Analysis of nonlinear vibrations of carbon nanotubes located in elastic environment

Dissertation

to obtain a master's degree

in the field of mechanics

Investigation and analysis of free and forced vibrations of a multi-walled carbon nanotube located in an elastic environment in order to achieve a clear mathematical understanding of the behavior of different nanotube walls under the influence of van der Waals forces and the medium Elasticity is one of the most important categories in investigating the behavior of double-walled carbon nanotubes.

Analysis of linear vibrations of carbon nanotubes under Euler-Bernoulli beam models as well as Timoshenko beam models has been one of the most extensive cases in the articles of recent years, but the analysis of free vibrations considering the geometric nonlinearity of nanotubes has been done once in 2006 in order to obtain frequency response curves. It has been done according to the vibration amplitude of the nanotube. This analysis is based on the composite Euler-Bernoulli beam model and using the "harmonic balance" numerical method. In the upcoming analysis, the attempt is to firstly analyze the nonlinear free vibrations based on the Euler-Bernoulli beam model using the analytical method of averaging in order to obtain nonlinear frequency relationships with the amplitude, and then at the end by comparing the results of the averaging method with the results of the harmonic balance method We pay attention to the accuracy of the method used.

1-2-Introduction to nanotechnology

Legally speaking, nanotechnology means any technology that is applicable on a nano scale and is used to meet the needs of the real world. This technology includes the production and application of physical, chemical and biological systems - in a wide range from the size of individual atoms or molecules to submolecular dimensions - as well as the combination of simple structures and the production of more complex structures.

For the first time on December 29, 1959, Nobel Prize winner Richard Feynman1 in his famous speech entitled "There is a lot of space down there" at the California Institute of Technology2 Meeting

1 Richard P. Feynman

2 California

The American Physical Society annual lecture about this revolution and new technology. Years before microchips were invented, he described a technology in which components with very small miniature dimensions could be created. He came up with the idea that structures can be made atom by atom or molecule by molecule in very small dimensions. The research and discoveries made in the field of nanoparticle production since the 1980s confirm his claims[1].

One ??year later in 1960, Roger Bacon1 described the properties of nanotubes. Until in 1985, Richard Smalley2 built the Buckyball structure with the help of a laser. It is reminded that pure carbon appears in various structures, which include: diamond-like structure3, in the form of a plate of carbon atoms with certain distances4, in spherical form5 (with a wing or C60 structure), in the form of single-walled nanotubes6 or multi-walled7, and in the form of strings and bunches of nanotubes together8 [1,2].

In 1990 at the Max Planck Research Institute, Buckyball was made by electric arc discharge, and finally in 1991 Sumiya Iijima9 at the NEC Institute discovered the multi-walled nano tube and initiated the nanotechnology revolution. Making single-walled nanotubes is more difficult than multi-walled ones, that's why it took two years since the discovery and production of multi-walled nanotubes until in 1993, with the cooperation of IBM and NEC, single-walled nanotubes were made. style="direction: rtl;">3 Diamond

4 Graphite

5 Buckyball / Fullerene / C60

6 Single-walled carbon nanotubes (SWNT)

7 Multi-walled carbon nanotubes (mWNT)

8 Bundle or Rope

9 S.Iijima

The electrical, mechanical, optical, magnetic, chemical, catalytic and biological properties of each one are points to consider in this new technology.

In many cases, we would like to predict the behavior of materials at the nano scale, but there are problems in this direction. One of the problems is the change of physical properties and as a result the change of physical laws, because the application of Newtonian physical laws does not give accurate results at the atomic scale, and the laws of molecular physics or quantum physics should be used to justify the phenomena that occur at this scale. In addition, at this scale, it is no longer possible to assume that their materials and structures are continuous. Since the formulas and relations of molecular physics are very complex and require a lot of calculation time and are so called expensive, in recent years the trend is to use the existing relations in engineering to investigate the behavior of nanostructures, taking into account that these relations qualitatively describe the process path in many cases. However, considering that the accuracy of using these relationships is not as accurate as the exact laws of molecular physics to justify phenomena and quantitatively calculate variables, there are certainly errors that may even question the accuracy of the results, but to solve this problem, existing relationships can be corrected in some cases to be closer to reality. Of course, even about the accuracy of the application of the laws of molecular physics - each of which is a mathematical description of a physical model to justify the behavior of particles on a very small scale - it is not possible to comment until practical and detailed experiments are carried out.

Another issue that exists is that in current engineering sciences, in many cases, we separate phenomena and discuss each one separately, and to simplify the relationships in many cases of the effect of variables and phenomena that We think that they do not have much effect on the desired phenomenon, while this separation in the nano scale is not very possible and correct because it completely changes the results, to be more precise, at this very small scale, different properties often affect each other, and this issue requires the creation of new knowledge, more accurate relationships and smarter modeling of the desired processes. The necessity of communication between nano to micro and also micro to macro scales is brought up. Also, the need to build unique devices to measure piconeton-sized forces and see and calculate on nanometer-sized materials is well felt. In the following, a brief description of nano production methods and applications will be given.

1-3- Classification and usual methods of nano material production

Since the discovery of carbon nanotubes in 1991, a lot of progress has been made in the production and application of these materials, among which the following can be mentioned Kord:

Materials

Chemical and biological separation, purification of materials and catalysts

Energy storage devices such as hydrogen storage devices, fuel cells and lithium batteries

Composite materials for covering, filling and also Title: Components of structures

Devices

Probes, sensors and actuators for imaging, sensing and manipulating particles on a molecular scale

Transistors, computer memories and other nanoelectronic devices

Nanoelectronic devices that work in a vacuum such as flat screen displays.

The advantages of these nanostructures include small size, low energy consumption, light weight and extremely good performance.

The most important groups of nanomaterials are: thin films, nanocomposites, nanoclusters, nanotubes and nanoparticles. Thin films are usually metallic or ceramic and are usually obtained from deposited nanoparticles and are used to protect and increase the efficiency of surfaces.