Exact solution for large amplitude flexural vibration of nanobeams using nonlocal Euler-Bernoulli theory

Abstract

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.

Nonlinear Vibration of an Elastic Soft String: Large Amplitude and Large Curvature

“…Moreover, using the different model, i.e., the Eringen's nonlocal elasticity theory, Simsek [19] calculated the nonlinear vibration frequency of a nanobeam with axially immovable ends. Similarly, Nazemnezhad et al [20] got the exact solution for the nonlinear vibration of a nanobeam, in use of the nonlocal Euler-Bernoulli theory. For the applications of devices, Feng et al [1] studied the nonlinear vibration of a dielectric elastomer-based microbeam resonator, where the gas damping and excitation are considered.…”