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.

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.

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.

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.

Suppressing Wind-Induced Oscillations of Prismatic Structures by Dynamic Vibration Absorbers

2017 ◽  
Vol 17 (06) ◽  
pp. 1750056 ◽  
Author(s):  
W. B. Liu ◽  
H. L. Dai ◽  
L. Wang
Keyword(s):  
Equations Of Motion ◽  
Oscillation Amplitude ◽  
Coupled System ◽  
Vibration Absorbers ◽  
Governing Equations ◽  
Dynamic Coupling ◽  
Dynamic Vibration Absorber ◽  
Dynamic Vibration ◽  
Linear Damping ◽  
Dynamic Vibration Absorbers

The suppression of oscillations of an elastically mounted prism under galloping by a dynamic vibration absorber (DVA) with linear damping and stiffness is investigated. A model considering the dynamic coupling of the prism and the DVA is constructed, with the aerodynamic loads acting on the system represented by a quasi-steady approximation. Based on the coupled nonlinear governing equations of motion, a linear analysis is first conducted to explore the coupled frequency and damping, and the onset speed of galloping in the presence of the DVA. Subsequently, the normal form of the Hopf bifurcation for the coupled system near the onset of galloping is derived to characterize the type of instability (supercritical or subcritical), while evaluating the effects of the DVA parameters. The results show that with appropriate parametric values, the DVA has great impact on the onset speed of galloping and can significantly alleviate the oscillation amplitude of the prism.

An active vibration control model for coupled flexible systems

2008 ◽  
Vol 222 (11) ◽  
pp. 2087-2098
Author(s):  
J C Niu ◽  
A Y T Leung ◽  
C W Lim ◽  
P Q Ge
Keyword(s):  
Optimal Control ◽  
Vibration Control ◽  
State Space ◽  
Power Flow ◽  
Passive Control ◽  
Flexible Structures ◽  
Coupled System ◽  
The State ◽  
Coupled Systems ◽  
Control Force

This paper presents a novel general model for complex flexible coupled systems. In this model, parallel structures of force actuators and passive spring isolators are installed between the machine and the foundation, and some moment actuators such as piezoelectric patches are installed on the flexible foundation whose vibration cancellation feature is the key object of vibration control. This model combines active and passive control, force and moment control into a single unit to achieve the efficient vibration control of flexible structures by multiple approaches. The state-space governing equations of the coupled system are deduced. Based on the description of the state-space equation of the coupled system, the transmission paths for the power flow transmitted into the foundation are discussed in the frequency domain, and then combined into a single function. The function includes two parts: the passive and active terms, which can be conveniently employed in an optimal control strategy to achieve power flow control. The transmission characteristics of the power flow by optimal control are discussed in detail. Numerical simulations are presented to show that both force and moment controls in the analytical model can achieve substantial vibration cancellation.

The Effects of Gravity on the Response of Centrifugal Pendulum Vibration Absorbers

2021 ◽  
pp. 1-61
Author(s):  
Darryl Tchokogoue ◽  
Ming Mu ◽  
Brian F. Feeny ◽  
Bruce K. Geist ◽  
Steven W. Shaw
Keyword(s):  
Equations Of Motion ◽  
Operating Conditions ◽  
Vibration Absorbers ◽  
Cyclic Symmetry ◽  
Passive Devices ◽  
Engine Order ◽  
Gravity Effects ◽  
Centrifugal Pendulum Vibration Absorbers ◽  
Automotive Powertrain ◽  
Linearized Model

Abstract This paper describes the effects of gravity on the response of systems of identical, cyclically arranged, centrifugal pendulum vibration absorbers (CPVAs). CPVAs are passive devices composed of movable masses suspended on a rotor, suspended such that they reduce torsional vibrations at a given engine order. These absorbers are becoming prevalent in automotive powertrain components in order to expand fuel-efficient engine operating conditions. Gravitational effects acting on the absorbers can be important for a horizontal rotor/CPVA system spinning at relatively low rotation speeds, for example, during engine idle conditions. The main goal of this investigation is to predict the response of a CPVA/rotor system in the presence of gravity. A linearized model which includes the effects of gravity and an order n torque acting on the rotor is analyzed by exploiting the cyclic symmetry of the system. The results show that the N absorbers respond in one or more groups, where the absorbers in each group respond with identical waveforms but shifted phases. The number of groups depends on the engine order n and the ratio Nn. It is shown that there are special resonant effects if the engine order is n = 1 or n = 2, the latter of which is particularly important in applications. In addition, it is shown that for N > 1 the rotor response is not affected by gravity, due to the symmetry of the gravity effects. The analytical predictions are verified by direct simulations of the equations of motion.

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