analytical approach to geometrically nonlinear free and forced vibration of piezoelectric functional gradient beams resting on elastic foundations in thermal environments

, , , &
Pages 131-143 | Received 05 Oct 2021, Accepted 18 Nov 2021, Published online: 16 Dec 2021

References

  • D. Wei, Y. Liu, and Z. Xiang, An analytical method for free vibration analysis of functionally graded beams with edge cracks, J. Sound Vib., vol. 331, pp. 1686–1700, 2012.
  • J.R. Banerjee and A. Ananthapuvirajah, Free vibration of functionally graded beams and frameworks using the dynamic stiffness method, J. Sound Vib., vol. 422, pp. 34–47, 2018. DOI: 10.1016/j.jsv.2018.02.010.
  • M. Amoozgar and L. Gelman, Vibration analysis of rotating porous functionally graded material beams using exact formulation, J. Vib. Control, pp. 1–12, 2021. DOI: 10.1177/10775463211027883.
  • J. Maruani, I. Bruant, F. Pablo, and L. Gallimard, Active vibration control of a smart functionally graded piezoelectric material plate using an adaptive fuzzy controller strategy, J. Intell. Mater. Syst. Struct., vol. 30, no. 14, pp. 2065–2078, 2019. DOI: 10.1177/1045389X19853628.
  • M. Farrokh, M. Afzali, and E. Carrera, Mechanical and thermal buckling loads of rectangular FG plates by using higher-order unified formulation, Mech. Adv. Mater. Struct., vol. 28, no. 6, pp. 608–617, 2021. DOI: 10.1080/15376494.2019.1578014.
  • M.H. Jalaei and Ö. Civalek, On dynamic instability of magnetically embedded viscoelastic porous FG nanobeam, Int. J. Eng. Sci., vol. 143, pp. 14–32, 2019. DOI: 10.1016/j.ijengsci.2019.06.013.
  • Ö. Civalek, S. Dastjerdi, Ş.D. Akbaş, and B. Akgöz, Vibration analysis of carbon nanotube-reinforced composite microbeams, Math. Meth. Appl. Sci., pp. 1–17, 2021.
  • Ş.D. Akbaş, H. Ersoy, B. Akgöz, and Ö. Civalek, Dynamic analysis of a fiber-reinforced composite beam under a moving load by the Ritz method, Mathematics, vol. 9, no. 9, pp. 1048, 2021. DOI: 10.3390/math9091048.
  • E. Carrera, I. Kaleel, and M. Petrolo, Elastoplastic analysis of compact and thin-walled structures using classical and refined beam finite element models, Mech. Adv. Mater. Struct., vol. 26, no. 3, pp. 274–286, 2019. DOI: 10.1080/15376494.2017.1378780.
  • F. Ebrahimi and M. Mokhtari, Transverse vibration analysis of rotating porous beam with functionally graded microstructure using the differential transform method, J. Braz. Soc. Mech. Sci. Eng., vol. 37, no. 4, pp. 1435–1444, 2015. DOI: 10.1007/s40430-014-0255-7.
  • S. Li, H. Su, and C. Cheng, Free vibration of functionally graded material beams with surface-bonded piezoelectric layers in thermal environment, Appl. Math. Mech.-Engl. Ed., vol. 30, no. 8, pp. 969–982, 2009. DOI: 10.1007/s10483-009-0803-7.
  • N. Shafiei, A. Mousavi, and M. Ghadiri, On size-dependent nonlinear vibration of porous and imperfect functionally graded tapered microbeams, Int. J. Eng. Sci., vol. 106, pp. 42–56, 2016. DOI: 10.1016/j.ijengsci.2016.05.007.
  • G.-L. She, Y.-R. Ren, F.-G. Yuan, and X.-S. Xiao, On vibrations of porous nanotubes, Int. J. Eng. Sci., vol. 125, pp. 23–35, 2018. DOI: 10.1016/j.ijengsci.2017.12.009.
  • Y. Wang and D. Wu, Free vibration of functionally graded porous cylindrical shell using a sinusoidal shear deformation theory, Aerosp. Sci. Technol., vol. 66, pp. 83–91, 2017. DOI: 10.1016/j.ast.2017.03.003.
  • F. Ebrahimi and M. R. Barati, Vibration analysis of piezoelectrically actuated curved nanosize FG beams via a nonlocal strain-electric field gradient theory, Mech. Adv. Mater. Struct., vol. 25, no. 4, pp. 350–359, 2018. DOI: 10.1080/15376494.2016.1255830.
  • G.-L. She, X. Shu, and Y.-R. Ren, Thermal buckling and postbuckling analysis of piezoelectric FGM beams based on high-order shear deformation theory, J. Therm. Stresses., vol. 40, no. 6, pp. 783–797, 2017. DOI: 10.1080/01495739.2016.1261009.
