On axial dynamic analysis of viscoelastic nanorods reinforced with particles

Abstract

This study proposes an analytical model for the size-dependent axial vibration of particle-reinforced viscoelastic nanorods. Size effects and viscoelastic damping are incorporated utilizing nonlocal elasticity theory and the Kelvin–Voigt model, respectively, while the effective mechanical properties are determined via the Mori–Tanaka homogenization scheme. A key novelty of this work is the analytical formulation and solution of characteristic equations for a broad range of boundary conditions, evolving in a generalized configuration where a lumped mass and an elastic spring are simultaneously present at the rod’s extremity. The study systematically investigates the influence of particle volume fraction, nonlocal size effects, material damping, and boundary mass-spring parameters. It is found that the particle reinforcement ratio, nonlocal scale dependency, and the inertial dominance of the attached mass play pivotal roles in modulating the axial vibration and attenuation performance of the nanorods. Ultimately, this comprehensive theoretical framework provides critical insights for the design and optimization of advanced nano-electro-mechanical systems (NEMS) and nanoresonators.