Riassunto analitico
In this thesis a thorough investigation has been done into the nonlinear dynamics of different Duffing oscillator systems by MATLAB simulation and experimentation. The first part of the research contained the development of a MATLAB framework in order to study the behavior of Duffing oscillator systems and procedures invented to solve the desired differential equations. The MATLAB code was purposefully set up to simplify the nonlinear dynamic analysis of Duffing oscillator systems to provide the reader with physical knowledge about the respective phenomena like bifurcations, chaos and resonances in the system.
The MATLAB program consisted in generating algorithms that were implemented to solve the nonlinear differential equations of the Duffing oscillator. In doing so, the dynamics of this system were experimentally realized for various parameters and forcing functions. The MATLAB code did successfully perform as it faithfully portrayed the nonlinear complexity of the behavior of the Duffing oscillator, offering evidence to the reader in the form of results and certain graphs.
MATLAB simulation results are tested in an experimental investigation during the second phase of the research. Three origami isolators are utilized in an experimental setup as a nonlinear structure. The nonlinearity of the origami isolators makes them ideal for analyzing intricate dynamics, much like the Duffing oscillator system. To describe the response of the nonlinear structure to different loading conditions, experimental data is modelled using a fifth-order polynomial approach.
The numerical model's accuracy and dependability are tested by comparing experimental data from the tests with the results obtained from MATLAB simulations. The comparative analysis yields significant information about the agreement between simulation and experimental results, indicating that the MATLAB-based approach is highly effective in accurately representing the dynamics of the Duffing oscillator system.
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