123
Views
10
CrossRef citations to date
0
Altmetric
Original Articles

A consistent shear beam theory for free vibration of functionally graded beams based on physical neutral plane

, & ORCID Icon
Pages 3844-3854 | Received 27 Dec 2022, Accepted 24 Feb 2023, Published online: 06 Mar 2023

References

  • H. Su, J. Banerjee, and C. Cheung, Dynamic stiffness formulation and free vibration analysis of functionally graded beams, Compos. Struct., vol. 106, pp. 854–862, 2013.
  • J. W. Lee, and J. Y. Lee, Free vibration analysis of functionally graded Bernoulli-Euler beams using an exact transfer matrix expression, Int. J. Mech. Sci., vol. 122, pp. 1–17, 2017.
  • J. 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.
  • J. Yang, Y. Chen, Y. Xiang, and X. Jia, Free and forced vibration of cracked inhomogeneous beams under an axial force and a moving load, J. Sound Vib., vol. 312, no. 1–2, pp. 166–181, 2008.
  • Y. A. Kang, and X. F. Li, Bending of functionally graded cantilever beam with power-law non-linearity subjected to an end force, Int. J. Nonlinear Mech., vol. 44, no. 6, pp. 696–703, 2009.
  • Y. A. Kang, and X. F. Li, Large deflections of a non-linear cantilever functionally graded beam, J. Reinf. Plast. Compos., vol. 29, no. 12, pp. 1761–1774, 2010.
  • C. Wang, L. Ke, A. R. Chowdhury, J. Yang, S. Kitipornchai, and D. Fernando, Critical examination of midplane and neutral plane formulations for vibration analysis of FGM beams, Eng. Struct., vol. 130, pp. 275–281, 2017.
  • G. Chen, X. Zeng, X. Liu, and X. Rui, Transfer matrix method for the free and forced vibration analyses of multi-step Timoshenko beams coupled with rigid bodies on springs, Appl. Math. Modell., vol. 87, pp. 152–170, 2020.
  • A. Chakraborty, S. Gopalakrishnan, and J. Reddy, A new beam finite element for the analysis of functionally graded materials, Int. J. Mech. Sci., vol. 45, no. 3, pp. 519–539, 2003.
  • S. Alimirzaei, M. Mohammadimehr, and M. Mohammadimehr, Nonlinear analysis of viscoelastic micro-composite beam with geometrical imperfection using FEM: MSGT electro-magneto-elastic bending, buckling and vibration solutions, Struct. Eng. Mech., vol. 71, pp. 485–502, 2019.
  • X.-F. Li, A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler-Bernoulli beams, J. Sound Vib., vol. 318, no. 4-5, pp. 1210–1229, 2008.
  • X. F. Li, B. L. Wang, and J. C. Han, A higher-order theory for static and dynamic analyses of functionally graded beams, Arch. Appl. Mech., vol. 80, no. 10, pp. 1197–1212, 2010.
  • K. Pradhan, and S. Chakraverty, Free vibration of Euler and Timoshenko functionally graded beams by Rayleigh-Ritz method, Composites, Part B., vol. 51, pp. 175–184, 2013.
  • H. Su, and J. Banerjee, Development of dynamic stiffness method for free vibration of functionally graded Timoshenko beams, Comput. Struct., vol. 147, pp. 107–116, 2015.
  • M. Simsek, 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.
  • M. Simsek, Vibration analysis of a functionally graded beam under a moving mass by using different beam theories, Compos. Struct., vol. 92, no. 4, pp. 904–917, 2010.
  • H.-T. Thai, and T. P. Vo, Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories, Int. J. Mech. Sci., vol. 62, no. 1, pp. 57–66, 2012.
  • W.-L. Ma, Z.-C. Jiang, and X.-F. Li, Effect of warping shape on buckling of circular and rectangular columns under axial compression, Appl. Math. Modell., vol. 89, pp. 1475– 1490, 2021.
  • M. Salamat-Talab, A. Nateghi, and J. Torabi, Static and dynamic analysis of third-order shear deformation FG micro beam based on modified couple stress theory, Int. J. Mech. Sci., vol. 57, no. 1, pp. 63–73, 2012.
  • M. Simsek, and J. Reddy, Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory, Int. J. Eng. Sci., vol. 64, pp. 37–53, 2013.
  • F. Ebrahimi, and N. Farazmandnia, Thermo-mechanical vibration analysis of sandwich beams with functionally graded carbon nanotube-reinforced composite face sheets based on a higher-order shear deformation beam theory, Mech. Adv. Mater. Struct., vol. 24, no. 10, pp. 820–829, 2016.
  • G. Shabanlou, S. Hosseini, and M. Zamanian, Vibration analysis of FG spinning beam using higher-order shear deformation beam theory in thermal environment, Appl. Math. Modell., vol. 56, pp. 325–341, 2018.
  • W. Li, W. Gao, and S. Chen, A material-based higher-order shear beam model for accurate analyses of FG beams with arbitrary material distribution, Compos. Struct., vol. 245, pp. 112253, 2020.
  • Y. Huang, and X. F. Li, Bending and vibration of circular cylindrical beams with arbitrary radial nonhomogeneity, Int. J. Mech. Sci., vol. 52, no. 4, pp. 595–601, 2010.
