# Equal damping calibration of a hybrid mechanical-piezoelectric vibration absorber

**At LMSSC, Paris, July 8th 2021, 1.30 p.m.**

Jan HÃ¸gsberg

Associate Professor, Solid Mechanics, Department of Mechanical Engineering,

Technical University of Denmark (DTU), Kongens Lyngby, Denmark

Vibration absorbers or tuned mass dampers are effective devices for mitigation of resonant vibrations in flexible structures. The absorber stiffness is initially calibrated to optimally synchronize the absorber with the structure's dominant resonance, while the absorber damping is subsequently adjusted to achieve sufficient energy dissipation and/or desired response mitigation.

When attaching a vibration absorber targeted to a specific structural vibration form, this form will split into two modes with frequencies below and above the natural frequency. For the classic tuned mass damper, it has been shown that optimal tuning relies on achieving equal damping in the two split modes. This equal modal damping concept is independent of the specific loading on the structure and thus entirely governed by the properties of the underlying characteristic equation for the damped structure.

The presentation demonstrates how the equal modal damping concept can be applied to a more complicated vibration problem, in which a resonantly shunted piezoelectric transducer is included in the classic mechanical tuned mass damper, resulting in an augmented absorber with two resonances. It is demonstrated how the absorber stiffness parameters can initially be tuned to secure the desired equal modal damping, while the single damping coefficient can then be chosen by a parameter optimization to attain nearly optimal response mitigation.

The present theory for the hybrid absorber has been further used to design both a double-inductive shunt for piezoelectric vibration damping and a smart pendulum absorber for offshore wind turbine applications.