Vol. 6, №1, 2014
РусскийEnglish

CONTINUUM PHYSICS



DIFFRACTION OF WAVES BY A SPHERICAL CAVITY IN A COSSERAT PSEUDO-CONTINUUM
Lai Thanh Tuan
Moscow Aviation Institute (National Research University), http://www.mai.ru
125993 Moscow, Russian Federation
thanhtuan711@yahoo.com
Tarlakovsky D. V.
Moscow Aviation Institute (National Research University), http://www.mai.ru
125993 Moscow, Russian Federation
tdv902@mail.ru

Received 08.04.2013
Represented by a Academician of RANS V.I. Erofeev 08.04.2013

We use the Cosserat model to simulate non-stationary processes in various structures of composite materials. Purpose of the work is the formulation and construction of analytical solutions of two dimensional problems of diffraction of waves by a spherical cavity in pseudo-continuum Cosserat. We assume that the front of the plane wave or spherical wave make contact with cavity surface at the initial time. The mathematical formulation of the initial boundary value problem is given in dimensionless form. In order to find out the solution, we use a serial expansion in Legendre and Gegenbauer polynomials, Laplace transform at each of the time and inversion images in the vicinity of start time using the Laurent series for images. Shown that the solutions obtained using limit methods coincide with the known results for the classical elastic medium. We provided examples of calculations for the granular composite material of aluminum fractions in the epoxy matrix.

Keywords: transient problem; the Cosserat pseudo-continuum; axial symmetry; Laplace transform; the asymptotic method

UDC 539.3

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RENSIT,
2013, 5(1):119-125

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