An analytical study of vibration in functionally graded piezoelectric nanoplates: nonlocal strain gradient theory  

作　　者：Z.SHARIFI R.KHORDAD A.GHARAATI G.FOROZANI 

机构地区：[1]Department of Physics,Payame Noor University,Tehran 19395-3697,Iran [2]department of physics,college of science,yasouj university,yasouj 75914-353,iran

出　　处：《Applied Mathematics and Mechanics(English Edition)》2019年第12期1723-1740,共18页应用数学和力学（英文版）

摘　　要：In this paper,we analytically study vibration of functionally graded piezoelectric(FGP)nanoplates based on the nonlocal strain gradient theory.The top and bottom surfaces of the nanoplate are made of PZT-5H and PZT-4,respectively.We employ Hamilton’s principle and derive the governing differential equations.Then,we use Navier’s solution to obtain the natural frequencies of the FGP nanoplate.In the first step,we compare our results with the obtained results for the piezoelectric nanoplates in the previous studies.In the second step,we neglect the piezoelectric effect and compare our results with those obtained for the functionally graded(FG)nanoplates.Finally,the effects of the FG power index,the nonlocal parameter,the aspect ratio,and the lengthto-thickness ratio,and the nanoplate shape on natural frequencies are investigated.In this paper, we analytically study vibration of functionally graded piezoelectric(FGP) nanoplates based on the nonlocal strain gradient theory. The top and bottom surfaces of the nanoplate are made of PZT-5 H and PZT-4, respectively. We employ Hamilton’s principle and derive the governing differential equations. Then, we use Navier’s solution to obtain the natural frequencies of the FGP nanoplate. In the first step, we compare our results with the obtained results for the piezoelectric nanoplates in the previous studies. In the second step, we neglect the piezoelectric effect and compare our results with those obtained for the functionally graded(FG) nanoplates. Finally, the effects of the FG power index, the nonlocal parameter, the aspect ratio, and the lengthto-thickness ratio, and the nanoplate shape on natural frequencies are investigated.

关 键 词：NONLOCAL strain gradient NANOPLATE functionally GRADED piezoelectric(FGP) 

分 类 号：O343.7[理学—固体力学]