Isogeometric analysis for size-dependent free vibration of generalized curved nanobeams using integral nonlocal models

In this study, a novel isogeometric finite element approach is proposed to analyze the free vibration of general curved nanobeams with small initial curvatures, within the framework of strain- and stress-driven two-phase local/nonlocal integral theory. An isogeometric analysis (IGA) framework, combined with the finite element method (FEM), is employed to compute the vibrational response of curved nanobeams with variable curvatures. The NURBS basis functions enable flexible curve modeling, ensuring accurate representation of complex geometric microstructures. This model features low computational cost, high accuracy, good convergence, and strong applicability for curved beam structures. Parabolic nanobeams are examined as case studies, and convergence and parameter sensitivity analyses are conducted to demonstrate the robustness of the proposed method. Results indicate that small initial curvature exhibits a significant influence on the vibration characteristics of curved nanobeams and cannot be ignored. This analysis provides valuable insights for researching vibrations in slightly curved beam structures with variable curvatures.