Nonlinear dynamic and vibrational analysis of carbon nanotube in nanoelectromechanical switch system using nonlocal theory of elasticity

Dissertation for Master's Degree

Mechanical Engineering (Applied Design)

Abstract:

Electromechanical micro and nano systems due to their distinctive features and unique characteristics, Mainly in the two fields of sensors and sensors, they have been noticed in various sciences such as mechanics, aerospace and medicine. Electrostatic stimulation is one of the simplest and most widely used methods of stimulating and starting these systems, which leads to instability in them.

Prediction of the static and dynamic behavior of electromechanical systems in nano dimensions with classical theories has been associated with errors. For this purpose, in this research, the electrostatic excitation of carbon nanoswitches and nanosensors is investigated using nonlocal stress theory. First, the non-linear equations and natural boundary conditions governing the problem are rewritten with non-local theory and the displacement of the nanobeam is divided into two static and dynamic parts. The solution of the static equation is done, and then by solving the eigenvalue problem of the dynamic equation, the natural frequency and the shape of the normal mode are extracted, which is a function of the initial static voltage and non-local parameter, so that it can be used in the Galerkin approximation method to solve the equations and determine the voltage and dynamic instability time of the nanoswitch as accurately as possible. In the vibration analysis, by introducing a new model of carbon nanosensor, its efficiency is tested in the presence of nanoparticles. Also, the non-local and non-linear tensile instability of boron nitride nanoswitch is investigated with non-local piezoelasticity theory. Finally, the results obtained from the analysis of static and dynamic and vibration diagrams show that the non-local effect affects the behavior of the electromechanical nanoswitch, especially in the field of instability quantities.

Key words: nanoelectromechanical systems, tensile instability voltage, carbon nanotube, boron nitride nanoswitch, nonlocal theory of elasticity, dynamics Nonlinear, electrostatic excitation

1-1-micro and nano electromechanical systems

Undoubtedly, one of the most important scientific advances in recent decades has been the miniaturization of macro systems and the development of microelectromechanical systems[1]. Micro-electromechanical systems have brought tremendous changes in industry and technology. Because they can be manufactured using existing manufacturing techniques and using semiconductor industry infrastructure, they are produced at low cost and in high commercial volume. Very small mass and volume, low energy consumption, high reliability and good durability are among the basic characteristics of these systems, which have made them more attractive [1]. Also, in recent years, with the rapid development of nano technology and the possibility of manufacturing parts in nano dimensions, nano electromechanical systems [2] have been proposed alongside micro electromechanical systems, and many devices that were previously made in micro dimensions found the possibility of manufacturing in nano dimensions. These systems are widely used in a wide variety of industrial parts, including mechanics, aerospace, medicine, transportation and communication technology.

Many examples of the application of micro and nano electromechanical systems are in capacitive micro and nano switches [3], resonators [4], pressure sensors [5], mass sensors [6], switches Radio frequency[7], accelerometers[8], micropumps[9], gyroscopes[10] and micro and nano electromechanical memories[11] can be seen[2].

Generally, there are two types of transmission and guidance methods in micro and nano electromechanical systems. Some transmission methods convert a change in a physical quantity such as pressure and temperature into a measurable electrical signal. Such styles are known as detection or sensing methods [12]. And piezoelectric electrostatic [13] and piezoresistive [14] methods are included in this category. Especially the vibrating sensors [15] that detect the change in the resonance frequencies of micro and nanostructures.Especially the vibrating sensors [15] that detect the change in resonance frequencies of micro and nanostructures as soon as they are sensed are in this group. Other methods of conduction convert the input energy of the system into motion of micro and nanostructures. They are known as stimulation methods [16] and include electrostatic, piezoelectric, electromagnetic and electrothermal methods [17] [3].

Choosing stimulation methods in these systems has been an important issue in recent years and depends on the intended system and its usability. The main stimulations and sensitivity characteristics of these systems are:

Piezoelectric materials: these materials are deformed under the influence of direct voltage, and also in the opposite direction and with deformation, a voltage is produced at both ends. which can be measured or controlled using this displacement property. So, according to what was said earlier, piezoelectric materials are used for both sensors and stimulators. Figure 1-1 describes well the basic concepts of piezoelectricity and the basic uses for sensing and stimulation.

Figure 1-1: Piezoelectric material in the state of stimulation and sensing (detection and measurement) [3]

Electrostatic: by creating two poles or a difference The voltage between the two plates generates an electrostatic force between the plates, which leads to the deformation and displacement of the system.

Heat: The deformation of the material due to heat can be used as stimulation, one way to increase the temperature is to pass current through the conductive plates, and another way is to shine a laser on the desired area.

Electromagnetic: a magnetic field due to the passage of current. It is created from a coil that can excite the magnetic materials in the environment.

All these methods have advantages and disadvantages. Piezoelectrics are used in excitation and detection (or measurement), but they have limitations in measurement due to the lack of direct voltage generation. And they cannot withstand high temperature operation. Other methods also have limitations, and the presence of thermal stresses and manufacturing stresses greatly reduce the accuracy of these systems. However, almost all problems are eliminated by using electrostatic excitation. It is very easy to make a capacitor with existing manufacturing methods. By using two parallel surfaces and by applying a potential to both ends, we reach a sensor or actuator with very good efficiency. Simplicity in construction and its proper efficiency have made the use of electric starter widespread. These capacitive stimulators are also economical. Micro-electromechanical systems that are stimulated through electrical actuators are widely used in micro- and nano-switches and micro- and nano-resonators.

Electrical stimulation is preferred over all stimulation methods due to its simplicity and high efficiency. And due to the establishment of an electric field in a very small volume, it is possible to access large forces for stimulation. For this reason, among the conduction methods, electrostatic excitation and detection mechanisms are the most used in micro and nano electromechanical systems, and more extensive research has been done in the field of electrostatic conduction [4]. Microswitches are highlighted and presented in a diverse role of elastic structures at the scale of micro-engineering. The basis of their structure is quite simple. The switch consists of a pair of electrodes. One electrode is usually rigid and fixed in space, and the other electrode is a deformable elastic structure. This electrode is made in designs and forms similar to elastic shell, elastic beam and elastic sheet. The switch is closed by applying a potential difference between two electrodes. This creates an electrostatic force, bends the deformable electrode, and leads to contact between the electrodes. Many groups have built and tested such structures. The mathematical models of these parts range from simple models based on the mass-spring model to fully developed models and 3D finite element simulators.