A Continuum Mechanics Approach for Smart Beams: Applications

This paper concerns the control of flexural vibrations in smart beams subject to external and inertial forces. Exemplarily, a flexible beam with integrated piezoelectric actuators is considered. The equations of motion are derived within the framework of Bernoulli-Euler beam theory considering arbitrary large rigid-body motions with super-imposed small elastic deformations. From the equations of motion the shape control solution is derived, i.e. the necessary distribution of actuation strains is computed in order to completely compensate the flexible vibrations of the beam. This shape control solution represents a feed-forward control strategy. Additionally, a feedback control algorithm is implemented in order to compensate the remaining vibrations. Experimental results for an aluminium beam of rectangular cross-section with a number of 18 piezoelectric patches are presented, showing a significant reduction of the flexible vibrations with the help of the implemented control algorithm.