A quasi-3D nonlocal theory for free vibration analysis of functionally graded sandwich nanobeams on elastic foundations

Mofareh Hassan Ghazwani, Ali Alnujaie, Pham Van Vinh and Abdelouahed Tounsi

Abstract

The main aims of this study are to develop a new nonlocal quasi-3D theory for the free vibration behaviors of the functionally graded sandwich nanobeams. The sandwich beams consist of a ceramic core and two functionally graded material layers resting on elastic foundations. The two layers, linear spring stiffness and shear layer, are used to model the effects of the elastic foundations. The size-effect is considered using nonlocal elasticity theory. The governing equations of the motion of the functionally graded sandwich nanobeams are obtained via Hamilton's principle in combination with nonlocal elasticity theory. Then the Navier's solution technique is used to solve the governing equations of the motion to achieve the nonlocal free vibration behaviors of the nanobeams. A deep parametric study is also provided to demonstrate the effects of some parameters, such as length-to-height ratio, power-law index, nonlocal parameter, and two parameters of the elastic foundation, on the free vibration behaviors of the functionally graded sandwich nanobeams.

Key Words

functionally graded; nanobeams; nonlocal theory; quasi-3D theory; sandwich beam

Address

Mofareh Hassan Ghazwani and Ali Alnujaie: Mechanical Engineering Department, Faculty of Engineering, Jazan University, P. O. Box 45142, Jazan, Kingdom of Saudi Arabia Pham Van Vinh:2Department of Solid Mechanics, Le Quy Don Technical University, Hoang Quoc Viet, Ha Noi, 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

← Back to Volume 16, No. 3