Vibration Absorbers for Cyclic Rotating Flexible Structures: Linear and Nonlinear Tuning

Abstract

The nonlinear performance of centrifugally-driven, order-tuned absorbers is investigated for vibration reduction of a cyclic rotating flexible structure under traveling wave (TW) engine order excitation. A key finding from previous work by the authors using a linearized model is the existence of a no-resonance zone, that is, an entire range of absorber designs that avoid system resonance for any rotation speed. Linearization is generally valid for the rotating structure but absorber motions can become large for typical loading conditions. This work generalizes the linear results to account for large-amplitude, nonlinear absorber motions. Existence and stability of the steady-state TW response to TW excitation are investigated in terms of the absorber path design, which fixes its linear and nonlinear tuning characteristics. A TW response is unique for the linearized system and is shown to exist for the weakly nonlinear model. The nonlinear model exhibits the usual characteristics of a weakly nonlinear system, including bistability and the attendant hysteresis near resonance. More significantly, no additional instabilities associated with the symmetry could be identified. Hence the desired TW response is robust to nonlinear absorber effects and can be described by an equivalent model, which is obtained by reduction using the symmetry. It is shown that good performance can be obtained by linear absorber tuning in the no-resonance zone and the absorber paths should have a slightly softening nonlinear characteristic.

Vibration absorbers for a rotating flexible structure with cyclic symmetry: nonlinear path design

“…This work investigates whether or not the desirable response features predicted by the linear theory persist when absorber amplitudes become large. The full details of the theory are presented here; see [21] for a summary of the main results.…”

“…These absorbers, which essentially consist of masses that move along prescribed paths relative to the structure [6], have the advantage that they remain tuned over all rotation speeds. Order-tuned absorbers have been widely studied and employed for reducing torsional vibrations in rotating systems [7][8][9][10][11][12][13][14][15][16][17], and more recently they have been proposed for reducing flexural vibrations in rotating systems [2,5,6,[18][19][20][21]. Recent studies have also included impacting dynamics of single flexible elements with absorbers, which will occur if loading becomes large [6,19].…”

“…A result of particular interest is the existence of the "no-resonance zone", that is, a range of linear absorber tuning values that completely avoids system resonances over all rotation speeds [2,5]. Systems fitted with absorbers tuned within this generally small, but finite parameter range experience steadystate responses with highly desirable features, according to linear analysis.…”

“…Several references to work on linear vibrations of cyclic systems are provided in [5]. Nonlinear vibrations of cyclic systems, including the response to standing and traveling wave (TW) excitation, nonlinear localized responses, and so on, have been considered in works by Vakakis, Bajaj, and coworkers [22][23][24][25][26][27][28][29].…”

“…Typical vibration absorbers utilize elastic elements and are thereby tuned to a particular frequency [4]. In contrast, order-tuned absorbers make use of the centrifugal field of the rotating system and are tuned to a given order of rotation [5][6][7]. These absorbers, which essentially consist of masses that move along prescribed paths relative to the structure [6], have the advantage that they remain tuned over all rotation speeds.…”