Статті в журналах: "Structural mistuning"

1

Wei, S. T., and C. Pierre. "Localization Phenomena in Mistuned Assemblies with Cyclic Symmetry Part I: Free Vibrations." Journal of Vibration and Acoustics 110, no. 4 (October 1, 1988): 429–38. http://dx.doi.org/10.1115/1.3269547.

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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).

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2

Fu, Zhi Zhong, and Yan Rong Wang. "Mistuning and Structural Coupling Effects on Flutter of Turbomachinery Blades." Applied Mechanics and Materials 482 (December 2013): 311–14. http://dx.doi.org/10.4028/www.scientific.net/amm.482.311.

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A fast numerical method based on aeroelastic eigenvalue analysis is applied to study the effects of mistuning on the aeroelastic stability of turbomachinery blades in which the structural coupling is included by a simplified method and an influence coefficient method is employed to deal with the unsteady aerodynamic effects. Results show that there exists an optimal mistuning amount at which the system has the best aeroelastic stability. Structural coupling almost has no effects on aeroelastic stability of a tuned system. But the benefit of alternate frequency mistuning to aeroelastic stability is inhibited drastically when structural coupling is introduced into the bladed disk system.

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3

Kenyon, J. A., J. H. Griffin, and D. M. Feiner. "Maximum Bladed Disk Forced Response From Distortion of a Structural Mode." Journal of Turbomachinery 125, no. 2 (April 1, 2003): 352–63. http://dx.doi.org/10.1115/1.1540118.

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A method is presented for obtaining maximum bladed disk forced response from distortion of a structural mode. It is shown that maximum response from mode distortion in a bladed disk occurs when the harmonic components of a distorted mode superimpose in a certain manner, causing localization of the mode and strong response in a particular blade. In addition, it is shown that the response of an intentionally mistuned system with maximum response does not change significantly when small random mistuning is added to the system. A method is described for calculating the structural mistuning necessary to obtain the distorted mode that gives maximum response. The theory is validated numerically.

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4

Kenyon, J. A., and J. H. Griffin. "Forced Response of Turbine Engine Bladed Disks and Sensitivity to Harmonic Mistuning." Journal of Engineering for Gas Turbines and Power 125, no. 1 (December 27, 2002): 113–20. http://dx.doi.org/10.1115/1.1498269.

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The mistuned forced response of turbine engine bladed disks is treated using harmonic perturbations in the properties of a continuous ring. A continuous shear spring is attached to the ring in which the stiffness is allowed to vary along the ring annulus. The modes of such a structure with a single harmonic mistuning pattern are shown to obey the Mathieu equation, which is solved to obtain the natural frequencies and modes of the mistuned system. The forced response of the system is then examined to determine the sensitivity of the system to small mistuning. The model is extended to include multiple harmonics, allowing for the possibility of general mistuning. An expression for the maximum amplitude magnification due to small mistuning is developed by showing that high response is caused by distortion of the structural modes. A method to intentionally mistune systems for maximum forced response is demonstrated, and numerical results demonstrate the accuracy of the analytical prediction. The intentionally mistuned system response is shown to be robust with respect to small random mistuning. Such a result might be useful for designing a test rotor for screening new bladed disk designs or for establishing the root cause of fatigue problems.

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5

Mignolet, Marc P., Wei Hu, and Ioan Jadic. "On the Forced Response of Harmonically and Partially Mistuned Bladed Disks. Part I: Harmonic Mistuning." International Journal of Rotating Machinery 6, no. 1 (2000): 29–41. http://dx.doi.org/10.1155/s1023621x0000004x.

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This series of two papers focuses on the determination and clarification of the characteristics of the forced response of bladed disks that exhibit a mistuning pattern that is either harmonic or partial. Harmonic mistuning refers to single wavelength variations in structural properties along the disk while partial mistuning is associated with blade characteristics that are random in a specific sector and tuned elsewhere. The results of this analysis demonstrate that many features of the response of these simple systems match not only qualitatively but also quantitatively their counterparts on randomly mistuned bladed disks. Relying on these similarities, simple and reliable approximations of the localization factor and of the mean response are easily derived that exemplify the usefulness of harmonic and partial mistuning patterns. Finally, it is demonstrated both theoretically and by comparison with simulation results that the maximum amplitude of response of a disk closely follows a Weibull-type distribution in all coupling situations, from very weak to very strong.

