Single point vibration control for a passive piezoelectric Bernoulli-Euler beam subjected to spatially varying harmonic loads

Passive vibration control of flexible structures can be achieved by bonding piezoelectric layers with attached electric circuits onto an elastic substrate. In this work, a new concept, denoted as single point control (SPC), is presented in order to cancel harmonic vibrations of slender beams. It is shown by an extended version of the Bernoulli-Euler theory for passive smart beams that the deflection or the slope at a specified location along the beam axis is nullified if the electric circuit is tuned and the shape of the piezoelastic layers are properly shaped. The proposed method holds for harmonic loads only, but the spatial part of the distributed external load may be unknown. A three-dimensional electromechanically coupled FE-analysis with ANSYS confirms these results obtained by the one-dimensional theory. The practical relevance of the derived theory becomes evident if optimal resistive-inductive shunts are used. The robustness of passively controlled systems is strongly increased if the piezoelectric layers are shaped according to the presented SPC-theory instead of using spatially uniformly distributed layers.