Bending of rough beam with axisymmetric surface

Surface roughness arising from manufacturing, wear, and corrosion significantly affects the mechanical performance of structural components. This study investigates the bending of cylinders with axisymmetric random rough surfaces. The rough surfaces are digitally characterized by two statistical parameters, namely, the root mean square height and correlation length. The differential equation governing bending deformation is derived in the context of Euler–Bernoulli beam theory, and solved by a combination of the perturbation method and fast Fourier transform. The solution is comprehensively validated analytically, numerically, and experimentally. The influence of surface roughness on deformation is quantified in terms of the RMS height and correlation length. A prediction model is obtained. The present work provides a deep insight into the effect of roughness on bending and will be beneficial to the further development of modern manufacturing technology.