Parametric-forced coupling resonance of core-shell nanowires with interfacial damage under weak viscoelastic boundary constraint

Abstract

Revealing the synergistic effects of size-dependency and nonlinearity on dynamics of core-shell nanowires plays an important role in nonlinear design of nanoelectromechanical system (NEMS) maintaining stable working state. The nonlinear principal resonance of core-shell nanowires with weak interface under parametric-forced coupling excitations is studied. The nanowire is simply supported at both ends, with one end movable and under a weak viscoelastic boundary described by Kelvin-Voight model. The weak interface obeys the interfacial cohesive law coupled into the refined displacement field. Geometric nonlinearity due to large deformation is reflected in three aspects. Stiffness nonlinearity is modeled by nonlinear curvature. Longitudinal inertia nonlinearity is modeled based on an in-extensive beam assumption. Nonlinear constraint force provided by the viscoelastic boundary is reflected in nonlinear damping and stiffness. Size-dependency including nonlocal stress, strain gradient and surface elasticity are all incorporated. The governing equations are derived by Hamilton's variational principle and solved via a perturbation-incremental harmonic balance method (IHBM). Results provide the bifurcation diagram of coupled resonance and the stability boundary of parametric resonance for analyzing the change mechanism of bifurcation topology. Decisive ways are revealed that weak interface, size dependency and constraints from foundation and boundary affect the linear and nonlinear properties of the system.