  • Y. Tadi Beni, Size-dependent electromechanical bending, buckling, and free vibration analysis of functionally graded piezoelectric nanobeams, J. Intell. Mater. Syst. Struct., vol. 27, no. 16, pp. 2199–2215, 2016. DOI: 10.1177/1045389X15624798.
  • P. Yu, W. Leng, L. Peng, and J. Guo, The bending and vibration responses of functionally graded piezoelectric nanobeams with dynamic flexoelectric effect, Results Phys., vol. 28, pp. 104624, 2021. DOI: 10.1016/j.rinp.2021.104624.
  • B. Akgöz and Ö. Civalek, Buckling analysis of functionally graded microbeams based on the strain gradient theory, Acta Mech., vol. 224, no. 9, pp. 2185–2201, 2013. DOI: 10.1007/s00707-013-0883-5.
  • K. El Harti, M. Sanbi, R. Miloud, R. Saadani, R. Agounoun, and M. Bentaleb, Active vibration control of sandwich FGM beam with piezoelectric sensor/actuator, Int. J. Appl. Eng. Res., vol. 12, pp. 9338–9345, 2017.
  • H. Yaghoobi and M. Torabi, Post-buckling and nonlinear free vibration analysis of geometrically imperfect functionally graded beams resting on nonlinear elastic foundation, Appl. Math. Modell., vol. 37, no. 1819, pp. 8324–8340, 2013. DOI: 10.1016/j.apm.2013.03.037.
  • H.-S. Shen, Y. Xiang, and F. Lin, Nonlinear bending of functionally graded graphene-reinforced composite laminated plates resting on elastic foundations in thermal environments, Compos. Struct., vol. 170, pp. 80–90, 2017. DOI: 10.1016/j.compstruct.2017.03.001.
  • A. Hadi, M.Z. Nejad, A. Rastgoo, and M. Hosseini, Buckling analysis of FGM Euler-Bernoulli nano-beams with 3D-varying properties based on consistent couple-stress theory, vol. 26, pp. 663–672, 2018.
  • Z. Li, Y. Xu, and D. Huang, Analytical solution for vibration of functionally graded beams with variable cross-sections resting on Pasternak elastic foundations, Int. J. Mech. Sci., vol. 191, pp. 106084, 2021. DOI: 10.1016/j.ijmecsci.2020.106084.
  • L. Hadji and F. Bernard, Bending and free vibration analysis of functionally graded beams on elastic foundations with analytical validation, Adv. Mater. Res., vol. 9, pp. 63–98, 2020.
  • V. Stojanović, Geometrically nonlinear vibrations of beams supported by a nonlinear elastic foundation with variable discontinuity, Commun. Nonlinear Sci. Numer. Simul., vol. 28, no. 1–3, pp. 66–80, 2015. DOI: 10.1016/j.cnsns.2015.04.002.
  • M. Javani, Y. Kiani, and M.R. Eslami, Geometrically nonlinear rapid surface heating of temperature-dependent FGM arches, Aerosp. Sci. Technol., vol. 90, pp. 264–274, 2019. DOI: 10.1016/j.ast.2019.04.049.
  • X.-L. Huang and H.-S. Shen, Vibration and dynamic response of functionally graded plates with piezoelectric actuators in thermal environments, J. Sound Vib., vol. 289, no. 12, pp. 25–53, 2006. DOI: 10.1016/j.jsv.2005.01.033.
  • Y. El Khouddar, A. Adri, O. Outassafte, S. Rifai, and R. Benamar, Non-linear forced vibration analysis of piezoelectric functionally graded beams in thermal environment, Int. J. Eng., vol. 34, pp. 2387–2397, 2021.
  • E. Mahmoudpour, S.H. Hosseini-Hashemi, and S.A. Faghidian, Nonlinear vibration analysis of FG nano-beams resting on elastic foundation in thermal environment using stress-driven nonlocal integral model, Appl. Math. Modell., vol. 57, pp. 302–315, 2018. DOI: 10.1016/j.apm.2018.01.021.
  • A. Mahi, E.A. Adda Bedia, A. Tounsi, and I. Mechab, An analytical method for temperature-dependent free vibration analysis of functionally graded beams with general boundary conditions, Compos. Struct., vol. 92, no. 8, pp. 1877–1887, 2010. DOI: 10.1016/j.compstruct.2010.01.010.
  • F. Pellicano and F. Mastroddi, Nonlinear dynamics of a beam on elastic foundation, Nonlinear Dyn., vol. 14, no. 4, pp. 335–355, 1997. DOI: 10.1023/A:1008297721253.
  • M. Rafiee, J. Yang, and S. Kitipornchai, Thermal bifurcation buckling of piezoelectric carbon nanotube reinforced composite beams, Comput. Math. Appl., vol. 66, no. 7, pp. 1147–1160, 2013. DOI: 10.1016/j.camwa.2013.04.031.
