Vol. 16, No. 3, 2021

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Nonlinear bending, buckling and vibration of functionally graded nonlocal strain gradient nanobeams resting on an elastic foundation

Dang Van Hieu, Do Quang Chan and Hamid M. Sedighi

Vol. 16 (2021), No. 3, 327–346

This work aims to provide a comprehensive theoretical framework for the nonlinear bending, vibration and buckling of functionally graded (FG) nanobeams resting on an elastic foundation through nonlocal strain gradient theory. To this end, both Timoshenko and Euler–Bernoulli beam theories are considered and the equations of motion are established by Hamilton’s principle. The analytical expressions of the nonlinear deflections, frequencies and critical buckling forces of FG nanobeams are presented with closed-form expressions. Comparing the obtained results with those published in the literature shows the accuracy of the current analysis. Finally, the impacts of some effective parameters are thoroughly investigated and discussed.

nonlocal strain gradient theory, nanobeams, nonlinear bending, nonlinear vibration, buckling
Received: 8 September 2020
Revised: 28 February 2021
Accepted: 20 April 2021
Published: 10 August 2021
Dang Van Hieu
Department of Mechanics
Thai Nguyen University of Technology
Do Quang Chan
Faculty of Mechanical Engineering and Mechatronics
PHENIKAA University
Hanoi 12116
PHENIKAA Research and Technology Institute (PRATI)
A&A Green Phoenix Group JSC
Hanoi 11313
Hamid M. Sedighi
Mechanical Engineering Department  and  Drilling Center of Excellence and Research Center
Shahid Chamran University of Ahvaz