Axial vibration of a viscoelastic FG nanobeam with arbitrary boundary conditions

Abstract

ObjectiveThis study investigates the axial vibration of a viscoelastic functionally graded (FG) nanobeam under deformable boundary conditions for the first time. The primary focus is on exploring the effects of damping and scale parameters on the dynamic behavior of the nanobeam.MethodsThe governing equation of the viscoelastic FG nanobeam is formulated by incorporating nonlocal elasticity theory and the Kelvin-Voigt viscoelastic model. The Fourier sine series is chosen as the axial displacement function, with higher-order derivatives obtained using Stokes transforms. The Fourier coefficient is determined through the governing equation and incorporated into the deformable boundary conditions. The resulting eigenvalue problem provides solutions for both rigid and constrained general boundary conditions.ConclusionsThe study presents solutions for various boundary conditions, comparing the results with existing literature. The analysis reveals significant findings, including the observation that damping has a greater influence on fundamental frequencies in higher modes, and that the impact of damping decreases as the nonlocal scale parameter increases. These findings are presented through tables and graphs to highlight the effects of damping and scale parameters on the dynamic behavior of the nanobeam.