A NONSTATIONARY DYNAMIC PROBLEM ON THE EFFECTS OF SURFACE LOADS ON A HALF-SPACE WITH A NANOSIZED STRUCTURE WITHIN THE FRAMEWORK OF THE COSSERAT MEDIUM MODEL

2016 ◽  
Vol 7 (1) ◽  
pp. 61-75 ◽  
Author(s):  
A. S. Okonechnikov ◽  
Lev N. Rabinskiy ◽  
D. V. Tarlakovskii ◽  
G. V. Fedotenkov
Keyword(s):  
Half Space ◽  
Dynamic Problem ◽  
Cosserat Medium ◽  
Medium Model ◽  
Surface Loads

DISTRIBUTION OF THE RAYLEIGH WAVE ALONG THE BORDER OF THE HALF-SPACE, DESCRIBED BY THE SIMPLIFIED MODEL OF THE COSSERAT

2019 ◽  
Vol 81 (3) ◽  
pp. 333-344
Author(s):  
A.M. Antonov ◽  
V.I. Erofeev
Keyword(s):  
Surface Wave ◽  
Phase Velocity ◽  
Rayleigh Wave ◽  
Stress Tensor ◽  
Half Space ◽  
Theory Of Elasticity ◽  
Simplified Model ◽  
Classical Dynamic ◽  
Cosserat Medium ◽  
Dispersion Branch

We consider a simplified (reduced) dynamic model of a Cosserat medium, which occupies an intermediate position between the classical dynamic theory of elasticity and the proper Cosserat medium model, which has asymmetry in the stress tensor and the presence of moment stresses. In contrast to the latter, in the simplified model, three of the six elastic constants are zero and, as a result, there is no moment stress tensor. In the two-dimensional formulation for the model of a reduced medium, the problem of the propagation of an elastic surface wave along the half-space boundary was solved. The solution of the equations was described as the sum of the scalar and vector potentials, and only one component of the vector potential is nonzero. It is shown that such a wave, in contrast to the classical surface Rayleigh wave, has a dispersion. In the plane “phase velocity-frequency” for such waves there are two dispersion branches: the lower (acoustic) and upper (optical). With increasing frequency, the phase velocity of the wave related to the lower dispersion branch decreases. The phase velocity of the wave related to the upper dispersion branch increases with increasing frequency. The phase velocity of the surface wave in the entire frequency range exceeds the phase velocity of the bulk shear wave. The stresses and displacements arising in the zone of propagation of the surface wave are calculated.

Dynamic Problem in Green-Naghdi (Type III) Thermoelastic Half-Space with Two Temperature

2014 ◽  
Vol 21 (7) ◽  
pp. 544-552 ◽  
Author(s):  
Praveen Ailawalia ◽  
Shilpy Budhiraja ◽  
Amit Singla
Keyword(s):  
Half Space ◽  
Dynamic Problem ◽  
Type Iii ◽  
Two Temperature
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