Nonlinear dynamics is crucial in understanding the complex behavior of systems across various engineering fields. Unlike linear systems, which exhibit predictable and proportional responses, nonlinear systems can display unexpected and complex behaviors. This complexity is often found in natural and engineered systems, such as the vibrations of mechanical structures or fluid flows, where traditional linear models may fall short of capturing their full dynamical responses. In mechanical engineering, understanding nonlinear dynamics is essential for accurately predicting and controlling the performance of vibratory devices and structures.
Traditionally, engineers have aimed to avoid nonlinearities due to the mathematical difficulties they present and the challenges in analyzing and predicting system behavior. Linear models are preferred because they are simpler and easier to work with, providing a straightforward and robust way to design and analyze systems. However, this simplification can lead to oversights of the complete behavior of systems, potentially limiting performance and innovation due to the restrictions that linearity imposes.
Recent research has started to explore how nonlinear dynamics can be harnessed to improve the performance of engineering applications. By embracing the complexity of nonlinearities, engineers can develop systems with enhanced capabilities, such as improved noise suppression and signal amplification. My research proposes a systematic approach to utilizing geometric nonlinearities in mechanical beams, which serve as resonators, to enhance performance in various applications. As I will show in my talk, by using a simple genetic algorithm, we can optimize the design of resonators, allowing them to take full advantage of their nonlinear properties and offering new possibilities for innovation in mechanical and structural engineering.
