Research Article Free Vibration and Static Bending Analysis of Piezoelectric Functionally Graded Material Plates Resting on One Area of Two-Parameter Elastic Foundation Hong Nguyen Thi Faculty of Mechanical Engineering, uyloi University, 175 Tay Son, Dong Da, Hanoi, Vietnam Correspondence should be addressed to Hong Nguyen i; hong_hh@tlu.edu.vn Received 10 August 2020; Revised 19 October 2020; Accepted 8 November 2020; Published 25 November 2020 Academic Editor: Nerio Tullini Copyright © 2020 Hong Nguyen i. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Free vibration and static bending analysis of piezoelectric functionally graded material plates resting on one area of the two- parameter elastic foundation is firstly investigated in this paper. e third-order shear deformation theory of Reddy and 8-node plate elements are employed to derive the finite element formulations of the structures; this theory does not need any shear correction factors; however, the mechanical response of the structure is described exactly. Verification problems are performed to evaluate the accuracy of the proposed theory and mathematical model. A wide range of parameter study is investigated to figure out the effect of geometrical, physical, and material properties such as the plate dimension, volume fraction index, piezoelectric effect, elastic foundation coefficients, and the square size of the area of the foundation on the free vibration and static bending of piezoelectric functionally graded material plates. ese numerical results of this work aim to contribute to scientific knowledge of these smart structures in engineering practice. 1. Introduction Nowadays, due to the development of the science of tech- nology, a huge range of smart materials such as functionally graded materials, shape memory alloys, shape memory polymers, magnetostrictive materials, and piezoelectric materials has been considered and applied to engineering practice, in which piezoelectric materials with mainly two- component actuators and sensors are employed and per- formed in a wide range of engineering structures [1–5]. Normally, one smart structure is commonly made of lam- inated composites from ceramic proportions. erefore, at the surfaces among such layers, due to discontinuities of different materials, the stress concentrations usually occur; thus, this is one of the main reasons deriving the failures of the laminated composite structures. However, this issue can be easily overcome by taking advantage of functionally graded piezoelectric materials (FGPM). In the last few de- cades, considering the mechanical behavior of piezoelectric FGM structures has become more irresistible. To confirm this knowledge, numerous published scientific papers re- lating to piezoelectric analyses for FGPM plates can be found in [6–16]. As a result, in this work, we do not need to talk about the basic information of FGM structures as several types of FGM materials such as power-law functionally graded materials (P-FGM), sigmoid law functionally graded materials (S-FGM), and exponential law functionally graded materials (E-FGM) were presented in detail in [17, 18]. e mechanical performances of these FGM structures are also investigated in the following papers. Tinh et al. [19] studied mechanical behaviors of heated functionally graded plates in the high-temperature environment by using the finite ele- ment method and a new third-order shear deformation plate theory. Nguyen and his coworkers [20] investigated the mechanical buckling of stiffened functionally graded ma- terial (FGM) plates. A wide range of studied parameters was carried out such as the effects of material distribution, the thickness-to-width ratio, and stiffener parameters on the buckling characteristics of the stiffened FGM plates. Nam et al. [21] used the finite element method and the phase-field Hindawi Mathematical Problems in Engineering Volume 2020, Article ID 9236538, 18 pages https://doi.org/10.1155/2020/9236538