  • M. Rafiee, J. Yang, and S. Kitipornchai, Large amplitude vibration of carbon nanotube reinforced functionally graded composite beams with piezoelectric layers, Compos. Struct., vol. 96, pp. 716–725, 2013. DOI: 10.1016/j.compstruct.2012.10.005.
  • A. Ahmed and B. Rhali, Linear and geometrically non-linear frequencies and mode shapes of beams carrying a point mass at various locations. an analytical approch and a parametric study, Diagnostyka, vol. 18, pp. 13–21, 2017.
  • R. Benamar, M.M.K. Bennouna, and R.G. White, The effects of large vibration amplitudes on the mode shapes and natural frequencies of thin elastic structures part I: Simply supported and clamped-clamped beams, J. Sound Vib., vol. 149, no. 2, pp. 179–195, 1991. DOI: 10.1016/0022-460X(91)90630-3.
  • L. Azrar, R. Benamar, and R.G. White, A semi-analytical approach to the non-linear dynamic response problem of beams at large vibration amplitudes, part II: Multimode approach to the steady state forced periodic response, J. Sound Vib., vol. 255, no. 1, pp. 1–41, 2002. DOI: 10.1006/jsvi.2000.3595.
  • O. Outassafte, A. Adri, Y. El Khouddar, S. Rifai, and R. Benamar, Geometrically non-linear free and forced vibration of a shallow arch, J. Vibroeng., vol. 23, no. 7, pp. 1508–1523, 2021. DOI: 10.21595/jve.2021.21857.
  • O. Outassafte, A. Adri, Y. El Khouddar, S. Rifai, and R. Benamar, Geometrically non-linear free in-plane vibration of circular arch elastically restrained against rotation at the two ends, IJETT., vol. 69, no. 3, pp. 85–95, 2021. DOI: 10.14445/22315381/IJETT-V69I3P215.
  • L. Azrar, R. Benamar, and R.G. White, Semi-analytical approach to the non-linear dynamic response problem of S–S and C–C beams at large vibration amplitudes part I: General theory and application to the single mode approach to free and forced vibration analysis, J. Sound Vib., vol. 224, no. 2, pp. 183–207, 1999. DOI: 10.1006/jsvi.1998.1893.
  • M. El Kadiri, R. Benamar, and R.G. White, Improvement of the semi-analytical method, for determining the geometrically non-linear response of thin straight structures. Part I: Application to clamped–clamped and simply supported–clamped beams, J. Sound Vib., vol. 249, no. 2, pp. 263–305, 2002. DOI: 10.1006/jsvi.2001.3808.
  • F. Ebrahimi and E. Salari, Thermo-mechanical vibration analysis of nonlocal temperature-dependent FG nanobeams with various boundary conditions, Compos. Part B: Eng., vol. 78, pp. 272–290, 2015. DOI: 10.1016/j.compositesb.2015.03.068.
  • N. Shegokar and A. Lal, Stochastic finite element nonlinear free vibration analysis of piezoelectric functionally graded materials beam subjected to thermo-piezoelectric loadings with material uncertainties, Meccanica, vol. 49, no. 5, pp. 1039–1068, 2014. DOI: 10.1007/s11012-013-9852-2.
  • M. Şimşek, Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories, Nucl. Eng. Des., vol. 240, no. 4, pp. 697–705, 2010. DOI: 10.1016/j.nucengdes.2009.12.013.
  • N. Wattanasakulpong and V. Ungbhakorn, Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities, Aerosp. Sci. Technol., vol. 32, no. 1, pp. 111–120, 2014. DOI: 10.1016/j.ast.2013.12.002.
  • N. Togun, Nonlocal beam theory for nonlinear vibrations of a nanobeam resting on elastic foundation, Bound. Value Probl., vol. 2016, no. 1, pp. 1–14, 2016. DOI: 10.1186/s13661-016-0561-3.
  • E. Ghavanloo, F. Daneshmand, and M. Rafiei, Vibration and instability analysis of carbon nanotubes conveying fluid and resting on a linear viscoelastic Winkler foundation, Phys. E, vol. 42, no. 9, pp. 2218–2224, 2010. DOI: 10.1016/j.physe.2010.04.024.
  • D.-G. Zhang, Thermal post-buckling and nonlinear vibration analysis of FGM beams based on physical neutral surface and high order shear deformation theory, Meccanica, vol. 49, no. 2, pp. 283–293, 2014. DOI: 10.1007/s11012-013-9793-9.
  • A.H. Nayfeh and D.T. Mook, Nonlinear Oscillations, John Wiley & Sons, 2008.
  • M. Amabili, Nonlinear vibrations of rectangular plates with different boundary conditions: Theory and experiments, Comput. Struct., vol. 82, no. 3132, pp. 2587–2605, 2004. DOI: 10.1016/j.compstruc.2004.03.077.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.