Flutter and Divergence Instability of Axially-Moving Nanoplates Resting on a Viscoelastic Foundation

Jingbo Duan,Dapeng Zhang,Wenjie Wang

doi:10.3390/app9061097

Jingbo Duan, Dapeng Zhang + Show 1 more

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https://doi.org/10.3390/app9061097

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Abstract

Moving nanosystems often rest on a medium exhibiting viscoelastic behavior in engineering applications. The moving velocity and viscoelastic parameters of the medium usually have an interacting impact on the mechanical properties of nanostructures. This paper investigates the dynamic stability of an axially-moving nanoplate resting on a viscoelastic foundation based on the nonlocal elasticity theory. Firstly, the governing partial equations subject to appropriate boundary conditions are derived through utilizing the Hamilton’s principle with the axial velocity, viscoelastic foundation, nonlocal effect and biaxial loadings taken into consideration. Subsequently, the characteristic equation describing the dynamic characteristics is obtained by employing the Galerkin strip distributed transfer function method. Then, complex frequency curves for the nanoplate are displayed graphically and the effects of viscoelastic foundation parameters, small-scale parameters and axial forces on divergence instability and coupled-mode flutter are analyzed, which show that these parameters play a crucial role in affecting nanostructural instability. The presented results benefit the designation of axially-moving graphene nanosheets or other plate-like nanostructures resting on a viscoelastic foundation.

Highlights

Nano structures have attracted a huge amount of attention from the scientific community due to their extraordinary mechanical, electrical, thermal and other physical/chemical properties.These novel properties can be for nanoelectromechanical systems (NEMS), nanoresonators, nanosensors and nanogenerators [1,2], which are always modeled as nanobeams [3], nanorods [4], nanoribbons [5], nanoplates [6], nanoshells [7], etc to investigate the mechanical properties and other physical properties
The objective of this study is to explore dynamical instability of an axially-moving nanoplate resting on a viscoelastic foundation
The dynamic instability of axially-moving nanoplates resting on a viscoelastic foundation was investigated based on the nonlocal elasticity theory

Summary

Introduction

Nano structures have attracted a huge amount of attention from the scientific community due to their extraordinary mechanical, electrical, thermal and other physical/chemical properties. These novel properties can be for nanoelectromechanical systems (NEMS), nanoresonators, nanosensors and nanogenerators [1,2], which are always modeled as nanobeams [3], nanorods [4], nanoribbons [5], nanoplates [6], nanoshells [7], etc to investigate the mechanical properties and other physical properties. The nonlocal elasticity theory established by Eringen [12,13] is one of the typical continuum mechanics theories. Based on the nonlocal elasticity theory, a couple of researchers have applied their works to the bending, vibration and stability of nanostructures [14,15,16]

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