As mentioned in the previous section, the surface atoms media have different conditions than the atoms environment located in bulk material. Thus, the surface layer has different properties than the bulk material and this is caused to create the forces between the surface layer and the bulk material. There are many different theories that they represented the ways to consider these forces. One of them is presented by Gurtin and Murdoch [19, 20]. In the recent years, this theory is used many times by the researchers to analyze the mechanical behavior of the nanostructures [56-64]. In the other hand, the nonlocal continuum theory is used to consider inter atomic forces in the nano scale structures [65-70]. The strain relation of the Euler Bernouli …show more content…
Also, the is a geometric parameter that it is related to the geometrical shape and size of the nanobeam. This parameter for the circular cross section nanobeam is equal to the diameter of the nanobeam cross section (D) and for the rectangular cross section nanobeam is the nanobeam width (2h). It is assumed that the nanobeam has isotropic property so the stress component can be expressed as [46, 70]
In the above equation, the denotes the nonlocal parameter. Here, the is introduced as the Young modulus. Based on the Euler Bernoulli beam theory and the surface energy, the motion equation of the nanobeam is given by [46, 70] where, is the density of the surface of the nanobeam. According to the Euler Bernoulli beam theory, the stress resultants are defined as [46, 70]
Where the notation is divided to two parts that the notations and are caused by the angular velocity and the compressive axial force, respectively. These terms are obtained as following form
The moment stress resultant is obtained by inserting the Eq. (4) into Eq. (6) as the following form [46, 70]
Here the notation is moment inertia of the nanobeam. By substituting the Eq. (8) and the Eq. (9) into the Eq. (4) yield to the following equilibrium equation of motion of the rotating nanobeam in the presence nonlocal continuum theory and surface energy as the following
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This force is named the Lorentz force; also, this force is shown by the notation . The Lorentz force is calculated as follows form
In this study, we consider that the nanobeam is located in the longitudinal varying magnetic field; thus, in the above equation, we insert that it shows the magnetic field varies as sinusoidal respect to the x direction. As mentioned, the magnetic field causes to produce the Lorentz force. Consequently, the Lorentz force is caused to act the transverse load on the nanobeam. This force is obtained by using the Eq. (17), so the transverse force can be written as [48]
In this work, it is assumed that the nanobeam is located in a longitudinal magnetic field. Therefore, in the Eq. (10) the transverse load is induced by the magnetic field and is stated by . So by substituting the Eq. (18) into the Eq. (10) the differential equation of motion for transverse displacement is obtained as follows form
Furthermore, to derive the buckling equation of the nanobeam, a similar way can be taken by inserting the Eq. (18) into the Eq. (11); thus, the buckling equation of the rotating nanobeam induced by the magnetic field is obtained as the following
3. I. Boldea and S.A. Nasar, Linear Motion and Electromagnetic Systems. John Wiley & Sons Inc., 1995.
Naivety as well as the longing to fit into society with a loving man and stable, well-to-do peasant family deceived an honorable woman. Bertrande de Rols’ young marriage had difficulties from the start. With the guidance from family, the Catholic Church and Basque customs, Bertrande attempted to follow the sixteenth-century expectations for women, but was misled by her own fear, loneliness and catastrophic past.
7 Serway, Raymond A., Robert J. Beichner, and John W. Jewett, Jr. Physics for Scientists and Engineers. 5th ed. Philadelphia: Saunders College Publishing, 2000.
He knew this because polar opposites attract to each other and polars of the same push away from each other. In both the test with electromagnets and the normal magnet he had observed that the beam would curve inside the tube towards the positively charged metal and propel from the negatively charged metal. If polar opposites attract and the beam attracts to the positive, then it must be a negatively charged beam of
Throughout the past century, investigations of quantum and particle physics phenomena have proven to show the most significant concepts and ideas in the physical and sub-atomic world. However, the discoveries yet to be made are endless. One of the most fascinating concepts in the sub-atomic universe is the idea of spintronics. Spintronics is the quantum study of the independent angular momentum (not to be confused with the orbital angular momentum of the electron) of a particle, typically that of an electron (Introduction). An electron is a fundamental particle, with a negative charge, and is independently studied in the process of spintronic devices. The spin angular momentum of electrons is ±½ћ. Devices that use the properties
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...
...nduced in a conductor moving at right angles to and cutting across a magnetic flux. On the other hand, magnet is a useful in our daily life such as it can hold some documents and use to move an object. For example, a bicycle dynamo is a small generator fitted by bicycle to provide electricity for the lights bulb, it using the principle of electromagnetism. There are 2 law of electromagnetic induction such as Faraday’s Law and Lenz’s Law. In the other hand, Lenz’s Law state that induced current always flows in such a direction so as to opposite the change causing it. When north pole is approach the solenoid, the front part of solenoid will creates a north pole to produce a force of repulsion to oppose the change of motion. And the direction of current in the solenoid can determined by Right-hand Grip Rule. Lenz’s Law also is a form of law of conservation of energy.
The results all show how metallic materials have elastic and plastic properties which can be observed on the stress vs strain curve. The Results also indicate that denser metal such as steel have greater strength than the lighter materials such as brass. The energy of rupture is in pascals which is also J/m3.
1 David Halliday, Robert Resnick, and Jearl Walker, Fundamentals of Physics, Extended, 5th ed. (NewYork:Wiley, 1997) 361
Serway, Raymond A, and Robert J Beichner. Physics: For Scientists and Engineers. United States of
Alford, Terry L., L. C. Feldman, and James W. Mayer. Fundamentals of Nanoscale Film Analysis. New York: Springer, 2007. Print.
2) Fundamentals of Physics Extended: Fifth Edition. David Hanley, Robert Resnick, Jearl Walker. Published by John Wiley & Sons, Inc, New York, Chichester, Brisbane, Toronto, Singapore. 1997.
Grundmann, Marius. Physics of Semiconductors: An Introduction Including Devices and Nanophysics. New York: Springer, 2006. Print.
Nanoparticles are defined as particulate materials with at least one dimension of less than 100 nanometers (nm), even the particles could be zero dimension in the case of quantum dots (Bar et al., 2009). Metal nanoparticles have been of great interest due to their distinctive features such as catalytic, optical, magnetic and electrical properties (Rassaei et al., 2008).
Electric currents produce magnetic fields, they can be as small as macroscopic currents in wires, or microscopic currents in atomic orbits caused by electrons. The magnetic field B is described in terms of force on a moving charge in the Lorentz force law. The relationship of magnetic field and charges leads to many practical applications. Magnetic field sources are dipolar in nature, with a north and south magnetic pole. The magnetic field SI unit is the Tesla, it can be seen in the magnetic part of the Lorentz force law F magnetic = qvB composed of (Newton x second)/(Coulomb x meter). The smaller magnetic field unit is the