SPACE-TIME EVOLUTION OF THE NONLINEAR SURFACE DISTRIBUTIONS OF THE SEALING CONCRETE MIXTURE IN THE VERTICAL VIBRATE CYLINDRICAL TANK DURING ITS IDEAL EXCITATION

Abstract

The method of modeling and analysis of space-time evolution of nonlinear surface perturbations for the sealing concrete mixture at the vertical vibrate cylindrical tank with its ideal excitation is based. In the limits of proposed method and accepted assumptions, one may receive the standard nonlinear evolution equation with particular derivatives which gives the possibility to realize the detail analysis of the generating nonlinear wavelets at the researched system. For the larger part of cases, this equation is the nonlinear Shredinger’s equation with dissipation. The all-around sides’ analysis of the obtained analytical solutions of this equation is made for such cases: a) the free motion of the concrete mixture with the absence of dissipation; b) the free motion of the concrete mixture with the presence of dissipation; c) quasisolitary motion of the concrete mixture at the conditions of the compensation of the damping process and at the presence of the special weight at the surface of cylindrical tank. The analytical solutions of the nonlinear evolution equation are found in the form of the periodic type (so called cnoidal waves). They may be determined with a help of Yacobi’s functions or Veirstrass’s functions. The quasisolitary solutions have at their determination the typical function for the solitary waves – ch-1 or they are proportional to sech. One may use the weight of the special form (with radial ribs) for sealing of products from the concrete mixture. This way gives the possibility to excite quasisoliton on the surface of sealing liquid/mixture and to determine precisely all physical constants (amplitude, velocity, the reference phase of oscillations) of quasisoliton wavelets which are usually present in the solution of evolution equation. The results of this investigation may be used at future for the improvement and refinement of the present engineering methods of calculation of the energy and force characteristics of the vibromachines for the sealing of the concrete and construction mixtures at the stages of their projection/design and at the regimes of real exploitation, as well.