Advances in Nano Research, Vol. 11, No. 3 (2021) 239-249 https://doi.org/10.12989/anr.2021.11.3.239 Copyright © 2021 Techno-Press, Ltd. http://www.techno-press.org/?journal=journal=anr&subpage=5 ISSN: 2287-237X (Print), 2287-2388 (Online) 1. Introduction The FGMs are novel generations of composite materials, these materials are generally composed of ceramic and metal which vary gradually in the direction of the thickness, this gradual change of the constituents leads to a gradual and continuous variation of the properties which eliminates the problems of the concentration of the stresses at the interfaces which is known in the traditional composites material. The advanced composites materials (FGM) have attracted the attention of several researchers (Kiani and Eslami 2010, Sedighi et al. 2015ab, Ebrahimi and Salari 2015, Kar and Panda 2015, Avcar 2016 and 2019, Kar and Panda 2016, Faleh et al. 2018, Karami and Janghorban 2019a, Safa et al. 2019, Zouatnia and Hadji 2019, Selmi 2020a, Yaylaci et al. 2020a and 2021ab). The micro/nano structures have been investigated for several times using the nonlocal theory of Eringen (Sedighi and Yaghootian 2016, Kolahchi 2017, Ebrahimi and Barati 2017a, Kolahchi et al. 2017a, Karami et al. 2018a, Al- Maliki et al. 2019, Fenjan et al. 2019, Abdulrazzaq et al. 2020ab, Asiri et al. 2020, Akbaş 2020a, Timesli 2020ab, Hadji and Avcar 2021, Bouhadra et al. 2021). Flexural behavior of P-FG nano-plates is examined by Kolahchi et al. (2015) employing the Eringen’s nonlocal theory and a Corresponding author, Professor, E-mail: abdelouahed.tounsi@yonsei.ac.kr new SSDT. Barati and Shahverdi (2016) developed a four variable plate theory to examine thermal vibration behavior of FG-nanoplate with various boundary conditions. The effect of the longitudinal magnetic field on dynamic analysis of S-FGM nanobeams on elastic medium is analyzed by Ebrahimi and Barati (2017b) based on EBT model and Eringen nonlocal theory. The non-local thermal stability of sandwich piezoelectric nanoplates with FG core is investigated by Karami et al. (2018b) using second-order shear deformation theory. Attia and Abdel Rahman (2018) analyzed the dynamic behaviors of the FG viscoelastic nanobeams by employing the Bernoulli-Euler beam theory and Alembert ’s principle. Based on nonlocal elasticity theory, Mehar et al . (2018) studied the vibrational characteristics of nanoplate structure by developing a novel higher-order mathematical model and finite-element method. Ahmed et al. (2019) investigated the post-buckling response of FG porous nanobeam using the nonlocal theory and HSDT model. Recently, Attia et al. (2019) investigated the nonlinear vibrational characteristics of size-dependent FG nanobeams using the Timoshenko beam theory and DQM. Shanab et al. (2020) examined the Microstructure effect and Surface Energy on bending and vibrational Characteristics of FG- Nanobeam Embedded in an Elastic foundation using the Timoshenko theory. Based on the nonlocal continuum theory and the Timoshenko model, Bensattalah et al. (2020) analyzed the stability of TWCNTs under axial compression. The effect of the porosity distribution on the dynamic response of the FG nanobeam is examined by Ghandourah and Abdraboh (2020) based on Natural frequencies of FGM nanoplates embedded in an elastic medium Halima Bouafia 1 , Abdelbaki Chikh 2,3 , Abdelmoumen Anis Bousahla 1 , Fouad Bourada 2,4 , Houari Heireche 1 , Abdeldjebbar Tounsi 2 , Kouider Halim Benrahou 2 , Abdelouahed Tounsi 2,5,6 , Mesfer Mohammad Al-Zahrani 6 and Muzamal Hussain 7 1 Laboratoire de Modélisation et Simulation Multi-échelle, Université de Sidi Bel Abbés, Algeria 2 Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria 3 Université Ibn Khaldoun, BP 78 Zaaroura, 14000 Tiaret, Algérie 4 Département des Sciences et de la Technologie, Université de Tissemsilt, BP 38004 Ben Hamouda, Algérie 5 YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea 6 Civil and Environmental Engineering Department, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia 7 Department of Mathematics, Govt. College University Faisalabad, 38000, Faisalabad, Pakistan (Received April 29, 2021, Revised June 10, 2021, Accepted June 21, 2021) Abstract. The small scale impact on the vibrational properties of “functionally graded” (FG) nanoplate embedded in an elastic medium is examined. The formulation is based on the four-unknown refined integral plate theory on aggregate with the nonlocal elasticity theory. Contrary to other theories, this one involves only four unknown variables. The solution procedure is obtained by employing the motion differential equations of physical phase that are converted into set of “linear algebraic equations”. After, these are solved by a computer code. The influences of aspect ratio, material index, nonlocal parameter and elastic medium stiffness on the different modal vibrations of FG nanoplate are explored. The results demonstrate the significant impact of different physical and geometrical parameters on the vibration behavior of FG nanoplate. Keywords: elastic medium; FG nanoplate; four-unknown refined integral plate theory; nonlocal theory; vibration 239