Tunable Bending Stiffness, Buckling Force, and Natural Frequency of Nanowires and Nanoplates

Hanxing Zhu,D Zhang,T X Fan,Z B Wang

doi:10.4236/wjnse.2012.23021

Abstract

This paper aims to obtain the simple closed-form results for the combined effects of surface elasticity, initial stress/ strain, and material Poisson ratio on the bending stiffness, natural frequency and buckling force of nanowires and nano-plates. The results demonstrate that all these properties of nanowires or nanoplates can be designed either very sensitive or not sensitive at all to the amplitude of an applied electric potential; show how much of those properties can be controlled to vary; and thus provide a reliable guide to the measurement of the Young’s modulus of nanowires/nanoplates and to the design of nano-devices, such as nano-sensors or the cantilever of an AFM.

Highlights

IntroductionOwing to the large surface area to volume ratio at the nanoscale, the mechanical properties, such as the bending stiffness [1,2,3,4,5,6,7], yield strength [8], resonant frequency [9,10,11,12,13,14,15,16,17] and buckling force [18,19,20,21], of nanowires (NWs) and nanoplates (NPs) are size-dependent
This paper aims to obtain the simple closed-form results for the combined effects of surface elasticity, initial stress/ strain, and material Poisson ratio on the bending stiffness, natural frequency and buckling force of nanowires and nanoplates
The results demonstrate that all these properties of nanowires or nanoplates can be designed either very sensitive or not sensitive at all to the amplitude of an applied electric potential; show how much of those properties can be controlled to vary; and provide a reliable guide to the measurement of the Young’s modulus of nanowires/nanoplates and to the design of nano-devices, such as nano-sensors or the cantilever of an AFM

Summary

Introduction

Owing to the large surface area to volume ratio at the nanoscale, the mechanical properties, such as the bending stiffness [1,2,3,4,5,6,7], yield strength [8], resonant frequency [9,10,11,12,13,14,15,16,17] and buckling force [18,19,20,21], of nanowires (NWs) and nanoplates (NPs) are size-dependent. In order to interpret the size-dependent mechanical behaviours of NWs and NPs, to extract the mechanical properties (e.g. the Young’s modulus) of the material from experimentally measured results, and to design nanoelectro-mechanical systems (NEMS) [22,23], one has to employ a mechanical model and the associated theoretical formula which relates all the parameters involved such as forces/stresses and dimensions. This paper aims to provide the precise theoretical results of the combined effects of surface elasticity, initial stress/strain and material Poisson ratio on the bending stiffness,natural frequency and buckling force of nanowires and nanoplates, to give the upper and lower bounds of those tunable properties, to serve as a guide for the design and experimental measurement of nanostructures, and to clarify some existing mistakes in the treatment of the initial surface stresses

Tunable Bending Stiffness

Tunable Compressive Buckling Force

Tunable Natural Frequency

Findings

Conclusion