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,...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.展开更多
The exact thermoelastic analysis of a functionally graded piezoelectrical （FGP） rotating cylinder is investigated analytically. The cylinder is subjected to a com- bination of electrical, thermal, and mechanical loa...The exact thermoelastic analysis of a functionally graded piezoelectrical （FGP） rotating cylinder is investigated analytically. The cylinder is subjected to a com- bination of electrical, thermal, and mechanical loads simultaneously. The structure is a simplified model of a rotational sensor or actuator. The basic governing differential equation of the system is obtained by using the energy method. A novel term, named as the additional energy, is introduced to exact the evaluation of the energy functional. The solution to the governing differential equation is presented for two types of boundary conditions including free rotating and rotating cylinders exposed to the inner pressure. The effect of the angular velocity is investigated on the radial distribution of various components. The mentioned structure can be considered as a sensor for measuring the angular velocity of the cylinder subjected to the pressure and temperature. The obtained results indicate that the electrical potential is proportional to the angular velocity.展开更多
文摘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.
文摘The exact thermoelastic analysis of a functionally graded piezoelectrical （FGP） rotating cylinder is investigated analytically. The cylinder is subjected to a com- bination of electrical, thermal, and mechanical loads simultaneously. The structure is a simplified model of a rotational sensor or actuator. The basic governing differential equation of the system is obtained by using the energy method. A novel term, named as the additional energy, is introduced to exact the evaluation of the energy functional. The solution to the governing differential equation is presented for two types of boundary conditions including free rotating and rotating cylinders exposed to the inner pressure. The effect of the angular velocity is investigated on the radial distribution of various components. The mentioned structure can be considered as a sensor for measuring the angular velocity of the cylinder subjected to the pressure and temperature. The obtained results indicate that the electrical potential is proportional to the angular velocity.
