SUPERSONIC VIBROTRANSPORT SOLUTIONS OF THE WAVE EQUATION AND THEIR PROPERTIES

Abstract

Here the effect of vibrotransport sources of wave radiation in media is investigated which are associated with moving objects, the speed of which can be subsonic, sonic, supersonic, in media with several sonic speeds (elastic, for example) also transonic. The fundamental and regular vibrotransport solutions of the wave equation are constructed for supersonic speeds of the disturbance source at any Mach numbers greater than 1, in spaces of physical dimension (N = 1, 2, 3). Fundamental solutions of these equations are constructed - Green's functions, which describe the dynamics of the medium during the movement of a source concentrated at a point, which moves with a constant speed and vibrates with a constant frequency. On its basis, generalized solutions of the vibrotransport equation are constructed under the action of both moving vibration sources distributed in space and concentrated on moving surfaces and lines. These solutions allow constructing solutions of many equations of continuum mechanics for this type of moving supersonic sources of disturbances in isotropic media and will find extensive applications in solving various engineering and technical problems.