Near the resonance behavior of a periodicaly forced partially dissipative three-degrees-of-freedom mechanical system

Abstract

In this paper, a nonlinear three-degrees-of-freedom dynamical system consisting of a variable-length pendulum mass attached by a massless spring to the forced slider is investigated. Numerical solution is preceded by application of Euler-Lagrange equation. Various techniques like time histories, phase planes, Poincaré maps and resonance plots are used to observe and identify the system responses. The results show that the variable-length spring pendulum suspended from the periodically forced slider can exhibit quasi-periodic, and in a resonance state, even chaotic motions. It was concluded that near the resonance the influence of coupling of bodies on the system dynamics can lead to unpredictable dynamical behavior.

Keywords
Euler-Lagrange equation; time history; phase plane; Poincaré map; resonance plot; dynamical analysis; quasi-periodic motion; chaos