Abstract
An analytical study to predict the behaviour of clamped FGM nanoplates based on Winkler-Pasternak’s elastic foundations using hyperbolic shear deformation theory. non-local elasticity theory is used to introduce the small-scale effect. This model has a forward displacement field which includes the effect of transverse shear deformation without using shear correction factors. The winkler-Pasternak medium is introduced by considering the damping effect of the foundation model. It’s modeled by the linear Winkler coefficient and the Pasternak foundation coefficient (shear). The influences of many parameters such as the non-local parameter, the geometric ratio, the Winkler-Pasternak coefficients, the damping parameter and the mode numbers on the vibrational response are studied and discussed.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Mechab, I., Benaissa, S., Ameri, M.: Probabilistic analysis of effect of the porosities in functionally graded material nanoplate resting on Winkler – Pasternak elastic foundations. Appl. Math. Model. 40, 1–12 (2015)
Sobhy, M.: Buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary conditions. Compos. Struct. 99, 76–87 (2013)
Brischetto, S., Torre, R.: 3D shell model for the thermo-mechanical analysis of FGM structures via imposed and calculated temperature profiles. Aerosp. Sci. Technol. 85, 125–149 (2019)
Bouamoud, A., Boucham, B., Bourada, F., Houari, M.S.A., Tounsi, A.: Thermomechanical bending investigation of FGM sandwich plates using four shear deformation plate theory. Steel Compos. Struct. 32(5), 611 (2019)
Javani, M., Kiani, Y., Sadighi, M., Eslami, M.R.: Nonlinear vibration behavior of rapidly heated temperature-dependent FGM shallow spherical shells. AIAA J. 57(9), 4071–4084 (2019)
Phung-Van, P., Ferreira, A.J.M., Nguyen-Xuan, H., Wahab, M.A.: An isogeometric approach for size-dependent geometrically nonlinear transient analysis of functionally graded nanoplates. Compos. Part B: Eng. 118, 125–134 (2017)
Heireche, H., Tounsi, A., Benzair, A., Maachou, M., Bedia, E.A.: Sound wave propagation in single-walled carbon nanotubes using nonlocal elasticity. Phys. E: Low-Dimension. Syst. Nanostruct. 40(8), 2791–2799 (2008)
Malekzadeh, P., Shojaee, M.: Free vibration of nanoplates based on a nonlocal two-variable refined plate theory. Compos. Struct. 95, 443–452 (2013)
Pradhan, S.C., Murmu, T.: Small scale effect on the buckling of single-layered graphene sheets under biaxial compression via nonlocal continuum mechanics. Comput. Mater. Sci. 47(1), 268–274 (2009)
Xu, Y.M., Shen, H.S., Zhang, C.L.: Nonlocal plate model for nonlinear bending of bilayer graphene sheets subjected to transverse loads in thermal environments. Compos. Struct. 98, 294–302 (2013)
Karami, B., Janghorban, M., Tounsi, A.: Galerkin’s approach for buckling analysis of functionally graded anisotropic nanoplates/different boundary conditions. Eng. Comput. 35(4), 1297–1316 (2018). https://doi.org/10.1007/s00366-018-0664-9
Farajpour, A., Yazdi, M.R.H., Rastgoo, A., Mohammadi, M.: A higher-order nonlocal strain gradient plate model for buckling of orthotropic nanoplates in thermal environment. Acta Mech. 227(7), 1849–1867 (2016). https://doi.org/10.1007/s00707-016-1605-6
Abdelbaki, C.: Free vibration analysis of simply supported P-FGM nanoplate using a nonlocal four variables shear deformation plate theory. Strojnícky časopis-J. Mech. Eng. 69(4), 9–24 (2019)
Chikh, A., Bakora, A., Heireche, H., Houari, M.S.A., Tounsi, A., Bedia, E.A.: Thermo-mechanical postbuckling of symmetric S-FGM plates resting on Pasternak elastic foundations using hyperbolic shear deformation theory. Struct. Eng. Mech. 57(4), 617–639 (2016)
Chikh, A., Tounsi, A., Hebali, H., Mahmoud, S.R.: Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT. Smart Struct. Syst. 19(3), 289 (2017)
Mokhtar, B., Abedlouahed, T., El Abbas, A.B., Abdelkader, M.: Buckling analysis of functionally graded plates with simply supported edges. Leonardo J. Sci. 22, 21–32 (2009)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Chikh, A. (2020). Dynamic Behavior Analysis of FGM Clamped Nano-Plates Based on Elastic Foundations. In: Benmounah, A., Abadlia, M.T., Saidi, M., Zerizer, A. (eds) Proceedings of the 4th International Symposium on Materials and Sustainable Development. ISMSD 2019. Springer, Cham. https://doi.org/10.1007/978-3-030-43268-3_9
Download citation
DOI: https://doi.org/10.1007/978-3-030-43268-3_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-43267-6
Online ISBN: 978-3-030-43268-3
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)