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http://dx.doi.org/10.12989/anr.2020.8.1.037

Porosity-dependent free vibration analysis of FG nanobeam using non-local shear deformation and energy principle  

Gafour, Youcef (University Djillali Liabes- Faculty of Technology)
Hamidi, Ahmed (Civil Engineering and Hydraulic Department, Faculty Technology, University of Bechar)
Benahmed, Abdelillah (Laboratory of Modeling and Multi-Scale Simulation, Department of Physics, Faculty of Exact Science, University of Sidi Bel Abbes)
Zidour, Mohamed (University of Tiaret)
Bensattalah, Tayeb (University of Tiaret)
Publication Information
Advances in nano research / v.8, no.1, 2020 , pp. 37-47 More about this Journal
Abstract
This work focuses on the behavior of non-local shear deformation beam theory for the vibration of functionally graded (FG) nanobeams with porosities that may occur inside the functionally graded materials (FG) during their fabrication, using the non-local differential constitutive relations of Eringen. For this purpose, the developed theory accounts for the higher-order variation of transverse shear strain through the depth of the nanobeam. The material properties of the FG nanobeam are assumed to vary in the thickness direction. The equations of motion are derived from Hamilton's principle. Analytical solutions are presented for a simply supported FG nanobeam with porosities. The validity of this theory is verified by comparing some of the present results with other higher-order theories reported in the literature, the influence of material parameters, the volume fraction of porosity and the thickness ratio on the behavior mechanical P-FGM beam are represented by numerical examples.
Keywords
nanobeam; non-local elasticity theory; vibration; functionally graded; porosity coefficient;
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85 Bourada, F., Bousahla, A.A., Bourada, M., Azzaz, A., Zinata, A. and Tounsi, A. (2019), "Dynamic investigation of porous functionally graded beam using a sinusoidal shear deformation theory", Wind Struct., Int. J., 28(1), 19-30. https://doi.org/10.12989/was.2019.28.1.019
86 Boutaleb, S., Benrahou, K.H., Bakora, A., Algarni, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. and Tounsi, A. (2019), "Dynamic analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT", Adv. Nano Res., Int. J., 7(3), 191-208. https://doi.org/10.12989/anr.2019.7.3.191
87 Chaabane, L.A., Bourada, F., Sekkal, M., Zerouati, S., Zaoui, F.Z., Tounsi, A., Derras, A., Bousahla, A.A. and Tounsi, A. (2019), "Analytical study of bending and free vibration responses of functionally graded beams resting on elastic foundation", Struct. Eng. Mech., Int. J., 71(2), 185-196. https://doi.org/10.12989/sem.2019.71.2.185
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94 Ehyaei, J., Akbarshahi, A. and Shafiei, N. (2017), "Influence of porosity and axial preload on vibration behavior of rotating FG nanobeam", Adv. Nano Res., Int. J., 5(2), 141-169. https://doi.org/10.12989/anr.2017.5.2.141
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100 Bensattalah, T., Zidour, M. and Hassaine Daouadji, T. (2018c), "Analytical analysis for the forced vibration of CNT surrounding elastic medium including thermal effect using nonlocal Euler-Bernoulli theory", Adv. Mater. Res., Int. J., 7(3), 163-174. https://doi.org/10.12989/amr.2018.7.3.163
101 Bensattalah, T., Zidour, M., Hassaine Daouadji, T. and Bouakaz, K. (2019), "Theoretical analysis of chirality and scale effects on critical buckling load of zigzag triple walled carbon nanotubes under axial compression embedded in polymeric matrix", Struct. Eng. Mech., Int. J., 70(3), 269-277. https://doi.org/10.12989/sem.2019.70.3.269
102 Bouadi, A., Bousahla, A.A., Houari, M.S.A., Heireche, H. and Tounsi, A. (2018), "A new nonlocal HSDT for analysis of stability of single layer graphene sheet", Adv. Nano Res., Int. J., 6(2), 147-162. https://doi.org/10.12989/anr.2018.6.2.147
103 Bouamoud, A., Boucham, B., Bourada, F., Houari, M.S.A. and Tounsi, A. (2019), "Thermomechanical bending investigation of FGM sandwich plates using four shear deformation plate theory", Steel Compos. Struct., Int. J., 32(5), 611-632. https://doi.org/10.12989/scs.2019.32.5.611
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105 Fourn, H., Ait Atmane, H., Bourada, M., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. (2018), "A novel four variable refined plate theory for wave propagation in functionally graded material plates", Steel Compos. Struct., Int. J., 27(1), 109-122. https://doi.org/10.12989/scs.2018.27.1.109
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119 Karami, B. and Karami, S. (2019), "Buckling analysis of nanoplate-type temperature-dependent heterogeneous materials", Adv. Nano Res., Int. J., 7(1), 51-61. https://doi.org/10.12989/anr.2019.7.1.051   DOI
120 Karami, B. and Shahsavari, D. (2019), "Nonlocal strain gradient model for thermal stability of FG nanoplates integrated with piezoelectric layers", Smart Struct. Syst., Int. J., 23(3), 215-225. https://doi.org/10.12989/sss.2019.23.3.215