Piezoelectric-shunt-based approach for multi-mode adaptive tuned mass dampers

This paper deals with the design and development of a multi-frequency adaptive tuned mass damper based on a cantilever beam equipped with shunted piezoelectric elements. It is demonstrated that the device is able to independently shift a number of eigenfrequencies equal to the number of piezoelectric elements and that the use of negative capacitances is able to strongly improve the adaptation capability of the device. Mathematical formulations are provided for linking the values of the capacitances used for shunting the piezoelectric elements and the resulting shifts of the eigenfrequencies, and vice versa. Furthermore, being the negative capacitances based on operational amplifiers, the stability of the electro-mechanical system is investigated, giving rules about the tuning of these negative capacitances. The resulting adaptive tuned mass damper can be fruitfully employed for lowering vibrations of a primary system whose eigenfrequencies undergo different frequency shifts, improving the robustness to possible mistuning of non-adaptive classical tuned mass dampers. All the theoretical outcomes are validated through an experimental campaign with a cantilever beam equipped with two piezoelectric patches.