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6

Mignolet, Marc P., Wei Hu, and Ioan Jadic. "On the Forced Response of Harmonically and Partially Mistuned Bladed Disks. Part II: Partial Mistuning and Applications." International Journal of Rotating Machinery 6, no. 1 (2000): 43–56. http://dx.doi.org/10.1155/s1023621x00000051.

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This series of two papers focuses on the determination and clarification of the characteristics of the forced response of bladed disks that exhibit a mistuning pattern that is either harmonic or partial. Harmonic mistuning refers to single wavelength variations in structural properties along the disk while partial mistuning is associated with blade characteristics that are random in a specific sector and tuned elsewhere. The results of this analysis demonstrate that many features of the response of these simple systems match not only qualitatively but also quantitatively their counterparts on randomly mistuned bladed disks. Relying on these similarities, simple and reliable approximations of the localization factor and of the mean response are easily derived that exemplify the usefulness of harmonic and partial mistuning patterns. Finally, it is demonstrated both theoretically and by comparison with simulation results that the maximum amplitude of response of a disk closely follows a Weibull-type distribution in all coupling situations, from very weak to very strong.

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7

Kan, Xuanen, and Tuo Xing. "A novel mathematical model for the design of the resonance mechanism of an intentional mistuning bladed disk system." Mechanical Sciences 13, no. 2 (December 20, 2022): 1031–37. http://dx.doi.org/10.5194/ms-13-1031-2022.

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Abstract. Bladed disk systems with advanced functions are widely used in turbo-machineries. However, there are always deviations in physical dynamic properties between blades and blades due to the tolerance and wear in operation. The deviations will lead to vibration localization, which will result in high cycle fatigue and accelerate the damage of the bladed disk system. Therefore, many intentional mistuning patterns are proposed to overcome this larger local vibration. Previous studies show that intentional mistuning patterns can be used to reduce the vibration localization of the bladed disk. However, the determination of the resonance mechanism of the intentional mistuning bladed disk system is still an unsolved issue. In this paper, a novel mathematical model of resonance of an intentional mistuning bladed disk system is established. Mistuning of blades and energy resonance are included in this theoretical model. The method of the mechanical power of the rotating blade for one cycle is applied to obtain the resonance condition. By using this theoretical model, the resonance mechanism of an intentional mistuning bladed disk is demonstrated. The results suggest that the ideal results can be obtained by adjusting the intentional mistuning parameter. This paper will guide the design of the dynamic characteristics of the intentional mistuning bladed disk.

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8

Lalanne, Bernard. "Perturbations Methods in Structural Dynamics and Applications to Cyclic Symmetric Domains." Journal of Engineering for Gas Turbines and Power 127, no. 3 (December 13, 2004): 654–62. http://dx.doi.org/10.1115/1.1924430.

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The design of components must take into account the irregularities inherent to the manufacturing process. When the structures have close eigenvalues, small mass and stiffness variations or the damping generate strong variations of the eigenmodes: these structures are then not robust. Here, their dynamics has been analyzed by perturbation method, in the dissipative cases and with coupling within a light fluid. A new perturbation method allows first order developments whatever the spectral density may be. Applications to many different vibration problems are presented: aeroelasticity, mode veering problem, maximum amplitude of forced response in cyclic symmetric domains, with detuning and/or mistuning, i.e., the most important reliability problem in turbomachinery. The results of this study provide a new estimation of the amplification factor and damping due to mistuning and aerodynamic coupling.

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9

Kenyon, J. A., and J. H. Griffin. "Experimental Demonstration of Maximum Mistuned Bladed Disk Forced Response." Journal of Turbomachinery 125, no. 4 (October 1, 2003): 673–81. http://dx.doi.org/10.1115/1.1624847.

