Effect of the Finite Element Type on Modeling, Analysis and Control of a Cantilevered Beam


Nader Ghareeb†*, Mohamad Farhat‡


†Mechanical Engineering Department Australian University, West Mishref, Kuwait
‡Electrical Engineering Department Australian University, West Mishref, Kuwait.

Corresponding Author Email: [email protected]

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This work demonstrates the importance of selecting the proper finite element (FE) in the modeling, analysis and control of a cantilevered beam. In the first step, the physical system is discretized into finite elements by using a finite element (FE) code written in MATLAB©. The optimal FE type is chosen after performing a static and modal analysis of a variety of FE types and comparing the numerical results regarding the tip deflection with the analytical results. In the next step, a transient analysis is performed, and the cantilevered beam is excited once with its first eigenfrequency only, and after that with its first three eigenfrequencies together before leaving it to vibrate freely. In the last step, a positive position feedback (PPF) controller is proposed and implemented to suppress the free beam vibrations at its tip. Results have shown that the PPF controller has reduced the tip vibration to the lowest level possible.