Numerical methods for solving the dynamic behavior of real systems

Abstract

In this paper are shown dynamic models which represent the real systems. As an example, one gear couple has been presented. In this case, the simplified model two discrete masses with elastic and damped connections. Using the of mechanics and taking into account initial and basic principles conditions, the system of differential equations is established which describes physicality of motion. Such system of equations represents mathematical model at dynamical behavior of gear transmission. Established system of differential equations has been solved in analytical way with the aim of obtaining data for numerical analysis. The proper estimate of dynamical behavior of gear transmission and other systems can be on the basis of own frequency and of own form of oscillating. In the paper is presented the solution of the main form of oscillating and stress condition using finite elements method.

Preisach Mathematical Model of Hysteresis

“…For understanding this issue, the paper of V. Nikolić at al. [15] can be helpful. Here we will consider a three element unit.…”

“…( 13) to (16), algorithm for elastoplastic analysis of trusses subjected to cyclic loading was defined in C++ code. During every step and iteration in expressions (13) to (15), in every bar of truss structure, plastic part from Eq. ( 15) is being calculated according to current state of corresponding bar and then assembled in global matrix in Eq.…”