scholarly journals Resonance Suppression in Multi-Degree-of-Freedom Rotating Flexible Structures Using Order-Tuned Absorbers

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Serif Gozen ◽  
Brian J. Olson ◽  
Steven W. Shaw ◽  
Christophe Pierre
Keyword(s):  
Structural Model ◽  
Flexible Structures ◽  
Coupled System ◽  
Degree Of Freedom ◽  
Tuning Parameter ◽  
Vibration Absorbers ◽  
Resonance Zone ◽  
Engine Order ◽  
Rotating Structure ◽  
Structural Mode

This paper considers the dynamic response and order-tuning of vibration absorbers fitted to a rotating flexible structure under traveling wave (TW) engine order excitation. Of specific interest is the extension of previous results on the so-called no-resonance zone, that is, a region in linear tuning parameter space in which the coupled structure/absorber system does not experience resonance over all rotation speeds. The no-resonance feature was shown to exist for cyclic rotating structures with one structural and one absorber degree of freedom (DOF) per sector. This work uses a higher-fidelity structural model to investigate the effects of higher modes on the cyclically-coupled system. It is shown that the no-resonance zone is replaced by a resonance-suppression zone in which one structural mode is suppressed, but higher-order resonances still exist with the addition of the absorbers. The results are general in the sense that one vibration mode can be eliminated using a set of identically-tuned absorbers on a rotating structure with arbitrarily many DOFs per sector.

Resonance Suppression in Multi-DOF Rotating Flexible Structures Using Order-Tuned Absorbers

2009 ◽  
Author(s):  
Serif Gozen ◽  
Brian J. Olson ◽  
Steven W. Shaw ◽  
Christophe Pierre
Keyword(s):  
Structural Model ◽  
Vibration Mode ◽  
Flexible Structures ◽  
Coupled System ◽  
Tuning Parameter ◽  
Vibration Absorbers ◽  
Resonance Zone ◽  
Engine Order ◽  
Rotating Structure ◽  
Structural Mode

This paper considers the dynamic response and order-tuning of vibration absorbers fitted to a rotating flexible structure under traveling wave (TW) engine order excitation. Of specific interest is the extension of previous results on the so-called no-resonance zone, that is, a region in linear tuning parameter space in which the coupled structure/absorber system does not experience resonance over all rotation speeds. The no-resonance feature was shown to exist for cyclic rotating structures with one structural and one absorber degree-of-freedom (DOF) per sector. This work uses a higher-fidelity structural model to investigate the effects of higher modes on the cyclically-coupled system. It is shown that the no-resonance zone is replaced by a resonance-suppression zone in which one structural mode is suppressed, but higher-order resonances still exist with the addition of the absorbers. The results are general, in the sense that one vibration mode can be eliminated using a set of identically-tuned absorbers on a rotating structure with arbitrarily many DOFs per sector.

Order-Tuned Vibration Absorbers for Cyclic Rotating Flexible Structures

2005 ◽  
Author(s):  
Brian J. Olson ◽  
Steve W. Shaw ◽  
Christophe Pierre
Keyword(s):  
Equations Of Motion ◽  
Flexible Structures ◽  
Closed Form Solution ◽  
Nonlinear Effects ◽  
Form Solution ◽  
Vibration Absorbers ◽  
Bladed Disk ◽  
Tuned Vibration Absorbers ◽  
Engine Order ◽  
Bladed Disk Assembly

This paper investigates the use of order-tuned absorbers to attenuate vibrations of flexible blades in a bladed disk assembly subjected to engine order excitation. The blades are modeled by a cyclic chain of N oscillators, and a single vibration absorber is fitted to each blade. These absorbers exploit the centrifugal field arising from rotation so that they are tuned to a given order of rotation, rather than to a fixed frequency. A standard change of coordinates based on the cyclic symmetry of the system essentially decouples the governing equations of motion, yielding a closed form solution for the steady-state response of the overall system. These results show that optimal reduction of blade vibrations is achieved by tuning the absorbers to the excitation order n, but that the resulting system is highly sensitive to small perturbations. Intentional detuning (meaning that the absorbers are slightly over- or under-tuned relative to n) can be implemented to improve the robustness of the design. It is shown that by slightly undertuning the absorbers there are no system resonances near the excitation order of interest and that the resulting system is robust to mistuning (i.e., small random uncertainties in the system parameters) of the absorbers and/or blades. These results offer a basic understanding of the dynamics of a bladed disk assembly fitted with order-tuned vibration absorbers, and serve as a first step to the investigation of more realistic models, where, for example, imperfections and nonlinear effects are considered, and multi-DOF and general-path absorbers are employed.

