Simple exact solutions for designing an optimal mechanical dynamic vibration absorber combined with a piezoelectric LR circuit based on the H∞, H2, or stability criterion

Abstract

Multiplexing dynamic vibration absorbers (DVAs) provide better vibration control compared to that obtained with single-mass DVAs; however, their structure is more complicated and they are 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 and its design formulas were derived. Such design formulas have been previously reported, but they are very long and impractical. In contrast, the proposed formulas are very simple and the optimal design conditions for a DVA can be easily obtained. The steady-state and free-vibration responses of a three-degree-of-freedom system with an optimized electromechanical DVA are compared with those of a vibratory system with a mechanical series-type double-mass DVA. It is confirmed that the electromechanical DVA exhibits exactly the same vibration suppression performance as that of the mechanical DVA.

Keywords

• dynamic vibration absorber
• formula manipulation
• piezoelectric shunt damper
• exact solution
• double-mass dynamic absorber
• h∞ optimization
• h2 optimization
• stability maximization