Magnetomechanics of a graphene sheet. Theory and solution of an applied problem

Мұқаба

Дәйексөз келтіру

Толық мәтін

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Рұқсат жабық Рұқсат берілді
Рұқсат жабық Рұқсат ақылы немесе тек жазылушылар үшін

Аннотация

Interest in graphene is due to a wide range of unique physical and mechanical properties: high Young's modulus, high shear modulus, high strength, etc., as well as high electrical and thermal conductivity. From this point of view, the study of the deformation properties of graphene is one of the most actual branches of modern nanomechanics of materials and structural members (nanodevices). The application of mechanics to the study of nanomaterials, in particular, two-dimensional nanomaterials (graphene, carbon nanotube) is aimed at creating and developing a continuum theory of deformation behavior and having based on this theory, studying a number of applied problems. The moment-membrane theory of elastic thin plates and shells gives an adequate continuum theory of the mechanical behavior of a graphene sheet and a single-layered carbon nanotube (which is constructed taking account of the natural modeling of interactions between atoms in their crystal lattices, i.e. considering this interaction as both force and moment). It is known that due to their unique electrical and mechanical properties, both graphene and carbon nanotube are can be treated as supersensitive elements in the creation of nanoelectromechanical systems. On this basis, it is actual to develop a magnetomechanical theory of the dynamic behavior of a graphene sheet (as well as a carbon nanotube) placed in a given homogeneous magnetic field. In this paper, based on the equations of three-dimensional magnetoelasticity as a moment theory of elasticity with independent fields of displacements and rotations, by using hypotheses concerning the characteristics of mechanical behavior and the characteristics of the behavior of the electromagnetic field in thin regions, a two-dimensional model of magnetoelasticity is proposed according to the moment-membrane theory of elastic plates, which then is applied to a modeling magnetoelastic dynamics of a graphene sheet. Based on the proposed model of magnetoelastic dynamics of a graphene sheet, a problem of free one-dimensional bending oscillations of a two-dimensional body placed in a given homogeneous magnetic field is considered. Analyzing the obtained numerical results, it is shown that magnetoelastic oscillations have a damping nature, the behavior of both the oscillation frequency and the oscillation damping parameter are established depending on the values of the induction of a given magnetic field. Based on these results, a possible range of application of a graphene sheet to a nanoelectromechanical resonator is discussed.

Авторлар туралы

S. Sargsyan

Shirak State University

Хат алмасуға жауапты Автор.
Email: s_sargsyan@yahoo.com
Gyumri, Armenia

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