Free and forced vibrations of nanowires on elastic substrates

Abstract

This work aims to study the free and forced transverse vibrations of a nanowire on elastic substrate, in a systematic way. To this end, the governing equations are obtained from an updated mechanical model integrating the effects of surface and elastic substrate. The Winkler, Pasternak and Generalized substrate models are taken into consideration to characterize various substrates. The characteristic equations, mode shapes and effective Young’s moduli are determined for nanowires with three typical boundary conditions: simply supported, clamped-clamped and clamped-free. The Laplace transform is employed to derive the exact solutions for forced vibrations of the three typical nanowires. Numerical calculations are performed to validate the proposed solutions and to analyze the effects of surface and elastic substrates on the free and forced vibrations.