  • A. Garg, H. D. Chalak, M.-O. Belarbi, and A. M. Zenkour, Hygro-thermo-mechanical based bending analysis of symmetric and unsymmetric power-law, exponential and sigmoidal FG sandwich beams, Mech. Adv. Mater. Struct., vol. 29, no. 25, pp. 4523–4545, 2021.
  • M. Taj, A. Majeed, M. Hussain, M.N. Naeem, M. Safeer, M. Ahmad, H.U. Khan and A. Tounsi, Non-local orthotropic elastic shell model for vibration analysis of protein microtubules, Comput. Concrete., vol. 25, no. 3, pp. 245–253, 2020.
  • M. Hussain, M. N. Naeem, M. S. Khan, and A. Tounsi, Computer-aided approach for modelling of FG cylindrical shell sandwich with ring supports, Comput. Concrete., vol. 25, no. 5, pp. 411–425, 2020.
  • F. Y. Addou, M. Meradjah, A. A. Bousahla, A. Benachour, F. Bourada, A. Tounsi, and S.R. Mahmoud, Influences of porosity on dynamic response of FG plates resting on Winkler/Pasternak/Kerr foundation using quasi 3D HSDT, Comput. Concrete., vol. 24, pp. 347–367, 2019.
  • Z. T. Beni, and Y. T. Beni, Dynamic stability analysis of size-dependent viscoelastic/piezoelectric nano-beam, Int. J. Struct. Stab. Dyn., vol. 22, no. 5, p. 2250050, 2022.
  • S.-R. Li, and R. C. Batra, Relations between buckling loads of functionally graded Timoshenko and homogeneous Euler-Bernoulli beams, Compos. Struct., vol. 95, pp. 5–9, 2013.
  • M. Eltaher, A. Alshorbagy, and F. Mahmoud, Determination of neutral axis position and its effect on natural frequencies of functionally graded macro/nanobeams, Compos. Struct., vol. 99, pp. 193–201, 2013.
  • M. Eltaher, A. Abdelrahman, A. Al-Nabawy, M. Khater, and A. Mansour, Vibration of nonlinear graduation of nano-Timoshenko beam considering the neutral axis position, Appl. Math. Comput., vol. 235, pp. 512–529, 2014.
  • W.-R. Chen, and H. Chang, Vibration analysis of functionally graded Timoshenko beams, Int. J. Struct. Stab. Dyn., vol. 18, no. 1, p. 1850007, 2018.
  • Y. Liu, S. Su, H. Huang, and Y. Liang, Thermal-mechanical coupling buckling analysis of porous functionally graded sandwich beams based on physical neutral plane, Composites, Part B., vol. 168, pp. 236–242, 2019.
  • N.-I. Kim, and J. Lee, Exact solutions for coupled responses of thin-walled FG sandwich beams with non-symmetric cross-sections, Composites, Part B., vol. 122, pp. 121–135, 2017.
  • F. A. Fazzolari, Generalized exponential, polynomial and trigonometric theories for vibration and stability analysis of porous FG sandwich beams resting on elastic foundations, Composites, Part B., vol. 136, pp. 254–271, 2018.
  • L. Hadji, and E. A. A. Bedia, Analyse of the behavior of functionally graded beams based on neutral surface position, Struct. Eng. Mech., vol. 55, pp. 703–717, 2015.
  • L. O. Larbi, A. Kaci, M. S. A. Houari, and A. Tounsi, An efficient shear deformation beam theory based on neutral surface position for bending and free vibration of functionally graded beams, Mech. Based Des. Struct. Mach., vol. 41, no. 4, pp. 421–433, 2013.
  • K. Al-Basyouni, A. Tounsi, and S. Mahmoud, Size dependent bending and vibration analysis of functionally graded micro beams based on modified couple stress theory and neutral surface position, Compos. Struct., vol. 125, pp. 621–630, 2015.
  • S. A. Farzam-Rad, B. Hassani, and A. Karamodin, Isogeometric analysis of functionally graded plates using a new quasi-3D shear deformation theory based on physical neutral surface, Composites, Part B., vol. 108, pp. 174–189, 2017.
  • J. N. Reddy, An Introduction to Continuum Mechanics, Cambridge University Press, New York, 2013.
  • S. M. Han, H. Benaroya, and T. Wei, Dynamics of transversely vibrating beams using four engineering theories, J. Sound Vib., vol. 225, no. 5, pp. 935–988, 1999.
  • S. S. Rao, Vibration of Continuous Systems, Wiley, Hoboken, 2019.
  • I. A. Karnovsky, and O. I. Leged, Formulas for Structural Dynamics: Tables, Graphs, and Solutions, McGraw-Hill, New York, 2004.
  • J. Yang, and Y. Chen, Free vibration and buckling analyses of functionally graded beams with edge cracks, Compos. Struct., vol. 83, no. 1, pp. 48–60, 2008.
  • H. A. Atmane, A. Tounsi, S. A. Meftah, and H. A. Belhadj, Free vibration behavior of exponential functionally graded beams with varying cross-section, J. Vib. Control., vol. 17, no. 2, pp. 311–318, 2010.
  • T. P. Vo, H.-T. Thai, T.-K. Nguyen, A. Maheri, and J. Lee, Finite element model for vibration and buckling of functionally graded sandwich beams based on a refined shear deformation theory, Eng. Struct., vol. 64, pp. 12–22, 2014.
  • P. Tossapanon, and N. Wattanasakulpong, Stability and free vibration of functionally graded sandwich beams resting on two-parameter elastic foundation, Compos. Struct., vol. 142, pp. 215–225, 2016.

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.