Математическое моделирование, компьютерный и натурный эксперимент в естественных науках
Электронный научный журнал

Физико-математические науки
MATHEMATICAL MODEL OF SPRING-DISK SYSTEM WITH HARDENING RESTORING FORCE
Popova A.A. 1

1. Yuri Gagarin State Technical University of Saratov

Abstract:

The paper presents a mathematical model for investigation of hard disk non-linear oscillation. We assume hard disk attached to a nonlinear spring of hardening type and interacting with viscous liquid layer. The hard disc is a wall of a narrow channel filled with a viscous liquid. The opposite channel wall is a stationary disk, which is coaxial and parallel to the disk attached to the spring. Hardening restoring force model with cubic nonlinearity is chosen for the nonlinear spring. The mathematical model of considered oscillatory system consists of the creeping motion equations of viscous incompressible fluid and the Duffing equations. The axisymmetric dynamic problem of viscous liquid layer is considered. The non-slip conditions at the channel walls and free discharge at the channel edge are chosen as boundary ones. The liquid layer pressure is obtained and the damping term of the Duffing equation is determined on the base of liquid layer dynamics equations solution.

Keywords: Mathematical modeling, hydroelasticity, viscous liquid, cubic restoring force, non-linear oscillations, Duffing equation

Сайт работает на RAE Editorial System