Effects of Boundary Conditions on a Self-Excited Vibration System with Clearance

Abstract

In this paper, the nonlinear dynamics of a single degree of freedom system for the rolling mills with clearance is investigated. The boundary conditions of the self-excited vibration system basically involve discontinuities, and the effects of boundary conditions on the vibrating system are analyzed by using asymptotic method and numerical simulation. Different forms of nonlinear vibrations such as periodic, quasi-periodic and chaotic motions are detected. Influence of the system parameters on the nonlinear vibration behaviors is also examined by applying the Poincare sections, phase portraits, waveforms, the bifurcation diagram and the largest Lyapunov exponent. New phenomena are observed in nonlinear motions of the rolling mill mechanism.

Nonlinear analysis of a rub-impact rotor with random stiffness under random excitation

“…where r = ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi X 2 + Y 2 p represents the radial displacement, and the general notations used in equation (1) are shown in Table 1.…”

“…With the fast development of uncertainty analysis and processing technology, researchers tend to use uncertainty to explain the rotor systems. 1 In this situation, parameter may submit random distribution which is caused by external environment, manufacture, material, and installation. 2 Igusa and Kiureghian 3 first studied uncertainty and found the uncertainty in the parameters of certain systems may have significant influence on the irreliability, even when the input is a wideband stochastic process.…”

Non-probabilistic analysis of a double-disk rotor system with uncertain parameters

“…The dynamic characteristics are frequently investigated by designers and researchers to understand the performance of a rotor system. Many efforts have been put in during the past few decades both theoretically and experimentally [1][2][3][4][5][6][7][8]. As can be seen, these contributions were mostly focused on rotor systems in which the parameters and loads are all deterministic.…”