Harmonic Balance-Based Approach for Quasi-Periodic Motions and Stability Analysis

Guskov, Mikhaïl; Thouverez, Fabrice

doi:10.1115/1.4005823

Cited by 63 publications

(30 citation statements)

References 24 publications

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“…where k 1 and k 2 are integers, representing the harmonic coefficients. The total quasi-periodic response of the rotor-bearing system can then be approximated by [51]:…”

Section: Generalised Harmonic Balance Methodsmentioning

confidence: 99%

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A parametric study of an unbalanced Jeffcott rotor supported by a rolling-element bearing

2020

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Rolling-element bearings are widely used in industrial rotating machines, and hence there is a strong need to accurately predict their influence on the response of such systems. However, this can be challenging due to an interaction between the dynamics of the rotor and the bearing nonlinearities, and it becomes difficult to provide a physical explanation for the nonlinear response. A novel approach, combining a Jeffcott rotor supported by a detailed bearing model with the generalised harmonic balance method, is presented, enabling an in-depth study of the complex rotor-stator interaction. This allows the quasi-periodic response of the rotor, due to variable compliance, to be captured, and the impact of clearance, ring and stator compliance, and centrifugal loading of the bearing on the response to be investigated. A strongly nonlinear response was observed due to the bearing, leading to large shifts in frequency as the excitation amplitude was increased, and the emergence of stable and unstable operating regions. The variable compliance effect generated sub-synchronous forcing, which led to sub-resonances when the ball pass frequency coincided with the frequency of one of the modes. Radial clearance in the bearing had by far the largest influence on

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“…where k 1 and k 2 are integers, representing the harmonic coefficients. The total quasi-periodic response of the rotor-bearing system can then be approximated by [51]:…”

Section: Generalised Harmonic Balance Methodsmentioning

confidence: 99%

“…In the GHBM, the set of frequencies specified by the set of integers P must be somehow truncated. There are several strategies for achieving this [51]. For this rotor-dynamic problem, the approach taken in [10] was used, since this includes the most frequencies so is the most thorough.…”

Section: Generalised Harmonic Balance Methodsmentioning

confidence: 99%

A parametric study of an unbalanced Jeffcott rotor supported by a rolling-element bearing

2020

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“…is not directly computed since displacement dependent nonlinear forces are, most of the times, defined in the time domain. Therefore, an alternating frequency-time (AFT) domain technique based on the hyper-time concept [27,28,30], as depicted in Fig. 1, is implemented.…”

Section: The Harmonic Balance Methodsmentioning

confidence: 99%

“…Without any additional information regarding the nonlinear forces f nl(x) , the vector of unknowns z can be reduced to roughly half of its original dimension due to the symmetry properties (odd/even) of the harmonic functions. In the literature, several different techniques have been suggested to decrease even more the dimension of z and, consequently, the computational efforts [27,31]. In this paper we are interested in localised vibrations induced by strong travelling wave responses.…”

Section: Harmonic Selectionmentioning

confidence: 99%

Computation of quasi-periodic localised vibrations in nonlinear cyclic and symmetric structures using harmonic balance methods

Fontanela

Grolet

Salles

et al. 2019

Journal of Sound and Vibration

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In this paper we develop a fully numerical approach to compute quasi-periodic vibrations bifurcating from nonlinear periodic states in cyclic and symmetric structures. The focus is on localised oscillations arising from modulationally unstable travelling waves induced by strong external excitations. The computational strategy is based on the periodic and quasi-periodic harmonic balance methods together with an arc-length continuation scheme. Due to the presence of multiple localised states, a new method to switch from periodic to quasi-periodic states is proposed. The algorithm is applied to two different minimal models for bladed disks vibrating in large amplitudes regimes. In the first case, each sector of the bladed disk is modelled by a single degree of freedom, while in the second application a second degree of freedom is included to account for the disk inertia. In both cases the algorithm has identified and tracked multiple quasi-periodic localised states travelling around the structure in the form of dissipative solitons.

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“…Therefore, hysteretic nonlinearities, such as dry friction, have to be re-formu-lated by incorporating appropriate internal variables into the set of differential equations, such that the phase space does no longer have a 'memory' [84]. Finally, it should be mentioned that for assessing the asymptotic stability of quasi-periodic motions, the Floquet stability theorem can be accordingly extended [55].…”

Section: Extension To Quasi-periodic Motionsmentioning

confidence: 99%

Vibration Prediction of Bladed Disks Coupled by Friction Joints

Krack

Salles

Thouverez

2016

Arch Computat Methods Eng

Self Cite

193

124

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The present review article addresses the vibration behavior of bladed disks encountered e. g. in aircraft engines as well as industrial gas and steam turbines. The utilization of the dissipative effects of dry friction in mechanical joints is a common means of the passive mitigation of structural vibrations caused by aeroelastic excitation mechanisms. The prediction of the vibration behavior is a scientific challenge due to (a) the strongly nonlinear and non-uniform contact interactions involving local sticking, sliding and liftoff, (b) topological complexity of the coupled structure, and (c) the multidisciplinary character of the problem associated with the need to account for structural mechanical as well as fluid dynamical effects. The purpose of this article is the overview and discussion the current state of the art of vibration prediction approaches. The modeling approaches in this work embrace the description of the rotating bladed disk, the contact modeling, the consideration of aeroelastic effects, appropriate model reduction techniques and the exploitation of the rotationally periodic nature of the problem. The simulation approaches cover the direct computation of periodic, steady-state externally forced and self-excited vibra

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Harmonic Balance-Based Approach for Quasi-Periodic Motions and Stability Analysis

Cited by 63 publications

References 24 publications

A parametric study of an unbalanced Jeffcott rotor supported by a rolling-element bearing

A parametric study of an unbalanced Jeffcott rotor supported by a rolling-element bearing

Computation of quasi-periodic localised vibrations in nonlinear cyclic and symmetric structures using harmonic balance methods

Vibration Prediction of Bladed Disks Coupled by Friction Joints

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