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A theory was previously developed for predicting robust maximum forced response in mistuned bladed disks from distortion of a structural mode. This paper describes an experiment to demonstrate the theory. A bladed disk is designed to be sufficiently sensitive to mistuning to obtain maximum response. The maximum amplitude magnification from mistuning is predicted using the theory, 1.918. The bladed disk is intentionally mistuned to obtain the maximum response, and the response to an engine order traveling wave excitation is measured. The measured amplitude magnification is in close agreement with the theory. The robustness of the maximum response is demonstrated.

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10

Liu, Zhanhe, Jinlou Quan, Jingyuan Yang, Dan Su, and Weiwei Zhang. "A High Efficient Fluid-Structure Interaction Method for Flutter Analysis of Mistuned." Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 36, no. 5 (October 2018): 856–64. http://dx.doi.org/10.1051/jnwpu/20183650856.

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The time cost is very high by direct fluid-structure interaction method for mistuned bladed disk structures, so aerodynamic loads generally are ignored or treated as small perturbations in traditional flutter analysis. In order to analyze the flutter characteristics of mistuned blade rapidly and accurately, this paper presents an efficient fluid-structure interaction method based on aerodynamic reduced order model. system identification technology and two basic assumptions are used to build the unsteady aerodynamic reduced order model. Coupled the structural equations and the aerodynamic model in the state space, the flutter stability of mistuned bladed disk can be obtained by changing the structural parameters. For the STCF 4 example, the response calculated by this method agrees well with the results obtained by the direct CFD, but the computational efficiency is improved by nearly two orders of magnitude. This method is used to study the stiffness mistuned cascade system, and the stability characteristics of the system are obtained by calculating the eigenvalues of the aeroelastic matrix. The results show that the stiffness mistuning can significantly improve the flutter stability of the system, and also lead to the localization of the mode. The mistuning mode, mistuning amplitude and fluid structure interaction can influence the flutter stability obviously.

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11

Beirow, B., A. Kühhorn, F. Figaschewsky, P. Hönisch, T. Giersch, and S. Schrape. "Model update and validation of a mistuned high-pressure compressor blisk." Aeronautical Journal 123, no. 1260 (February 2019): 230–47. http://dx.doi.org/10.1017/aer.2018.149.

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ABSTRACTIn order to prepare an advanced 4-stage high-pressure compressor rig test campaign, details regarding both accomplishment and analysis of preliminary experiments are provided in this paper. The superior objective of the research project is to contribute to a reliable but simultaneously less conservative design of future high pressure blade integrated disks (blisk). It is planned to achieve trend-setting advances based on a close combination of both numerical and experimental analyses. The analyses are focused on the second rotor of this research compressor, which is the only one being manufactured as blisk. The comprehensive test program is addressing both surge and forced response analyses e.g. caused by low engine order excitation. Among others the interaction of aeroelastics and blade mistuning is demanding attention in this regard. That is why structural models are needed, allowing for an accurate forced response prediction close to reality. Furthermore, these models are required to support the assessment of blade tip timing (BTT) data gathered in the rig tests and strain gauge (s/g) data as well. To gain the maximum information regarding the correlation between BTT data, s/g-data and pressure gauge data, every blade of the second stage rotor (28 blades) is applied with s/g. However, it is well known that s/g on blades can contribute additional mistuning that had to be considered upon updating structural models.Due to the relevance of mistuning, efforts are made for its accurate experimental determination. Blade-by-blade impact tests according to a patented approach are used for this purpose. From the research point of view, it is most interesting to determine both the effect s/g-instrumentation and assembling the compressor stages on blade frequency mistuning. That is why experimental mistuning tests carried out immediately after manufacturing the blisk are repeated twice, namely, after s/g instrumentation and after assembling. To complete the pre-test program, the pure mechanical damping and modal damping ratios dependent on the ambient pressure are experimentally determined inside a pressure vessel. Subsequently the mistuning data gained before is used for updating subset of nominal system mode (SNM) models. Aerodynamic influence coefficients (AICs) are implemented to take aeroelastic interaction into account for forced response analyses. Within a comparison of different models, it is shown for the fundamental flap mode (1F) that the s/g instrumentation significantly affects the forced response, whereas the impact of assembling the compressor plays a minor role.

