Acknowledgement
The authors would like to thank Mustansiriyah university (www.uomustansiriyah.edu.iq) Baghdad-Iraq and Middle Technical University (https://www.mtu.edu.iq) for their support in the present work.
References
- Abderezak, R., Daouadji, T.H. and Rabia, B. (2021), "Modeling and analysis of the imperfect FGMdamaged RC hybrid beams", Adv. Comput. Des., 6(2), 117-133. https://doi.org/10.12989/acd.2021.6.2.117.
- Abdullah, W.N., Khalaf, B.S., Ahmed, R.A., Fenjan, R.M. and Faleh, N.M. (2021), "Thermal effects on dynamic response of GOP-Reinforced beams under blast load", Adv. Concr. Constr., 12(3), 167-174. https://doi.org/10.12989/acc.2021.12.3.167.
- Abdulrazzaq, M.A., Muhammad, A.K., Kadhim, Z.D. and Faleh, N.M. (2020), "Vibration analysis of nonlocal strain gradient porous FG composite plates coupled by visco-elastic foundation based on DQM", Coupled Syst. Mech., 9(3), 201-217. https://doi.org/10.12989/csm.2020.9.3.201.
- Ahmed, R.A., Fenjan, R.M. and Faleh, N.M. (2019), "Analyzing post-buckling behavior of continuously graded FG nanobeams with geometrical imperfections," Geomech. Eng., 17(2), 175-180. https://doi.org/10.12989/gae.2019.17.2.175.
- Ahmed, R.A., Fenjan, R.M., Hamad, L.B. and Faleh, N.M. (2020), "A review of effects of partial dynamic loading on dynamic response of nonlocal functionally graded material beams", Adv. Mater. Res., 9(1), 33-48. https://doi.org/10.12989/amr.2020.9.1.033.
- Ahmed, R.A., Al-Toki, M.H., Faleh, N.M. and Fenjan, R.M. (2021), "Nonlinear stability of higher-order porous metal foam curved panels with stiffeners", Transp. Porous Med., 1-16. https://doi.org/10.1007/s11242-021-01691-2.
- Akbas, S.D. (2016), "Forced vibration analysis of viscoelastic nanobeams embedded in an elastic medium", Smart Struct. Syst., 18(6), 1125-1143. http://doi.org/10.12989/sss.2016.18.6.1125.
- Al-Maliki, A.F., Faleh, N.M. and Alasadi, A.A. (2019), "Finite element formulation and vibration of nonlocal refined metal foam beams with symmetric and non-symmetric porosities", Struct. Monit. Maint., 6(2), 147-159. https:// doi.org/10.12989/smm.2019.6.2.147.
- Al-Maliki, A.F., Ahmed, R.A., Moustafa, N.M. and Faleh, N.M. (2020), "Finite element based modeling and thermal dynamic analysis of functionally graded graphene reinforced beams", Adv. Comput. Des., 5(2), 177-193. https://doi.org/10.12989/acd.2020.5.2.177.
- Eringen, A.C. (1972), "Linear theory of nonlocal elasticity and dispersion of plane waves", Int. J. Eng. Sci., 10(5), 425-435. https://doi.org/10.1016/0020-7225(72)90050-X.
- Fenjan, R.M., Ahmed, R.A., Alasadi, A.A. and Faleh, N.M. (2019), "Nonlocal strain gradient thermal vibration analysis of double-coupled metal foam plate system with uniform and non-uniform porosities", Coupled Syst. Mech., 8(3), 247-257. https://doi.org/10.12989/csm.2019.8.3.247.
- Fenjan, R.M., Hamad, L.B. and Faleh, N.M. (2020a), "Mechanical-hygro-thermal vibrations of functionally graded porous plates with nonlocal and strain gradient effects", Adv. Aircr. Spacecr. Sci., 7(2), 169-186. https://doi.org/10.12989/aas.2020.7.2.169.
- Fenjan, R.M., Ahmed, R.A., Hamad, L.B. and Faleh, N.M. (2020b), "A review of numerical approach for dynamic response of strain gradient metal foam shells under constant velocity moving loads", Adv. Comput. Des., 5(4), 349-362. https://doi.org/10.12989/acd.2020.5.4.349.
