Applying Eringen’s nonlocal elasticity theory for analyzing the nonlinear free vibration of bidirectional functionally graded Euler–Bernoulli nanobeams

The present study develops a size-dependent Euler–Bernoulli beam model to analyze the nonlinear free vibration of a bidirectional functionally graded (BFG) nanobeam with immovable ends, based on the nonlocal theory. In order to eliminate the stretching and bending coupling caused by the asymmetrical material variation along the thickness, the problem is formulated relative to the physical neutral surface. By using Hamilton’s principle, the...