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12

Basu, P., and J. H. Griffin. "The Effect of Limiting Aerodynamic and Structural Coupling in Models of Mistuned Bladed Disk Vibration." Journal of Vibration and Acoustics 108, no. 2 (April 1, 1986): 132–39. http://dx.doi.org/10.1115/1.3269313.

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A model has been developed for studying the effect of mistuning on bladed disk vibration. Its unique feature is the extent of aerodynamic and structural interaction which it simulates can be readily varied from full coupling of all blades on the disk to coupling of each blade with only its nearest neighbors. Simulations utilizing the resulting algorithm shows that limited coupling models may be used to predict the statistical distribution of blade amplitudes that characterizes the mistuning effect, which in turn determines stage durability. This approach is used to study the effect of changing various system parameters on amplitude scatter. Gas density, the number of blades on the disk, disk stiffness, and the engine order of the excitation are considered. The results are used to draw some conclusions about how to improve laboratory tests and component design.

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13

Afolabi, D. "Vibration Amplitudes of Mistuned Blades." Journal of Turbomachinery 110, no. 2 (April 1, 1988): 251–57. http://dx.doi.org/10.1115/1.3262188.

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Due to the mistuning effect, the nominally identical blades on a rotor are forced to vibrate with greatly unequal amplitudes under certain circumstances. It is, therefore, desirable to have the capability of predicting the highest responding blades so that such blades may be instrumented during engine tests. However, the predictions of various investigators in this regard are apparently inconsistent. Usually, the inconsistency is attributed to differences in mathematical models. By using modal analysis, it is shown that the various results are really not in conflict, but merely reflect the local and contrasting features in the global characteristics of a typical bladed disk. Good agreement is obtained when the results of this study, which is based on a model with structural coupling, are compared with those of other investigators utilizing models with aerodynamic and structural coupling. It is concluded that if the primary resonance being excited is not in a “crossover” zone, the highest responding blades are most likely to be those with extreme mistuning.

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14

Ibrahim, R. A. "Structural Dynamics with Parameter Uncertainties." Applied Mechanics Reviews 40, no. 3 (March 1, 1987): 309–28. http://dx.doi.org/10.1115/1.3149532.

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The treatment of structural parameters as random variables has been the subject of structural dynamicists and designers for many years. Several problems have been involved during the last few decades and resulted in new theorems and interesting phenomena. This paper reviews a number of topics pertaining to structural dynamics with parameter uncertainties. These include direct problems such as random eigenvalues and random responses of discrete and continuous systems. The impact of these problems on related areas of interest such as sensitivity of structural performance to parameter variations, design optimization, and reliability analysis is also addressed. The paper includes the results of experimental investigations, the phenomenon of normal modes localization, and the effect of mistuning of turbomachinery blades on their flutter and forced response characteristics.

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15

Bladh, R., M. P. Castanier, and C. Pierre. "Effects of Multistage Coupling and Disk Flexibility on Mistuned Bladed Disk Dynamics." Journal of Engineering for Gas Turbines and Power 125, no. 1 (December 27, 2002): 121–30. http://dx.doi.org/10.1115/1.1498267.

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The effects of disk flexibility and multistage coupling on the dynamics of bladed disks with and without blade mistuning are investigated. Both free and forced responses are examined using finite element representations of example single and two-stage rotor models. The reported work demonstrates the importance of proper treatment of interstage (stage-to-stage) boundaries in order to yield adequate capture of disk-blade modal interaction in eigenfrequency veering regions. The modified disk-blade modal interactions resulting from interstage-coupling-induced changes in disk flexibility are found to have a significant impact on (a) tuned responses due to excitations passing through eigenfrequency veering regions, and (b) a design’s sensitivity to blade mistuning. Hence, the findings in this paper suggest that multistage analyses may be required when excitations are expected to fall in or near eigenfrequency veering regions or when the sensitivity to blade mistuning is to be accounted for. Conversely, the observed sensitivity to disk flexibility also indicates that the severity of unfavorable structural interblade coupling may be reduced significantly by redesigning the disk(s) and stage-to-stage connectivity. The relatively drastic effects of such modifications illustrated in this work indicate that the design modifications required to alleviate veering-related response problems may be less comprehensive than what might have been expected.

