References
- Bernoulli, D. 1751. De vibrationibus et sono laminarum elasticarum. In: Commentarii Academiae Scientiarum Imperialis Petropolitanae, Petropoli.
- Bickford, W. B. 1982. A consistent higher order beam theory. In Developments in theoretical and applied mechanics. Proceedings of the eleventh southeastern conference on theoretical and applied mechanics, eds. T. C. and G. Karr, 137–50. Huntsville, Alabama.
- Carrera, E., A. Pagani, M. Petrolo, and E. Zappino. 2015. Recent developments on refined theories for beams with applications. Mechanical Engineering Reviews 2 (2):14-00298. doi:https://doi.org/10.1299/mer.14-00298.
- Carrera, E., S. Valvano, and G. M. Kulikov. 2018. Multilayered plate elements with node-dependent kinematics for electro-mechanical problems. International Journal of Smart and Nano Materials 9 (4):279–317. doi:https://doi.org/10.1080/19475411.2017.1376722.
- Dwaikat, M., and V. Kodur. 2010. Effect of location of restraint on fire response of steel beams. Fire Technology 46:109–28. doi:https://doi.org/10.1007/s10694-009-0085-9.
- Eltaher, M. A., A. E. Alshorbagy, and F. F. Mahmoud. 2013. Determination of neutral axis position and its effect on natural frequencies of functionally graded macro/nanobeams. Composite Structures 99:193–201. doi:https://doi.org/10.1016/j.compstruct.2012.11.039.
- Euler, L. 1744. De curvis elasticis. In Bousquet. Chap. Methodus Inveniendi Lineas Curvas Maximi Minimive Proprietate Gaudentes, Sive Solutio Problematis Isoperimetrici Lattissimo Sensu Accept.
- Fernando, D., C. M. Wang, and A. N. Roy Chowdhury. 2018. Vibration of laminated-beams based on reference-plane formulation: effect of end supports at different heights of the beam. Engineering Structures 159:245–51. doi:https://doi.org/10.1016/j.engstruct.2018.01.004.
- Filippi, M., E. Carrera, and S. Valvano. 2018. Analysis of multilayered structures embedding viscoelastic layers by higher-order, and zig-zag plate elements. Composites Part B: Engineering 154:77–89. doi:https://doi.org/10.1016/j.compositesb.2018.07.054.
- Gere, J. M., and S. P. Timoshenko. 1991. Mechanics of materials, 3rd SI ed. London: Chapman & Hall.
- Heyliger, P. R., and J. N. Reddy. 1988. A higher order beam finite element for bending and vibration problems. Journal of Sound and Vibration 126 (2):309–26. doi:https://doi.org/10.1016/0022-460X(88)90244-1.
- Iyengar, K. T. S. R. 2008. Application of Maclaurin series in structural analysis. Journal of the Indian Institute of Science 8 (3):879–87.
- Jena S. K., S. Chakraverty, M Malikan and F Tornabene. 2019. Stability analysis of single-walled carbon nanotubes embedded in Winkler foundation placed in a thermal environment considering the surface effect using a new refined beam theory. Mechanics Based Design of Structures and Machines 1–15. doi:https://doi.org/10.1080/15397734.2019.1698437.
- Jun, L., and H. Hongxing. 2009. Variationally consistent higher-order analysis of harmonic vibrations of laminated beams. Mechanics Based Design of Structures and Machines 37 (3):299–326. doi:https://doi.org/10.1080/15397730902932608.
- Kant, T., and A. Gupta. 1988. A finite element model for a higher-order shear-deformable beam theory. Journal of Sound and Vibration 125 (2):193–202. doi:https://doi.org/10.1016/0022-460X(88)90278-7.
- Kim, N.-I., and J. Lee. 2015. Refined series methodology for the fully coupled thin-walled laminated beams considering foundation effects. Mechanics Based Design of Structures and Machines 43 (2):125–49. doi:https://doi.org/10.1080/15397734.2014.931811.
- Krishna Murty, A. V. 1985. On the shear deformation theory for dynamic analysis of beams. Journal of Sound and Vibration 101 (1):1–12. doi:https://doi.org/10.1016/S0022-460X(85)80033-X.
- Larbi, L. O., et al. 2013. An efficient shear deformation beam theory based on neutral surface position for bending and free vibration of functionally graded beams. Mechanics Based Design of Structures and Machines 41(4):421–33. doi:https://doi.org/10.1080/15397734.2013.763713.
- Levinson, M. 1981. A new rectangular beam theory. Journal of Sound and Vibration 74 (1):81–7. doi:https://doi.org/10.1016/0022-460X(81)90493-4.
- Levinson, M. 1985. On Bickford’s consistent higher order beam theory. Mechanics Research Communications 12 (1):1–9. doi:https://doi.org/10.1016/0093-6413(85)90027-8.
- Radice, J. J. 2012. On the effect of local boundary condition details on the natural frequencies of simply-supported beams: eccentric pin supports. Mechanics Research Communications 39 (1):1–8. doi:https://doi.org/10.1016/j.mechrescom.2011.08.007.
- Reddy, J. N. 1997. On locking-free shear deformable beam finite elements. Computer Methods in Applied Mechanics and Engineering 149 (1–4):113–32. doi:https://doi.org/10.1016/S0045-7825(97)00075-3.
- Rehfield, L. W., and P. L. N. Murthy. 1982. Toward a new engineering theory of bending: fundamentals. AIAA Journal 20 (5):693–9. doi:https://doi.org/10.2514/3.7938.
- Stephen, N. G., and M. Levinson. 1979. A second order beam theory. Journal of Sound and Vibration 67 (3):293–305. doi:https://doi.org/10.1016/0022-460X(79)90537-6.
- Timoshenko, S. P. 1923. On the correction for shear of differential equation for transverse vibration of prismatic bars. Philosophical Magazine 6 (41):744–6. doi:https://doi.org/10.1080/14786442108636264.
- Wang, C. M., L. L. Ke, A. N. Roy Chowdhury, J. Yang, S. Kitipornchai, and D. Fernando. 2017. Critical examination of midplane and neutral plane formulations for vibration analysis of FGM beams. Engineering Structures 130:275–81. doi:https://doi.org/10.1016/j.engstruct.2016.10.051.
- Wang, C. M., J. N. Reddy, and K. H. Lee. 2000. Shear deformable beams and plates: relationships with classical solutions. Amsterdam: Elsevier.
- Zhang, D.-G., and Y.-H. Zhou. 2008. A theoretical analysis of FGM thin plates based on physical neutral surface. Computational Materials Science 44 (2):716–20. doi:https://doi.org/10.1016/j.commatsci.2008.05.016.