Propagation of non-stationary kinematic disturbances from a spherical cavity in the pseudo-elastic cosserat medium
Faculty of Special Equipment, Le Quy Don Technical University, 100000, Hanoi City, Vietnam
2 Faculty of Mechanical Engineering, Le Quy Don Technical University, 100000, Hanoi City, Vietnam
3 Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, 21589, Jeddah, Saudi Arabia
Accepted: 17 November 2021
Published online: 1 December 2021
In this work, the Cosserat model is used to simulate non-stationary processes in various structures of composite materials. A non-stationary axisymmetric problem of the propagation of kinematic perturbations from a spherical cavity in a space filled with a homogeneous isotropic pseudo-elastic Cosserat medium is considered. The motion of the medium is represented by a set of three equations written in a spherical coordinate system with the origin at the center of the cavity and nonzero components of the displacement vector and rotation field potentials. At first, it is supposed that the plane wave or spherical wave’s front makes contact with the hollow surface. The initial-boundary value issue is mathematically formulated in dimensionless form. A serial expansion of Legendre and Gegenbauer polynomials, as well as the Laplace transform in time, is utilized to obtain the solution. The issue is simplified to a set of independent ordinary differential equations with the Laplace operator applied to the series coefficients. Due to the complexity of images of the series coefficients, to determine the originals in the linear approximation, the Laurent series for images in the vicinity of the start time is employed. The findings indicate that the solutions found using limit techniques are consistent with previously published results for the classical elastic medium. For the granular composite material of aluminum fractions in the epoxy matrix, examples of computations are presented.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021