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16

Bai, Bin, Qi Yang, Guang Wei Zhu, Qi Liang Wu, and Xin ye Li. "Nonproportional Intentionally Mistuned Turbine Blisk Design with Improved Component Modal Synthesis." Shock and Vibration 2021 (January 29, 2021): 1–16. http://dx.doi.org/10.1155/2021/6658694.

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An improved component modal synthesis-based nonproportional mistuning method (ICMS-NPMM) is proposed to investigate mistuned turbine blisks (MTBs) since the high-fidelity finite element models (HFEMs) involve large number of computations, which leads to low calculation efficiency. To reduce degrees of freedom and suppress the flutter of MTB, it is divided into mistuned blade structure and tuned disk structure, and the intentional mistuning is considered. Furthermore, the mistuned parameters, nonproportional mistuning, and complex loads are also considered. Firstly, the basic theory of ICMS-NPMM is investigated; secondly, the model of MTB is established via ICMS-NPMM; finally, the intentionally mistuned design of modal shape amplitudes (MSAs) is investigated via ICMS-NPMM. The results indicate that the calculation efficiency is enhanced via ICMS-NPMM relative to that of via HFEM. In addition, the sensitivity and the flutter are decreased; meanwhile, the amplitude fluctuations of MSAs are distinctly decreased and become comparatively smooth. This investigation provides an important guidance for the vibration characteristic study of complex mechanical structures in engineering practice.

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17

Wang, Shuai, Chuanxing Bi, Bin Zi, and Changjun Zheng. "Vibration Characteristics of Rotating Mistuned Bladed Disks considering the Coriolis Force, Spin Softening, and Stress Stiffening Effects." Shock and Vibration 2019 (November 12, 2019): 1–22. http://dx.doi.org/10.1155/2019/9714529.

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Bladed disks of engine rotors usually operate at harsh conditions of high rotating speeds, which may lead to nonnegligible rotordynamic effects, including Coriolis force, spin softening, and stress stiffening effects. These effects on the vibration of mistuned bladed disks are seldom discussed in available investigations. In this paper, the vibration characteristics of rotating mistuned bladed disks are addressed by considering these rotordynamic effects. First, finite element (FE) models of bladed disks are used to obtain the governing equations of motion, and an efficient method for getting the stress stiffening matrix of sector model is developed. Then, the effective component-mode mistuning method (CMM) is employed to create compact, yet accurate, reduced-order models (ROMs). Finally, the models are validated and used to study the influences of Coriolis force, spin softening, and stress stiffening effects on the vibration of bladed disks with frequency mistuning factors. Numerical results show that these rotordynamic effects could significantly affect the vibrations of mistuning bladed disks, especially in the ranges of high speed, and should be carefully considered during analysis.

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18

Lin, R. M., and T. Y. Ng. "Prediction of mistuning effect of bladed disks using eigensensitivity analysis." Engineering Structures 212 (June 2020): 110416. http://dx.doi.org/10.1016/j.engstruct.2020.110416.

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19

Rogge, Timo, Ricarda Berger, Linus Pohle, Raimund Rolfes, and Jörg Wallaschek. "Efficient structural analysis of gas turbine blades." Aircraft Engineering and Aerospace Technology 90, no. 9 (November 14, 2018): 1305–16. http://dx.doi.org/10.1108/aeat-05-2016-0085.

