Numerical simulation of chaotic vibration

• Main Author: Ng, Kheng Hong.
• Other Authors: Lin Rongming
• Format: Final Year Project
• Language: English
• Published: 2009
• Subjects: DRNTU::Engineering::Mechanical engineering::Mechanics and dynamics
• Online Access: http://hdl.handle.net/10356/17111
• Institution: Nanyang Technological University

Chaotic vibration is a new nonlinear vibration phenomenon where a periodic input to a nonlinear system will lead to a non-periodic output. Extensive simulation of chaotic vibration for a single degree of freedom mechanical system with backlash stiffness nonlinearity will be carried out based on certain excitation range in this project. MATLAB will be used to solve a set of nonlinear equations in time that represents the system by the means of numerical algorithms. Both qualitative and quantitative techniques to detect the existence of chaotic vibration will be studied. However, the focus for this project will be only on the qualitative analysis. Graphical solutions such as time responses, state space trajectories, Poincaré maps, power spectrum and bifurcation diagrams will be used to demonstrate the chaotic nature of the vibration. The time response plots will indicate the behavior of the system with respect to time. The state space trajectories represent the state of the system as a whole while Poincaré maps will aim to show the presence of strange attractors. The power spectrums portray the nature of the system with respect to frequency. Bifurcation diagrams are able to prove the infinite periodic doubling effect that lead to chaos. This simulation seeks to investigate the influence of parameters on the behavior of the system. The parameters used will be the both the excitation amplitude and frequency of the sinusoidal loading force, damping and the initial conditions. At each time, only a set of parameters will be varied.