Background <p>For some nanostructures with initial geometric imperfection caused by limitations such as technological level, preparation conditions and production environment, size-dependent behaviors on dynamic characters are necessary issue that will provide significant assistance for optimization design and perfect fabrication of Nano-Electro-Mechanical Systems (NEMS).</p> Purpose <p>To understand the size-dependent behaviors of geometrically imperfect nanostructures, this work proposes a size-dependent nanobeam model with initial imperfection for nonlinear forced vibration. The model includes the effects of the nonlocal (NL) theory, modified couple stress (MCS) theory, surface elasticity (SE) theory and their combinatorial theory.</p> Method <p>The nonlinear differential governing equation of the geometrically imperfect nanobeams is exactly derived by Hamilton’s principle. Then, the Galerkin method and the incremental harmonic balance method (IHBM) together with pseudo arclength continuation algorithm is applied to discretize the differential system.</p> Results <p>The influence mechanisms of various size-dependent theories on natural frequency, frequency-amplitude, force-amplitude responses of the nanobeam are revealed, especially the size-dependent behaviors on nonlinear dynamic with initial imperfection are paid to special attention.</p> Conclusions <p>Results show that all of SE, MCS and NL theory have a significant effect on the dynamic behaviors of the geometrically imperfect nanobeams.</p>