Frequency domain modeling has been developed to different engineering applications. In particular, the Spectral Element method (SEM) has been discussed in literature mainly for vibration control design and structural health monitoring once it allows to study unlimited range of frequencies. However, although different authors discuss classical control techniques like PID for SEM formulations there is a limited number of works involving modern control theory based on state space representation. In this context, this work introduces a new approach that allows to use feedback techniques in vibration control design based on SEM. The formulation is presented and numerical simulations are performed using the Timoshenko beam model with two PZT patch bonded. The PZT transducer effects are included too. Results show vibrations reductions of the first three modes of a campled-clamped beam and the proposed approach offers promise to control design using SEM.
Sanderson M. Conceição, Douglas D. Bueno, and Vicente Lopes, "Feedback control design and SHM based on spectral element method (Conference Presentation)," Proc. SPIE 10172, A Tribute Conference Honoring Daniel Inman, 1017207 (Presented at SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring: March 29, 2017; Published: 11 May 2017); https://doi.org/10.1117/12.2261971.5427850867001.
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