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Research Papers

Real-Time Tuning of Delayed Resonator-Based Absorbers for Spectral and Spatial Variations

[+] Author and Article Information
Ryan Jenkins

Department of Mechanical Engineering,
University of Connecticut,
Storrs, CT 06269-3139
e-mail: ryan.jenkins@uconn.edu

Nejat Olgac

Department of Mechanical Engineering,
University of Connecticut,
Storrs, CT 06269-3139
e-mail: olgac@engr.uconn.edu

1Corresponding author.

2In Ref. [10], the term “noncollocated” refers to the sensor and actuator being placed at separate locations. It is important to note that this lexicon is commonly found in the literature but differs from our usage, in which the absorber (including the sensor-actuator pair) is at a location other than the point of suppression.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received February 27, 2018; final manuscript received September 19, 2018; published online November 14, 2018. Assoc. Editor: Lei Zuo.

J. Vib. Acoust 141(2), 021011 (Nov 14, 2018) (9 pages) Paper No: VIB-18-1085; doi: 10.1115/1.4041592 History: Received February 27, 2018; Revised September 19, 2018

This paper offers two interlinked contributions in the field of vibration absorption. The first involves an active tuning of an absorber for spectral and spatial variations. The second contribution is a set of generalized design guidelines for such absorber operations. “Spectral” tuning handles time-varying excitation frequencies, while “spatial” tuning treats the real-time variations in the desired location of suppression. Both objectives, however, must be achieved using active control and without physically altering the system components to ensure practicality. Spatial tuning is inspired by the concept of “noncollocated vibration absorption,” for which the absorber location is different from the point of suppression. This concept is relatively under-developed in the literature, mainly because it requires the use of part of the primary structure (PS) as the extended absorber—a delicate operation. Within this investigation, we employ the delayed resonator (DR)-based absorber, a hybrid concept with passive and active elements, to satisfy both tuning objectives. The presence of active control in the absorber necessitates an intriguing stability investigation of a time-delayed dynamics. For this subtask, we follow the well-established methods of frequency sweeping and D-subdivision. Example cases are also presented to corroborate our findings.

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Figures

Grahic Jump Location
Fig. 1

The DR attached to a single degree-of-freedom (DOF) PS

Grahic Jump Location
Fig. 2

Five degrees-of-freedom PS with DR mounted on m2

Grahic Jump Location
Fig. 3

The stability map showing curves for the DR tuned to m4 suppression superposed with the CS stability curves. Stable DR-tuning segments A1A2¯, B1B2¯, etc. are labeled along with the operating point P1. Stable regions are shaded. The number of unstable roots (NU) for CS is also marked in some regions.

Grahic Jump Location
Fig. 4

Case 1: The vibration absorber is passive until t = 40 s when the DR tuning is activated to P1. Harmonic excitation is applied to m5. The percentage change in amplitude between passive and active zones is also denoted.

Grahic Jump Location
Fig. 5

The CS stability map superposed with the tuning curves for S1 (case 2). Stable operating zones F1F2¯, G1G2¯, etc. are labeled along with the selected control scheme P2. Stable regions are shaded. Some NU are given for CS.

Grahic Jump Location
Fig. 6

Case 2: The vibration absorber is passive until t = 40 s when the DR tuning is activated to P2 (Fig. 5). Harmonic excitation is applied to m5. The percentage change in amplitude between passive and active zones is also denoted.

Grahic Jump Location
Fig. 7

Case 3: Violation of Theorem 1 occurs by aiming to suppress m5 oscillations while fe is applied to m3, which is within the resonant substructure. Vibration suppression is unsuccessful. The vibration absorber is passive until t = 40 s, at which time the DR tuning is activated to P2 (Fig. 5).

Grahic Jump Location
Fig. 8

Case 4: Simulation of (a) x4, (b) x5 for demonstration of simultaneous spectral and spatial tuning

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