Аxisymmetric perturbations from the surface of a sphere filled with pseudo-elastic Cosserat medium
Mathematics. Physics. Mechanics
Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia
AbstractAxisymmetric kinematics of perturbation from the surface of a sphere filled with homogeneous isotropic medium with restricted rotation (the Cosserat pseudo-continuum) are considered. These models are used in the study of the behavior of different structures, which are made from composite materials, including objects of aviation, rocket and space technology. In order to find out the solution, we use a serial expansion in Legendre polynomials and Laplace transform of the time. To find the original function we use asymptotic method – representation of functions as power series in time, which corresponds to expansion of the image of functions in a Laurent series in a neighborhood of infinity
Keywords:the Cosserat pseudo-continuum; Laplace transform; axial symmetry; the asymptotic solutions.