PERIODIC OSCILLATIONS IN NONLINEAR MECHANICAL SYSTEMS.

摘要

A new quantitative method of estimating steady state periodic behaviour in nonlinear systems, based on the trigonometric collocation method (TCM), is outlined. A procedure is developed to analyze large mechanical systems with nonlinear components by the use of the above method in conjunction with Component Mode Synthesis. The algorithm discussed is seen to reduce the original problem to solving nonlinear algebraic equations in terms of only the coordinates associated with the nonlinear subsystems and is a big improvement over commonly used integration methods. Based on the above procedure, a computer code is written with specific application to rotor dynamic systems. Also outlined are two stability algorithms that can be used to investigate the existence of the periodic solutions obtained by TCM.;Several examples are worked out using the procedure developed. Parametric studies are carried out for the problem of a journal on a hydrodynamic bearing. The effect of Coulomb friction in a coupling connecting two rigid rotors is analyzed using the TCM as well as analytical approximation method. A simple model of a squeeze film damper is considered and parametric studies are carried out to compare centered and eccentric operations. The extent of applicability of this procedure is demonstrated by analyzing limit cycle oscillations in a nonlinear control system and in an aeroelastic oscillator.;As an illustration of the possible use of the method as a design tool, an example of a typical rotor dynamic system with an uncentered squeeze film damper and another rotor system with a journal bearing are studied.