Accounting for Roller Dynamics in the Design of Bifilar Torsional Vibration Absorbers

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
Ryan J. Monroe ◽  
Steven W. Shaw ◽  
Alan H. Haddow ◽  
Bruce K. Geist
Keyword(s):  
Finite Amplitude ◽  
Tuning Parameter ◽  
System Response ◽  
Vibration Absorbers ◽  
Engine Order ◽  
Constant Rate ◽  
Centrifugal Pendulum Vibration Absorbers ◽  
Roller System ◽  
First Time ◽  
Selection Of

Centrifugal pendulum vibration absorbers are used for reducing engine-order torsional vibrations in rotating machines. The most common configuration of these devices utilizes a bifilar suspension in which the absorber mass is suspended by a pair of cylindrical rollers that allow it to move along a prescribed path that is determined by the shape of machined cutouts on the rotor and the absorber mass. Previous studies have considered how to account for the roller inertia in selecting the linear (small amplitude) tuning characteristics of the absorber system. Here, we describe a systematic study of the nonlinear (finite amplitude) aspects of this system and show that there exists an absorber path for which the absorber/roller system maintains the same frequency of free oscillation over all physically possible amplitudes when the rotor spins at a constant rate. This tautochronic path has been well known for the case with zero roller inertia, and herein, for the first time, the corresponding path with rollers is shown to exist, and a method for its construction is presented. In addition, we carry out a perturbation analysis of the steady-state dynamic response of the rotor/absorber/roller system in order to quantify the effects of various approximations commonly used with regard to the roller dynamics. The results show that if one accounts for the rollers in the linear absorber tuning, the nonlinear system response is essentially insensitive to the selection of the nonlinear tuning parameter, so long as it is close to the tautochronic value.

Fractal Boundary Explorations for a Nonlinear Two Degree-of-Freedom System

2012 ◽  
Author(s):  
Benjamin A. M. Owens ◽  
Brian P. Mann
Keyword(s):  
Initial Conditions ◽  
Coupled System ◽  
Basins Of Attraction ◽  
Degree Of Freedom ◽  
Fractal Boundary ◽  
Final State ◽  
Potential Wells ◽  
Mechanical Coupling ◽  
Mass Spring ◽  
Two Degree Of Freedom

This paper explores a two degree-of-freedom nonlinearly coupled system with two distinct potential wells. The system consists of a pair of linear mass-spring-dampers with a non-linear, mechanical coupling between them. This nonlinearity creates fractal boundaries for basins of attraction and forced well-escape response. The inherent uncertainty of these fractal boundaries is quantified for errors in the initial conditions and parameter space. This uncertainty relationship provides a measure of the final state and transient sensitivity of the system.

SOFTENING BRANCHES OF A TWO-DEGREE-OF-FREEDOM SYSTEM INDUCED BY SPATIAL BUCKLING

2006 ◽  
Vol 06 (04) ◽  
pp. 493-512 ◽  
Author(s):  
NOËL CHALLAMEL
Keyword(s):  
Structural Model ◽  
Structural Parameters ◽  
Degree Of Freedom ◽  
Lateral Loading ◽  
Load Parameter ◽  
Imperfection Sensitivity ◽  
Softening Effect ◽  
Out Of Plane ◽  
Secondary Bifurcation ◽  
Two Degree Of Freedom

The aim of this paper is to show how geometrical non-linearity may induce equivalent softening in a simple two-degree-of-freedom spatial elastic system. The generic structural model studied is a generalization of Augusti's spatial model, incorporating lateral loading. This model could be used as a teaching model to understand the softening effect induced by out-of-plane buckling. The lateral loading in the plane of maximal stiffness is considered as the varying load parameter, whereas the vertical load is perceived as a constant parameter. It is shown that a bifurcation occurs at the critical horizontal load. The fundamental path becomes unstable, beyond this critical value. However, two symmetrical bifurcate solutions appear, whose stability depend on the structural parameters value. No secondary bifurcation is observed for this system. The presented system possesses imperfection sensitivity, and imperfection insensitivity, depending on the values of the structural parameters. In any case, for sufficiently large rotations, collapse occurs with unstable softening branches induced by spatial buckling.

