Numerical simulation of chaotic vibration

• Main Author: Muhammad Yasser Roslan
• Other Authors: Lin Rongming
• Format: Final Year Project
• Language: English
• Published: Nanyang Technological University 2021
• Subjects: Engineering::Mechanical engineering
• Online Access: https://hdl.handle.net/10356/150755
• Institution: Nanyang Technological University

Chaotic vibration is a new nonlinear vibration mechanism in which a periodic input causes a non-periodic response. This project would carry out extensive simulations of disorderly vibration for a single degree of freedom mechanical device with backlash stiffness nonlinearity based on a specific excitation spectrum. By using numerical algorithms, MATLAB can solve a series of nonlinear equations in time that describes the system. The presence of disorderly vibration can be detected using both qualitative and quantitative methods. However, the qualitative research will be the sole subject of this initiative. To explain the unpredictable existence of the vibration, graphical solutions such as time reactions, state space trajectories, Poincaré maps, power spectrum, and bifurcation diagrams will be used. The time reaction plots will show how the system behaves in relation to time. Poincaré maps will tend to demonstrate the existence of odd attractors, while state space trajectories will reflect the state of the system. The power spectrums depict the system's existence in terms of frequency. The infinite periodic doubling phenomenon that leads to anarchy can be shown using bifurcation diagrams. The aim of this simulation is to see how parameters affect the system's actions. The excitation amplitude and frequency of the sinusoidal loading power, damping, and the initial conditions can all be used as parameters.