Simple exact solutions for designing an optimal mechanical dynamic vibration absorber combined with a piezoelectric LR circuit based on the H∞ criterion

Multiplexing dynamic vibration absorbers (DVAs) provide better vibration control compared to that obtained with single-mass DVAs; however, their structure is more complicated and thus difficult to apply in practice. This paper proposes several optimal design formulas for an electromechanical DVA in which a mechanical single-mass DVA with a piezoelectric element between the primary and absorber masses and a series LR circuit is coupled to the element. The inductor and piezoelectric element act as a virtual mass and a virtual spring, respectively, and thus the circuit works as a kind of double-mass DVA. In the present study, such an electromechanical DVA was optimized based on three design criteria (H∞, H2, and stability criteria) and its simple design formulas were derived.