Study of the vibration pattern synthesis in structures using dynamic mode decomposition (DMD)

Abstract

This thesis studies the vibration pattern synthesis in structures using the Dynamic Mode Decomposition (DMD) method. This numerical model is used for one degree of freedom, to know the axial response, according to x. Firstly the effectiveness of the DMD method is evaluated and give good results to reconstruct the signal, applying to initial conditions of the structure's vibration to extract the shape and temporal characteristics of the DMD modes, which were then used to synthesize the desired vibration pattern in the structure. Next, QR factorization is used in order to find sensor placement. Results showed that the DMD method, combined with QR factorization, can effectively synthesize the desired vibration pattern in structures. However, conditions about spacing of the sensors is necessary to optimize the interpolation. Regarding further research, it’s needed to study the method's limitations and potential application in more complex systems or when dealing with high-frequency data.