Vibrations on (i) Piezoelectric and (ii) Multi-layer Sandwich Beams
These Wolfram Demonstration Projects are produced for the "AMS - PME Undergraduate Student Poster Session" of the Joint Mathematics Meeting'23 presentation in Boston, USA, held on Friday, January 6, 2023.
Project members: Jacob Walterman, Ahmet Kaan Aydin
This material is based upon work supported by the National Science Foundation under Cooperative Agreement No. 1849213. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
Abstract: Novel reduced models of partial differential equations (PDE) for piezoelectric (smart material) beam equations are developed by Finite Differences and Finite Elements. These reduced models accurately predict feedback-controlled vibrations on piezoelectric beams. The paired controller and sensor are collocated at the tip of the beam. First, it is shown that the feedback sensor placed at the tip of the beam can be designed by eliminating the short wavelength and high-frequency components of the solutions through the direct Fourier filtering technique. This way, the sensor becomes more able to distinguish one vibrational frequency from another. The filtered sensor data is then fed back to the controller, resulting in all of the vibrations on the beam being successfully suppressed exponentially fast, replicating the dynamics of the PDE case. Another approach, based on order reduction, accurately simulates the suppressed dynamics without the need for direct filtering. Finally, all Mathematica simulations are converted to the computational framework Wolfram’s Computable Document Format (CDF) to be published at open-source-code website called Wolfram Demonstrations Project (WDP). As a side note, each Demonstration Project is peer-reviewed and edited by Wolfram experts and engineers for content, clarity, presentation, quality, and reliability.
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