Nonlinear microstructure-dependent Bernoulli–Euler beam model based on the modified couple stress theory and finite rotation of section

Based on Hamilton's principle and the modified couple stress theory, a Bernoulli–Euler microbeam model is developed with the finite rotation of the cross-section. The present model includes three couple-stress-induced nonlinear terms, and these nonlinear terms have a significant influence on the mechanic response of the beam.