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In graphene in the presence of strain the elasticity theory metric naturally appears. However, this is not the one experienced by fermionic quasiparticles. Fermions propagate in curved space, whose metric is defined by expansion of the effective Hamiltonian near the topologically protected Fermi point. We discuss relation between both types of metric for different parametrizations of graphene surface. Next, we extend our consideration to the case, when the dislocations are present. We consider the situation, when the deformation is described by elasticity theory and calculate both torsion and emergent magnetic field carried by the dislocation. The dislocation carries singular torsion in addition to the quantized flux of emergent magnetic field. Both may be observed in the scattering of quasiparticles on the dislocation. Emergent magnetic field flux manifests itself in the Aharonov–Bohm effect while the torsion singularity results in Stodolsky effect. 相似文献
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Changzheng Huang 《Applied Acoustics》2009,70(5):730-736
The problem of sound transmission through layered panel structures is studied with the exact theory of three-dimensional (3-D) elasticity. The exact solution to the 3-D elasticity equations is obtained by the use of the Fourier spectral method. Based on this analytical solution, a transfer matrix is derived that relates the spectral displacements and stresses on the one surface of the panel to those on the opposite panel surface. The transfer matrix is then used to develop the analytical solutions for sound reflection and transmission coefficients. Explicit, concise expressions are obtained for the analytical solutions of the acoustic transmission and reflection coefficients under the general conditions of layered anisotropic panels. Examples are given for both single-layer and sandwich panels. Predictions on sound transmission from the 3-D elasticity theory are compared with available data from other methods, and the results are discussed. 相似文献
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A one-dimensional stress-based elasticity model with limited strain extensibility is developed in this paper, based on thermodynamics arguments. Such nonlinear elastic models can be used to model certain rubber-like and biological materials with limiting chain extensibility. The derived constitutive function is a non-smooth piecewise expression, which can be regularized for numerical or physical considerations. This non-smooth constitutive expression is derived from a Gibbs potential. A three-dimensional extension of this stress-based model is also proposed in the paper. Some simple structural examples are investigated for a bar composed of this non-smooth elastic body. A homogeneous bar composed of this new class of nonlinear elastic material that is loaded is studied for different tension states, namely for concentrated or distributed axial loading. It is shown that the displacement limit extensibility can be observed at the structural scale, with finite or infinite axial load parameters. 相似文献
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In this Letter, the dynamic plane elasticity problems of 2D quasicrystals is considered. By use of the Fourier transform and matrix transformations the system is reduced to uncoupled ordinary differential equations. Fourier images of Green's functions for dynamic plane elasticity problems of 2D dodecagonal, pentagonal and decagonal quasicrystals are obtained explicitly by the suggested method. 相似文献
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W.F. Espinosa-GarcíaC.M. Ruiz-Tobón J.M. Osorio-Guillén 《Physica B: Condensed Matter》2011,406(20):3788-3793
The elastic properties of the compound family of the sulvanite Cu3TMX4 (TM=V, Nb, Ta; X=S, Se) have been calculated using first-principles total energy calculations within the density functional theory along with the local density and the generalized gradient approximations. The calculated elastic properties are the bulk modulus (B), the elastic constants (c11, c12 and c44), the Zener anisotropy factor (A), the isotropic shear modulus (G) and the Young modulus (E). By means of these quantities we have also computed other thermodynamic properties such as the average sound velocity (s) and the Debye temperature (ΘD). The calculated values of the elastic properties led to the conclusion that these compounds are brittle and fragile. We have also calculated the electron localization function, which exhibits the bonding characteristics in these compounds, showing that the Cu-X bond as well as the TM-X bond have a covalent character, but there is also present some ionicity in these compounds due to the Cu-TMX4 bond. 相似文献
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Nikolay Banichuk Alexander Barsuk S. Y. Ivanova Juha Jeronen Evgeni Makeev 《基于设计的结构力学与机械力学》2018,46(1):1-17
We consider an infinite, homogenous linearly elastic beam resting on a system of linearly elastic supports, as an idealized model for a paper web in the middle of a cylinder-based dryer section. We obtain closed-form analytical expressions for the eigenfrequencies and the eigenmodes. The frequencies increase as the support rigidity is increased. Each frequency is bounded from above by the solution with absolutely rigid supports, and from below by the solution in the limit of vanishing support rigidity. Thus in a real system, the natural frequencies will be lower than predicted by commonly used models with rigid supports. 相似文献
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Nonlinear elastic vibrations of cylindrical piezoelectric transducers are investigated both experimentally and theoretically. A particular behaviour, that relates the space distribution of the fundamental mode vibration to those of the second and third harmonic components, is observed. A simplified physical interpretation of the phenomenon is given. 相似文献