Numerical modeling of three-dimensional wave motions in couple-stress media

Abstract

A computational algorithm for the solution of three-dimensional dynamic problems of the Cosserat elasticity theory using multiprocessor computer systems is worked out. Computations of 3D Lamb's problem of the action of a concentrated load on the surface of a homogeneous elastic half-space and the problem of the action of a concentrated impulsive periodic load are performed. The symmetry boundary conditions permitting us to reduce computations many times are formulated. The shock waves of four types, longitudinal, transverse, torsional and rotational waves, characteristic of couple-stress elastic medium, are recognized numerically. The oscillations of the rotational motion of particles on the wave fronts are also found. The results of the analysis of oscillation processes show that the Cosserat medium possesses the eigenfrequency of acoustic resonance, which appears under certain conditions of perturbation and depends only on the inertial properties of the microstructure particles and the elasticity parameters of the material.