Characterization of Practically Assessed Nanobeams via Parametric Vibration Using the Homotopy Perturbation Technique

The governing equations are derived from classical beam theory modified to account for the gradient of material properties. The nonlinear equation is solved using the Homotopy Perturbation Method (HPM), which provides a reliable solution for small to moderate amplitude vibrations. The study presents a nonlinear vibration analysis of functionally graded nanobeams (FGNBs) using the Homotopy Perturbation Method (HPM). The model takes into consideration the inherent nonlinearity of the beam's material properties and the significant effects of nanoscale interactions. Numerical results are presented, demonstrating the influence of material grading and beam dimensions on the vibration characteristics. This research aims to enhance the design of nanostructural components by integrating material property gradation into dynamic analysis. Keywords Functionally Graded Nanobeams (FGNBs), Nonlinear Vibrations, Homotopy Perturbation Method (HPM), Material Property Gradients, Nanoscale Mechanics