A new Bernoulli–Euler beam model based on a simplified strain gradient elasticity theory and its applications

A new Bernoulli–Euler beam model based on a simplified strain gradient elasticity theory is established in the current investigation. The generalized Euler–Lagrange equations and corresponding boundary conditions are naturally derived from the Hamilton’s principle. Then axial wave propagation of small scale bars, static bending of cantilever beams, buckling and free vibration of simply supported beams are analytically solved by using the...