Exact solution for large amplitude flexural vibration of nanobeams using nonlocal Euler-Bernoulli theory
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School of Engineering, Damghan University, Damghan
School of Mechanical Engineering, Iran University of Science and Technology, Narmak and Center of Excellence in Railway Transportation, Iran University of Science and Technology, Narmak, Tehran
Publication date: 2017-04-15
Journal of Theoretical and Applied Mechanics 2017;55(2):649–658
In this paper, nonlinear free vibration of nanobeams with various end conditions is studied using the nonlocal elasticity within the frame work of Euler-Bernoulli theory with von K´arm´an nonlinearity. The equation of motion is obtained and the exact solution is established using elliptic integrals. Two comparison studies are carried out to demonstrate accuracy and applicability of the elliptic integrals method for nonlocal nonlinear free vibration analysis of nanobeams. It is observed that the phase plane diagrams of nanobeams in the presence of the small scale effect are symmetric ellipses, and consideration the small scale effect decreases the area of the diagram.