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 Kármán 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.
AUTHOR KEYWORDS: Elliptic integrals; Exact solution; Nanobeam; Nonlinear free vibration; Nonlocal elasticity INDEX KEYWORDS: Elasticity; Equations of motion; Integral equations; Nanowires, Elliptic integrals; Exact solution; Nano beams; Non-linear free vibration; Non-local elasticities, Vibration analysis PUBLISHER: Polish Society of Theoretical and Allied Mechanics
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