# Residue Stress On The Vibration Of Nanowires Biology

Nanowires (NWs) [1] have been intensely researched by both the scientific and engineering communities over the past decade. Nanowires (NWs) can be defined as any solid material in the form of wire with diameter smaller than about 100 nanometer (nm). 1 nanometer corresponds to 10−9 meters which is around 50,000th of a typical human hair width. Because of their exceptional mechanical, electrical and thermal properties, nanowires have a great potential for building blocks of nanodevices and nanoelectronics that have a wide range of applications in nanotechnology. Together with carbon nanotubes [2, 3], various NWs discovered recently are fundamental quasi one-dimensional engineering materials in the emerging area of nanotechnology.

At the moment, nanowires still belong to the experimental world of laboratories. However, they may complement or replace carbon nanotubes in many applications. To name a few, in early experiments it was shown that NWs are promising for the next generation of computing devices [4]. Recently, researchers have found a way to use silicon NWs to reinvent the rechargeable lithium-ion battery. The NWs battery produces 10 times the amount of electricity of the existing Li-ion battery [5]. As a result, there is a great interest for scientists to further develop characterizing techniques, bring in an in-depth understanding of their unique structural responses and find new avenues towards the novel application of NWs in nanotechnology. In the last decade the world has witnessed extensive studies on the mechanical, electrical and piezoelectric properties of various NWs [1].

**Material Properties of NWs**

Mechanical properties [1, 6]:

(a) Elastic properties (Young's modules, High flexibility, Superelasticity),

(b) Bulking properties,

(c) Vibration properties.

(d) DOWN

(Since the sizes of these nanowires are so tiny, the normal physics could not be applied to explain their behaviour. In classical continuum mechanics, the effect of surface energy is ignored as it is very small compared to the bulk energy. For nanoscale materials and structures, however, the small scale effect arising from large surface-to-volume ratio will significantly affect their mechanical behaviour and thus has to be considered in study of the nanomechanics of NWs. Therefore, surface effects often play an important role in the physical properties of nanosized materials. The stiffness and natural frequency of nanowire will be affected by both surface elasticity and residual surface tension

Electric and Piezoelectric Properties [1]:

(a) Semiconductors,

(b) Piezoelectricity,

1.3 The potential application of NWs [1]

Nanosensors, actuators, transducers, nanoresonators, nanogenerators, others see references [1, 4-7]

Although NWS (NOTE: use 'NWs' to replace nanowires throughout the thesis) are not available in commercial or industrial applications yet, the most obvious use for NWs is in electronics. Some NWs are very good conductors or semiconductors, and their miniscule size means that manufacturers could fit millions more transistors on a single microprocessor. As a result, computer speed would increase dramatically. However, the high costs required to create NWs transistors is a barrier to wider manufacturing [Refs ??].

Moreover, recent research shows that piezoelectric NWs such as Zinc oxide NWs, can be used to capture waste vibrations and convert back into useable energy. When piezoelectric materials are strained, they develop an electric field. Straining the material causes positive and negative ions in each unit cell to displace in different directions. This produces a small electrical field but, when it's summed over moles of unit cells, it can be quite substantial. To convert vibrations into energy, piezoelectric materials must be packaged into a device so that the vibrations cause strain that can be extracted through a connection to an appropriate electrical circuit. And nanowires are being tested for their piezoelectric potential. Nanowire mechanical energy harvesting devices place piezoelectric ZnO nanowires vertically on a flat substrate. When the device vibrates, the free-moving, zig-zag electrode flexes the nanowires and generating an electrical potential.

Apart from the application mentioned above, nanowires can also be used in advanced hearing aids and battery which directly related to our daily life. Since scientist are still learning about the properties of nanowires and other nanoscale structures, there could be thousands of applications that have not been considered yet.

From these wide ranges of applications, it shows that nanotechnology can benefit to our society and improve the environment by harnessing waste energy.

**Vibration Analysis Method**

**Studies of vibration**

(i)Where vibration of NWs has been observed and what the vibration patterns look like

(ii) Why vibration is of importance for the applications of NWs.

Positive : Many applications of NWs directly exploit the unique vibration properties of NWs, such as nanoresonanotrs, nanogenerators and stress sensors, actuators….

Negative : Cause uncertainty of NW positions and impair structural integrity

Unique features:

At nanosclae, large surface-to-volume ratio of NWs leads to strong surface effect, i.e., surface stress/ surface elasticity (mention the physical origin of the surface effect) . This results in vibration behavior different from those of their macroscopic counterpart.

