Effect of uncertainty in material properties on wave propagation characteristics of nanorod embedded in elastic medium

Abstract

The effect of uncertainty in material properties on wave propagation characteristics of nanorod embedded in an elastic medium is investigated by developing a nonlocal nanorod model with uncertainties. Considering limited experimental data, uncertain-but-bounded variables are employed to quantify the uncertain material properties in this paper. According to the nonlocal elasticity theory, the governing equations are derived by applying the Hamilton's principle. An iterative algorithm based interval analysis method is presented to evaluate the lower and upper bounds of the wave dispersion curves. Simultaneously, the presented method is verified by comparing with Monte-Carlo simulation. Furthermore, combined effects of material uncertainties and various parameters such as nonlocal scale, elastic medium and lateral inertia on wave dispersion characteristics of nanorod are studied in detail. Numerical results not only make further understanding of wave propagation characteristics of nanostructures with uncertain material properties, but also provide significant guidance for the reliability and robust design of the next generation of nanodevices.

Axial vibration of double-walled carbon nanotubes using double-nanorod model with van der Waals force under Pasternak medium and magnetic effects

“…The present model extends the investigation by including the effect of the Pasternak medium and magnetic environment. By ignoring Winkler and damping moduli, c u =0 and k 1 =0 (Mohammadimehr et al [33] and Lv et al [34]), the axially distributed force per unit length f u with magnetic effect by neglecting terms of nonlocal (Murmu et al [35]) assumes as,…”

“…Here k up and η m represent the Pasternak medium (Mohammadimehr et al [33] and Lv et al [34]) and magnetic effects (Murmu et al [35]) for nanorod. Aydogdu [31] defined the axial force in the following form as f ij = c ′ (u j − u i ) for linear analysis.…”

“…The first research work about modelling of Pasternak medium support while investigating the frequency analysis of nanorod is reported by Mohammadimehr et al [33]. Later, Lv et al [34] investigated the wave propagation of nanorods using the Pasternak medium with uncertainty in material properties using the nonlocal model. Murmu et al [35] proposed the magnetic force term for the axial frequency analysis of nanorods.…”

A consistent variational formulation of Bishop nonlocal rods

“…[30], Eq. (1a); [41], Eq. 1)(1) with , and denoting, respectively, nonlocal stress, local strain field and elastic stiffness.…”

“…The motivation of the present study is therefore to re-formulate the elastic equilibrium problem of a thick rod in an appropriate variational setting which provides proper constitutive boundary conditions, overlooked in previous contributions [29][30][31][32][33][34][35][36][37][38][39][40][41]. In papers dealing with nonlocal thick rods, EIM is preliminarily introduced as (see e.g.…”