Localization Phenomena in Mistuned Assemblies with Cyclic Symmetry Part I: Free Vibrations

1988 ◽  
Vol 110 (4) ◽  
pp. 429-438 ◽  
Author(s):  
S.-T. Wei ◽  
C. Pierre
Keyword(s):  
Periodic Structures ◽  
Coupled System ◽  
Companion Paper ◽  
Free Vibrations ◽  
Forced Response ◽  
Cyclic Symmetry ◽  
Coupling Ratio ◽  
Mode Localization ◽  
Weakly Coupled ◽  
Weakly Coupled System

An investigation of the effects of small structural irregularities on the dynamics of nearly periodic structures with cyclic symmetry is presented. The system studied may be regarded as a simple model of a continuously shrouded blade assembly accounting for one structural mode per blade. A key aspect of the approach is the use of perturbation methods that lead to a physical insight into the effects of mistuning. The study shows that the sensitivity to mistuning depends primarily upon the ratio of mistuning strength to coupling strength. For a small mistuning to coupling ratio, the mistuned system behaves like a perturbation of the corresponding tuned system, in which case mistuning has a relatively small effect on both the free and forced responses. On the other hand, for a large mistuning to coupling ratio (i.e., weak coupling), the mistuned system behaves like a perturbation of the corresponding decoupled mistuned system, in which case small mistuning dramatically changes the dynamics of the system. This paper, Part I, investigates the effects of small mistuning on the free response of the system. Specifically, it is shown that strong mode localization and eigenvalue loci veering phenomena occur in the weakly coupled system when mistuning is introduced. The effects of mistuning on the forced response are studied in the companion paper, Part II (Wei and Pierre, 1987).

Localization Phenomena in Mistuned Assemblies with Cyclic Symmetry Part II: Forced Vibrations

1988 ◽  
Vol 110 (4) ◽  
pp. 439-449 ◽  
Author(s):  
S.-T. Wei ◽  
C. Pierre
Keyword(s):  
Periodic Structures ◽  
Forced Vibrations ◽  
Forced Response ◽  
Coupled Systems ◽  
Force Model ◽  
Cyclic Symmetry ◽  
Important Conclusion ◽  
Weakly Coupled ◽  
Weakly Coupled Systems ◽  
Internal Coupling

The effects of disorder on the forced response of nearly periodic structures with cyclic symmetry are investigated. The force model adopted here is relevant to blade assemblies. Perturbation methods for the forced response are developed to gain a physical insight into the effects of mistuning. The study shows that the internal coupling between component systems is the key parameter governing the sensitivity to mistuning and that localized forced vibrations do occur in the disordered assembly for weak internal coupling. However, although both localized free and forced vibrations occur for finite or large values of the mistuning to coupling ratio, the deflection patterns for these two types of localized vibrations are different. Also, for the forced response, the degree of localization does not necessarily increase as this ratio increases—a fundamental difference from localized free modes. An important conclusion is that the common periodicity assumption for cyclic structures may lead to qualitative errors for the forced response of weakly coupled systems when small mistuning is present.

Geometric Mistuning Reduced-Order Model Development Utilizing Bayesian Surrogate Models for Component Mode Calculations

2019 ◽  
Vol 141 (10) ◽  
Author(s):  
Joseph A. Beck ◽  
Jeffrey M. Brown ◽  
Alex A. Kaszynski ◽  
Emily B. Carper ◽  
Daniel L. Gillaugh
Keyword(s):  
Periodic Structures ◽  
Model Development ◽  
Element Model ◽  
Forced Response ◽  
Mode Shapes ◽  
Order Model ◽  
Mode Localization ◽  
Reduced Order ◽  
Structural Periodicity ◽  
Computationally Intensive

AbstractIntegrally bladed rotors (IBRs) are meant to be rotationally periodic structures. However, unique variations in geometries and material properties from sector-to-sector, called mistuning, destroy the structural periodicity. This results in mode localization that can induce forced response levels greater than what is predicted with a tuned analysis. Furthermore, mistuning and mode localization are random processes that require stochastic treatments when analyzing the distribution of fleet responses. Generating this distribution can be computationally intensive when using the full finite element model (FEM). To overcome this expense, reduced-order models (ROMs) have been developed to accommodate fast calculations of mistuned forced response levels for a fleet of random IBRs. Usually, ROMs can be classified by two main families: frequency-based and geometry-based methods. Frequency-based ROMs assume mode shapes do not change due to mistuning. However, this assumption has been shown to cause errors that propagate to the fleet distribution. To circumvent these errors, geometry-based ROMs have been developed to provide accurate predictions. However, these methods require recalculating modal data during ROM formulations. This increases the computational expense in computing fleet distributions. A new geometry-based ROM is presented to reduce this cost. The developed ROM utilizes a Bayesian surrogate model in place of sector modal calculations required in ROM formulations. The method, surrogate modal analysis for geometry mistuning assessments (SMAGMA), will propagate uncertainties of the surrogate prediction to forced response. ROM accuracies are compared to the true forced response levels and results computed by a frequency-based ROM.

Alternate Mistuning of Turbine Bladings Coupled by Underplatform Dampers

2012 ◽  
Author(s):  
S. Tatzko ◽  
L. Panning-von Scheidt ◽  
J. Wallaschek ◽  
A. Kayser
Keyword(s):  
Turbine Blades ◽  
Steady State Solution ◽  
Computational Effort ◽  
Forced Response ◽  
Nonlinear Coupling ◽  
Cyclic Symmetry ◽  
Periodic Excitation ◽  
Blade Vibration ◽  
Mode Localization ◽  
Bladed Disk

In turbo machinery design it is important to avoid vibrations that can destroy the turbine in the last resort. The rotating structure is exposed to periodic excitation forces. Two main types of periodic excitation can be distinguished. Flutter is the effect when mass flow forces couple with a natural vibration mode. The result is a negative damping coefficient and amplitudes will rise up to malfunction of the structure. The engine order excitation is a periodic excitation where the force signal is directly related to the speed of the rotor. A forced response calculation gives information about the blade vibration. Nonlinear coupling, i.e. friction coupling, between blades is used to increase damping of the bladed disk. Dynamic analysis of turbine blades with nonlinear coupling is a complex task and computer simulations are inevitable. Various techniques have been developed to reduce computational effort. The cyclic symmetry approach assumes each blade around the disk to be identical. Thus only one sector of the disk is sufficient to compute the steady state solution of the whole turbine blading. However, it has been observed that mistuning of blades reduces the flutter instability. On the other hand statistical mistuning can lead to dangerously high forced response amplitudes due to mode localization. A compromise is intentional mistuning. The simplest approach is alternate mistuning with every other blade exhibiting identical mechanical properties. This work explains in detail how a turbine bladed disk can be modeled when alternate mistuning is applied intentionally. Cyclic symmetry is used and each sector comprises two blades. This untypical choice of the sector size has significant impact on results of a cyclic modal analysis. Simulation results show the influence of alternate mistuned turbine bladings which are coupled by underplatform damper elements.

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