Conclusion : Vibration of NWs forms one of major issues in nanomechanics that deserves to be investigated. To facilitate the development of nanotechnology it is imperative to study the vibration of NWs and substantially advance the physics behind their distinct properties.

(iii) What you would like to do here and how to do it.

Start with ''Motivated by these ideas this project aims to…..''

**''These urgent needs provide impetus for us to study …. ''**

**'' To facilitate the development of NW-based nanotechnology we would like to study …'**

Also mention ''You will incorporate the surface effect, i.e., surface stress and surface elasticity, into classical mechanics theory''

**Vibration of NWs**

Vibration refers to the study of mechanical oscillatory motions about an equilibrium point. Many applications of NWs directly exploit the unique vibration properties of NWs, such as nanoresonanotrs, nanogenerators and stress sensors. On the other hand, since vibration of the nanowires could threaten structural integrity inside any nanostructures, impair the performance and cause uncertainty of NW positions. Thus vibration behavior forms a fundamental consideration in the characterization and design of the nanowires. Therefore, vibration is of importance for the applications of NWs.

Fig.1. Vibration of a cadmium sulphide NWs

At nanosclae, large surface-to-volume ratio of NWs leads to strong surface effect. The physical properties and mechanical response of surfaces will be distinct from those of bulk materials. This results in vibration behavior different from those of their macroscopic counterpart.

As a result, vibration of NWs forms one of major issues in nanomechanics that deserves to be investigated. To facilitate the development of nanotechnology it is imperative to study the vibration of NWs and substantially advance the physics behind their distinct properties.

Motivated by these ideas, this project aims to investigate the effects of both surface elasticity and residual surface tension on the natural frequency of nanowires. In this paper, we will incorporate the surface effect into classical mechanics theory. A thin surface layer was introduced on the upper and lower surfaces of a rectangular cross-section nanowire to rationalize the near-surface material properties that are different from the bulk material. We will also consider a circular cross-section nanowire to show the relationship between the natural frequency and cross-section differences on nanowires.

**Vibration Analysis Method**

**Structure of NWs**

Fig. 2 Illustrations for NWs

(ii) Mention surface stress and surface elasticity to distinguish NWs from regular

beams.

As mentioned earlier, the structure and properity

When the characteristic sizes of materials shrink to nanometers, since the atoms within a very thin layer near surfaces experience a different local environment form that experienced by atoms in bulk, the physical properties and mechanical response of surfaces will be distinct from those of bulk materials. surface effects often play an important role in their mechanical behavior due to the increasing ratio between surface/interface area and volume.

(iii) Clarify the origin of the surface effect:

**Multilayer Euler beam model**

Due to the increasing ratio of surface area to volume, the physical and mechanical properties of nanowires often exhibit distinct size dependence. In this study we are interested in the effect of surface stress and surface elasticity on the vibration of NWs. Considering the unique features of NWs, we will use a surface layer and inner bulk material model to investigate the surface effects on the natural frequency of NWs. To account for consider the surface effect, we treat divide a microbeam NWs as two-layer laminated composites, including two surface layers and a core or bulk layer as the figure shown below,

Fig. 3 Illustration of rectangular and circular NWs with surface layer

The Young's modulus and thickness of the bulk are denoted as E and H, respectively, and assume that the surface layers has the identical Young's modulus E1 and thickness h1.. The surface layers are assumed to be very thin. Thus the in-plan stiffness of the thin surface layer calculated as Es=E1h1 is considered as a material constants. Here h1 is the thickness of the surface layer. Obviously, the present sandwich-beam model enables us to capture the physical origin of surface effects in a finite-thick layer and thus give a reliable description to the vibration responses of NWs.

**Governing equations**

Based on the above models and Euler beam theory [7] the equation for the vibration of NWs is as follows [8]

(1)

**(i) Define all the notations used in the equation**

**Particularly,**

**(ii) Define EI and give formula to calculate EI for NWs with**

**Rectangular**

**Circular cross-sections**

**(ii) Do the same thing for PR and PA**

Consider simply supported boundary conditions the solutions to Eq. 1 reads

(2)

**Again please define all the notations used in (2)**

Substitute Eq. (2) to (1) we get

(3)

**Derive the Formulae of frequency (4)**

**For rectangular cross-section**

The equation for calculate the natural frequency:

(1)

where ρis the mass density and A the cross-section area of the nanowire.

To illustrate the surface effects, we considered the both ends of the nanowire are simply supported.

In this case, the conditions are satisfied by

(2.1)

where

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