- Guo, J., Chen, J. and Pan, E. (2016), "Static deformation of anisotropic layered magnetoelectroelastic plates based on modified couple-stress theory", Compos. Part B Eng., 107, 84-96. https://doi.org/10.1016/j.compositesb.2016.09.044.
- Hamad, L.B., Khalaf, B.S. and Faleh, N.M. (2019), "Analysis of static and dynamic characteristics of strain gradient shell structures made of porous nano-crystalline materials", Adv. Mater. Res., 8(3), 179-96. https://doi.org/10.12989/amr.2019.8.3.179.
- Heydari, A. (2020), "Buckling analysis of noncontinuous linear and quadratic axially graded Euler beam subjected to axial span-load in the presence of shear layer", Adv. Comput. Des., 5(4), 397-416. https://doi.org/10.12989/acd.2020.5.4.397.
- Jiang, L., Wang, Y., Wang, X., Ning, F., Wen, S., Zhou, Y. and Zhou, F.L. (2021), "Electrohydrodynamic printing of a dielectric elastomer actuator and its application in tunable lenses", Compos. Part A Appl. S., 147, 106461. https://doi.org/10.1016/j.compositesa.2021.106461.
- Ke, L.L., Wang, Y.S., Yang, J. and Kitipornchai, S. (2014), "The size-dependent vibration of embedded magneto-electro-elastic cylindrical nanoshells", Smart Mater. Struct., 23(12), 125036. https://doi.org/10.1088/0964-1726/23/12/125036.
- Kumaravel, A., Ganesan, N. and Sethuraman, R. (2007), "Buckling and vibration analysis of layered and multiphase magneto-electro-elastic beam under thermal environment", Multidiscip. Model. Mater. Struct., 3(4), 461-476. https://doi.org/10.1163/157361107782106401.
- Li, Y. and Shi, Z. (2009), "Free vibration of a functionally graded piezoelectric beam via state-space based differential quadrature", Compos. Struct., 87(3), 257-264. https://doi.org/10.1016/j.compstruct.2008.01.012.
- Liu, H., Liu, H. and Yang, J. (2018), "Vibration of FG magneto-electro-viscoelastic porous nanobeams on visco-Pasternak foundation", Compos. Part B Eng., 155, 244-256. https://doi.org/10.1016/j.compositesb.2018.08.042.
- Muhammad, A.K., Hamad, L.B., Fenjan, R.M. and Faleh, N.M. (2019), "Analyzing large-amplitude vibration of nonlocal beams made of different piezo-electric materials in thermal environment", Adv. Mater. Res., 8(3), 237-257. https://doi.org/10.12989/amr.2019.8.3.237.
- Pan, E. and Han, F. (2005), "Exact solution for functionally graded and layered magneto-electro-elastic plates", Int. J. Eng. Sci., 43(3-4), 321-339. https://doi.org/10.1016/j.ijengsci.2004.09.006.
- Polatov, A.M., Khaldjigitov, A.A. and Ikramov, A.M. (2020), "Algorithm of solving the problem of small elastoplastic deformation of fiber composites by FEM", Adv. Comput. Des., 5(3), 305-321. https://doi.org/10.12989/acd.2020.5.3.305.
- Raheef, K.M., Ahmed, R.A., Nayeeif, A.A., Fenjan, R.M. and Faleh, N.M. (2021), "Analyzing dynamic response of nonlocal strain gradient porous beams under moving load and thermal environment", Geomech. Eng., 26(1), 89-99. https://doi.org/10.12989/gae.2021.26.1.089.
- Singh, A. and Kumari, P. (2020), "Analytical free vibration solution for angle-ply piezolaminated plate under cylindrical bending: A piezo-elasticity approach", Adv. Comput. Des., 5(1), 55-89. https://doi.org/10.12989/acd.2020.5.1.055.
- Thai, H.T. and Vo, T.P. (2012), "A nonlocal sinusoidal shear deformation beam theory with application to bending, buckling, and vibration of nanobeams", Int. J. Eng. Sci., 54, 58-66. https://doi.org/10.1016/j.ijengsci.2012.01.009.
- Zhou, H., Xu, C., Lu, C., Jiang, X., Zhang, Z., Wang, J. and Wang, L. (2021), "Investigation of transient magnetoelectric response of magnetostrictive/piezoelectric composite applicable for lightning current sensing", Sensors Actuat. A Phys., 329, 112789. https://doi.org/10.1016/j.sna.2021.112789.