Nonlocal Mindlin plate theory with the application for vibration and bending analysis of nanoplates with the flexoelectricity effect

Pham Ba Khien , Du Dinh Nguyen , Abdelouahed Tounsi , Bui Van Tuyen

Abstract

This work is the first of its kind to integrate Mindlin's theory with analytical methods in order to produce an exact solution to a specific vibration issue as well as a bending problem involving a nanoplate that is supported by a viscoelastic foundation. The plate is exposed to the simultaneous effects of a compressive load in the plate plane and a force operating perpendicular to the plane of the nanoplate. In addition, the flexoelecity effect is included into the plate. The strain gradient component is taken into consideration while calculating the plate equilibrium equation using the nonlocal theory and Hamilton's principle. The free vibration and static responses of the nanoplate seem to be both real and imaginary components because of the appearance of the viscoelastic drag coefficient of the viscoelastic foundation. This study also shows that when analyzing the mechanical response for nanostructure, taking into account the flexoelectricity effect and the influence of the nonlocal parameter, the results will be completely different from the case in which this parameter is ignored. This indicates that it is vital to take into consideration the effects of nonlocal parameters on the nanosheet structure while also taking into consideration the effect of flexoelectricity.

Key Words

analytical method; bending; flexoelectricity; free vibration; nanoplates; viscoelastic foundation

Address

Pham Ba Khien — HUTECH institute of Engineering, HUTECH University, Ho Chi Minh, Vietnam
Du Dinh Nguyen — Faculty of Civil Engineering, Lac Hong University, Dong Nai Province, Viet Nam
Abdelouahed Tounsi — Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia/ Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria/ Department of Civil and Environmental Engineering, Lebanese American University, 309 Bassil Building, Byblos, Lebanon/ YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea
Bui Van Tuyen — Faculty of Mechanical Engineering, Thuyloi University, 175 Tay Son, Dong Da, Hanoi, Vietnam

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