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.
