International Conference
"Modern Problems of Applied Mathematics and Mechanics: Theory, Experiment and Applications", devoted to the 90th anniversary of professor Nikolai N. Yanenko

Kaishibaeva G.   Алексеева Л.А.  

Dynamics of Elastics Media by the Action of Transonic Transport Loads

Reporter: Kaishibaeva G.

For decision of the problems media mechanics simulating processes with loads
connected with moving the transport in different perturbation, or displacement transported cargo in subway and pipe line of the different purpose, as well as difraction of the seismic waves on stretch underground buildings, were used boundary integral function method and apply generalised function theories.
Mathematical simulation of such processes requires the buildings of the decision of equations in "running" function class, parametric and automodel on row variables. The velocity of the moving the source of the perturbations in media greatly influences upon type of the equations of the motion, which depends on velocities of the waves spreading in media, so named sound velocities. The type of the differential equations, describing moving of media, is changed depending on relations of the velocities of the source of the perturbations to sound velocities (the Mah’s numbers).
There are considered shock waves, which appear in media under supersonic source of the perturbations, and is offered determination method of the conditions on jumps of the decisions and their derivatives on shock waves front. There presented analogues of formula Grin, Gauss, allowing build the boundary integral equations for initial-border problems.
Will built generalised decisions of the Lame equation, describing moving the elastics media at transonic velocity the source of the perturbations moving.
It’s worked out program of the calculation of the moving elastics media at action of the portioned loads at transonic velocity motion. Organized calculations by vector fields for vertically loaded band in transonic range velocities