Daily Labor Supply and Adaptive Reference Points

2021 ◽  
Vol 111 (8) ◽  
pp. 2417-2443
Author(s):  
Neil Thakral ◽  
Linh T. Tô
Keyword(s):  
Labor Supply ◽  
Reference Point ◽  
Structural Model ◽  
Reference Points ◽  
Degree Of Freedom ◽  
Reference Dependence ◽  
Field Evidence ◽  
Dynamic View ◽  
Expected Earnings ◽  
Dependence Models

This paper provides field evidence on how reference points adjust, a degree of freedom in reference-dependence models. Examining this in the context of cabdrivers’ daily labor-supply behavior, we ask how the within-day timing of earnings affects decisions. Drivers work less in response to higher accumulated income, with a strong effect for recent earnings that gradually diminishes for earlier earnings. We estimate a structural model in which drivers work toward a reference point that adjusts to deviations from expected earnings with a lag. This dynamic view of reference dependence reconciles conflicting “neoclassical” and “behavioral” interpretations of evidence on daily labor-supply decisions. (JEL J22, J31, L94)

On Degeneracy of Eigenvalues and Recursive Solution of Symmetrically Coupled Dynamic Systems

1970 ◽  
Vol 37 (4) ◽  
pp. 1180-1182
Author(s):  
Fan Y. Chen
Keyword(s):  
Dynamic Systems ◽  
Coupled System ◽  
Circulant Matrix ◽  
Mathematical Induction ◽  
Degree Of Freedom ◽  
Recursive Solution ◽  
Direct Inspection

Based on mathematical induction, we can prove that the eigenvalues of a special nth order circulant matrix are degenerate. Hence the eigenvibration problem of an n degree-of-freedom symmetrically coupled system with equal masses and equal spring stiffnesses can be solved by direct inspection of the system schematic.

Investigation of Flow Distortion Generated Forced Response of a Radial Turbine with Vaneless Volute

2020 ◽  
Vol 37 (2) ◽  
pp. 141-151
Author(s):  
Zhi Huang ◽  
Chaochen Ma ◽  
Hong Zhang
Keyword(s):  
Structural Model ◽  
Turbine Rotor ◽  
Forced Response ◽  
Superposition Method ◽  
Flow Distortion ◽  
Fourier Decomposition ◽  
Mode Superposition Method ◽  
Radial Turbine ◽  
Engine Order ◽  
Computational Structural Dynamics

AbstractFor a radial turbine with vaneless volute, the inflow of turbine rotor usually has a circumferential flow distortion due to the influence of the volute tongue. The rotating blades of the rotor are exposed to harmonic aerodynamic loads caused by the distortion, which may induce rotor resonance and lead to high cycle failures (HCF). To understand the forced response mechanism clearly, a numerical analysis was carried out based on a fluid structure interaction (FSI) method. The pressure functions were extracted from the results of a computational fluid dynamics (CFD) analysis by Fourier decomposition. The first three harmonic pressures were identified as the primary engine order (EO) excitations and imposed on the structural model for computational structural dynamics (CSD) simulation. The quantification and assessment of the rotor response were attained by mode superposition method. The simulation results are shown to be consistent with the predictions of Singh’s advanced frequency evaluation (SAFE) diagram.

Parametric Vibration of a Flexible Structure Excited by Periodic Passage of Moving Oscillators

2020 ◽  
Vol 87 (7) ◽  
Author(s):  
Hao Gao ◽  
Bingen Yang
Keyword(s):  
Dynamic Stability ◽  
Parametric Resonance ◽  
Flexible Structures ◽  
Coupled System ◽  
Analytical Form ◽  
Stability Criteria ◽  
Analysis Method ◽  
State Equations ◽  
Supporting Structure ◽  
Moving Oscillator

Abstract Flexible structures carrying moving subsystems are found in various engineering applications. Periodic passage of subsystems over a supporting structure can induce parametric resonance, causing vibration with ever-increasing amplitude in the structure. Instead of its engineering implications, parametric excitation of a structure with sequentially passing oscillators has not been well addressed. The dynamic stability in such a moving-oscillator problem, due to viscoelastic coupling between the supporting structure and moving oscillators, is different from that in a moving-mass problem. In this paper, parametric resonance of coupled structure-moving oscillator systems is thoroughly examined, and a new stability analysis method is proposed. In the development, a set of sequential state equations is first derived, leading to a model for structures carrying a sequence of moving oscillators. Through the introduction of a mapping matrix, a set of stability criteria on parametric resonance is then established. Being of analytical form, these criteria can accurately and efficiently predict the dynamic stability of a coupled structure-moving oscillator system. In addition, by the spectral radius of the mapping matrix, the global stability of a coupled system can be conveniently investigated in a parameter space. The system model and stability criteria are illustrated and validated in numerical examples.

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