According to nonlocal piezoelasticity theory, the stress and electric displacement filed of a specific point depend not only on strain and electric filed components at the same point but also on all other points of the body. This statement of nonlocal theory can be formulated as nonlocal constitutive behavior as follows [34, 35]: (1) where and are nonlocal stress tensor and local stress tensor, respectively. and denote components of nonlocal and local electric displacement, respectively. represents small scale effect on the response of structures in nanosize and is Laplacian operator. 3. Modelling of the problem 3.1. Geometrical description of the problem A schematic configuration of the problem is illustrated in Figure 1. As can be seen in this figure, a double layer graphene sheet is covered by two ZnO piezoelectric layers. The thicknesses of graphene and piezoelectric layer are distinct and denoted by and , respectively. The interaction between graphene layers is modeled by Vdw force. The whole system surrounded by Pasternak foundation. Magnetic and electric field are applied to graphene and piezoelectric layers, respectively. Moreover, a biaxial force applied to the GSs. Before keeping on, it must be noted that the system shown in Figure 1 is divided into two systems. System 1 is considered upper piezoelectric and graphene layers, and system 2 is considered the lower ones. …show more content…
Governing equations of motion In this section, the aim is to obtain governing equations of motion by means of Hamilton’s principle. In this study, all layers have been modeled by CPT. Displacement field for CPT is given by
tension of the system. Their orientation at the interface varies, depending on the components of
In section II of this paper, theoretical background relevant to this problem is presented. Section III is a brief summary of the numerical data from Giorgini, Boronat, and Casulleras.
The evolution of a fluid (gas) can also be described by the exact dynamics of the individual particles that constitutes the fluid (gas) in terms of Newton equations. However, this is complicated in the sense that in order to compute the time evolution of the fluid, one will have to solve a system of 6N first order differential equations with 6N unknowns constituting the position and velocity vectors. A perquisite for this computation is the knowledge of 6N initial
Continuum Mechanics is the branch of mechanics which deals with the study of deformation and motion of continuous bodies. Primarily, a continuous solid body can be categorized into two types: (i) Rigid body and (ii) Elastic body. When external forces are applied on the body and the relative positions of its particles do not change at all, the body is said to be perfectly rigid body, otherwise it is said to be elastic body. A body is called strained, if under the influence of some external forces, the relative positions of its particles get altered. The change in the relative position of particles is called deformation. In practice, all solid bodies undergo deformation up to some extent by the application of suitable forces upon them. There are certain bodies which regain their original configuration when the deforming forces are removed. For example, the wire regains its original length after
Deviance is a natural part of and necessary for stability and social order in society, this according to functionalist theorist Emile Durkheim (MindEdge, Inc., 2016). Traditionally, society is generally successful in providing motivation for individuals to aspire for goals of some sort, whether through wealth, prestige or perceived power (Henslin, 2011). However, from a functional perspective, theories have been developed in identifying when lawful and equal access is not afforded to certain individuals in the process of obtaining such goals. This restriction and inequality to opportunity for access in the quest to achieve success is what is now referred to as structural strain theory, which was developed by sociologist Robert Merton (Henslin,
Based on the piezoelectric effect, the transducer’s function is to emit short pulses and receive echoes of the pulse, a process repeated “over a sequence of directions to cover a 2D sectional fie...
Understanding the plate tectonics theory is very important, especially when investigating natural disasters like earthquakes, and volcanic eruptions. It is also gives scientists the ability to understand how mountains were formed between two tectonic plates. There are three types of interactions between plate boundaries: convergent, divergent and transform. Looking back at the history of these three different interactions, earthquakes, like the one in Haiti, volcanic eruptions, like at Mount St. Helens, and the creation of mountain belts, like the Mid-Atlantic Oceanic ridge, gives information on future consequences of tectonic movement, and what can happen when the plates interact with each other.
General Strain Theory was discussed by Robert Agnew, and first published in 1992. According to General Strain Theory individuals engage in crime because of strains or stressors which produce anger and anxiety (Agnew, 1992). Crimes become the outlet that the individual uses to cope with or remedy the strains or stressors. Agnew states that there are three different types of deviance producing strains.
Nanotechnology is the manipulation of structures at nano levels. It uses incredibly small materials, devices, and systems to manipulate matter. These structures are measured in nanometers, or one billionth of a meter, and can be used by themselves or as part of larg...
Mechanical Engineering 130.2 (2008): 6 - 7. Academic Search Complete. Web. The Web. The Web.
Graphene refers to a single layer of graphite, with sp2 hybridized carbon atoms arranged in a hexagonal...
On a more scientific note I am interested in mechanics of fluids. This interest was enforced last year when I had the opportunity to attend a lecture on fluid mechanics at P&G. At the conference I greatly expanded my knowledge regarding the physical aspect of fluids and their properties. In last year's AS course we have met a topic in this field. I will be applying ideas and knowledge gathered from last year for this investigation.
Alford, Terry L., L. C. Feldman, and James W. Mayer. Fundamentals of Nanoscale Film Analysis. New York: Springer, 2007. Print.
These materials conduct by a process known as hole conduction. Within such a material there are locations, called holes, that would normally be occupied by an electron but are actually empty. A missing negative charge is equivalent to a positive charge. When an electron moves in one direction to fill a hole, it leaves another hole behind it. The hole migrates in the direction opposite to that of the electron. In terms of the coordinate axes in Fig. T10.1b, the electrostatic field E for the positive-q case is in the −z-direction; its z-component Ez is negative. The magnetic field is in the +y-direction, and we write it as By . The magnetic force (in the +zdirection) is qvd By. The current density Jx is in the +x-direction. In the steady state, when the forces qEz and qvdBy are equal in magnitude and opposite in direction, This confirms that when q is positive, Ez is negative. The current density Jx is Eliminating vd between these equations, we find (T10.1) Note that this result (as well as the entire derivation) is valid for both positive and negative q. When q is negative, Ez is positive, and conversely. We can measure Jx , By , and Ez, so we can compute the product nq. In both metals and semiconductors, q is equal in magnitude to the electron charge, so
Grundmann, Marius. Physics of Semiconductors: An Introduction Including Devices and Nanophysics. New York: Springer, 2006. Print.