dynamic processes

Abstract. Goal of the work is to apply periodic Ateb-functions to investigate dynamic processes of strongly nonlinear systems with a finite number of degrees of freedom. Significance. Practically all problems in mechanics and engineering related to system oscillations, when strictly formulated, are nonlinear, as they are mathematically described by nonlinear differential equations. This often poses significant challenges in studying their behaviour, as finding a solution in exact form can be difficult.

The mathematical model of dynamic processes which arise during frictional hardening of the flat surfaces of machine parts using the tool with transverse grooves cut into the working surface is presented.

The universal mathematical model of dynamic processes in a radial plunger hydromashine pump with ball-pistons is created. This model takes into account inertial properties of piston balls, a stator, elastic liquid properties in a cylinder control, eccentricity, replenishment pressure and pressure in cavity pumping, and rotor frequency rotation. The law of pressure changes is established; this law takes into consideration its reproaches in pump cylinders.