The mathematical model of the mechanical system, which is a section of the pipeline with built-in motor pump system and damper for vibration damping, has been developed. The mathematical model is represented by a system of partial differential equations of hydrodynamics for moving fluid in the pipeline and a system of two ordinary differential equations for the damping device. Solution the system of equations is performed using analytical and numerical methods. The numerical solution of the equations of hydrodynamics carried out using the finite element method, implemented in the programming environment of mathematical package freeFEM ++.
The article is devoted to numerical study of convergence of calculation results obtained on the basis of two nonlinear models of the theory of shells with thickness decrease. As models are considered nonlinear theory of thin shells, based on the hypotheses of the Kirchhoff-Chernykh and hypotheses type Tymoshenko, modified K.F. Chernykh for the case of hyperelastic rubber-like material. As an example, we consider the problem of axisymmetric conical compression and spherical shell by axial force. The convergence of results with decreasing thickness is disturbed in areas stability loss(buckling). Also happens when in the deformation process is violated the basic assumption of the theory of shells -the thickness is much smaller than radius of curvature (h < < R).
A nonlinear mathematical model of the system of drilling rig, consisting of the rig, the control cabin, the working platform and platforms with engines has been developed. The mathematical model of the rig with six degrees of freedom is represented by a system of nonlinear ordinary differential equations. The methodology for calculation the basic characteristics of oscillation using the method of polynomial transformations was developed. The formulas for the calculation by the method of polynomial transformations were obtained.
The mathematical model of malignant tumor, which represents itself an initial boundary task for system of differential equations in partial derivatives, has been developed. In model there are 3 types of cells, which interact between each other, it is a dividing, normal and dead cells. An inhibiting influence of cells at each other is considered in that way that the growth of continuously dividing cells is accompanied by destruction of normal cells and emergence of dead cells. Analysis of stability of stationary decisions has been done. Evaluation of velocity of distribution tumor on a straight line has been given.
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