Resonant inerter based vibration absorbers on flexible structures

• Published in: Journal of the Franklin Institute Vol. 356; no. 14; pp. 7704 - 7730
• Main Author: Krenk, Steen
• Format: Journal Article
• Language: English
• Published: Elmsford Elsevier Ltd 01.09.2019; Elsevier Science Ltd
• Subjects: Absorbers; Calibration; Coupling; Dampers; Damping; Flexibility; Flexible structures; Inertia; Parameters; Representations; Resonance; Stiffness; Vibration
• ISSN: 0016-0032; 1879-2693; 0016-0032
• DOI: 10.1016/j.jfranklin.2018.11.038

The paper presents an explicit two-step calibration procedure for tuned inerter based vibration absorbers on flexible structures. It makes use of a local approximate representation of the structural response to the device force, in which the contribution of the non-resonant modes is represented approximately around the resonance frequency by a background flexibility and a background inertia term. The calibration procedure then consists of two steps. The first step calibrates an equivalent vibration absorber including the background terms, and the second step subsequently evaluates the parameters of the actual device by extracting the background flexibility and inertia parameters. The first step represents the classic idealized single degree of freedom representation of the structure, whereas the second step leads to an increase of stiffness, inertia and damping parameters of the actual device due to background flexibility of the structure. The procedure is illustrated in detail for three inerter based vibration absorbers: parallel coupling of damper and stiffness, parallel coupling of damper and inerter, and finally a device with two dampers in parallel with stiffness and inerter elements, respectively. Explicit expressions for the calibration are obtained for each device, and it is demonstrated that the procedure leads to a balanced plateau of amplification around the resonance frequency of the magnitude assumed as the basis for the device parameter calibration.