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Purpose The purpose of this study a fast procedure for the structural analysis of gas turbine blades in aircraft engines. In this connection, investigations on the behavior of gas turbine blades concentrate on the analysis and evaluation of starting dynamics and fatigue strength. Besides, the influence of structural mistuning on the vibration characteristics of the single blade is analyzed and discussed. Design/methodology/approach A basic computation cycle is generated from a flight profile to describe the operating history of the gas turbine blade properly. Within an approximation approach for high-frequency vibrations, maximum vibration amplitudes are computed by superposition of stationary frequency responses by means of weighting functions. In addition, a two-way coupling approach determines the influence of structural mistuning on the vibration of a single blade. Fatigue strength of gas turbine blades is analyzed with a semi-analytical approach. The progressive damage analysis is based on MINER’s damage accumulation assuming a quasi-stable behavior of the structure. Findings The application to a gas turbine blade shows the computational capabilities of the approach presented. Structural characteristics are obtained by robust and stable computations using a detailed finite element model considering different load conditions. A high quality of results is realized while reducing the numerical costs significantly. Research limitations/implications The method used for analyzing the starting dynamics is based on the assumption of a quasi-static state. For structures with a sufficiently high stiffness, such as the gas turbine blades in the present work, this procedure is justified. The fatigue damage approach relies on the existence of a quasi-stable cyclic stress condition, which in general occurs for isotropic materials, as is the case for gas turbine blades. Practical implications Owing to the use of efficient analysis methods, a fast evaluation of the gas turbine blade within a stochastic analysis is feasible. Originality/value The fast numerical methods and the use of the full finite element model enable performing a structural analysis of any blade structure with a high quality of results.

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20

Repetckii, Oleg, and Dinh Cuong Hoang. "Numerical Analysis for Optimization of the Lifetime Characteristics of Radial Wheels Turbomachines by Introducing the Intentional Mistuning Parameters." System Analysis & Mathematical Modeling 5, no. 2 (May 14, 2023): 192–204. http://dx.doi.org/10.17150/2713-1734.2023.5(2).192-204.

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Due to manufacturing tolerances, small deviations in the mass of the blade always introduce changes in the geometry and structural properties of the design. Changed geometry and parameters of the blade significantly affect the characteristics of the wheel and the performance of the design of the entire turbomachine. These deviations break the cyclic symmetry of the turbine wheel and are called system mistuning. Generally, the tighter the manufacturing tolerance, the smaller the blade mass deviation. However, if the manufacturing tolerances are tighter, then the manufacturing cost becomes higher. Therefore, in the manufacturing process, the manufacturing cost has an impact on the efficiency and durability of the overall turbomachine. To analyze the problem of the influence of manufacturing tolerance and the cost of manufacturing the wheel, this paper analyzes the type of blade arrangement and mass deviation at the level of block arrangement of blades along the disk rim (block model). The idea is that each block model provides a uniform structure in terms of weight (the unbalance value of the radial disk), can significantly reduce vibration during operation compared to using a blade with a mass deviation. The analysis of the obtained results showed that the introduction of intentional mistuning parameters significantly affects the durability of the radial wheel. The process of optimizing a radial wheel consists in introducing intentional mistuning parameters to manage the resource and ensure the required level of strength, reliability and durability of radial turbomachines.

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21

Cha, D., and A. Sinha. "Statistics of Response of a Mistuned Bladed Disk Assembly Subjected to White Noise and Narrow Band Excitation." Journal of Engineering for Gas Turbines and Power 121, no. 4 (October 1, 1999): 710–17. http://dx.doi.org/10.1115/1.2818531.

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This paper deals with the statistics of the response of a mistuned bladed disk assembly subjected to random excitation. Analytical techniques are developed to compute this statistics for two types of random excitation: white noise and narrow band. The validity of the analytical methods has been established by comparison with the results from numerical simulations. The sensitivities of the response to mistuning have been examined as a function of the width of the frequency band of the random excitation, the dominant frequency of the random excitation and the structural coupling between adjacent blades.

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22

Mignolet, M. P., and W. Hu. "Direct Prediction of the Effects of Mistuning on the Forced Response of Bladed Disks." Journal of Engineering for Gas Turbines and Power 120, no. 3 (July 1, 1998): 626–34. http://dx.doi.org/10.1115/1.2818192.

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In this paper, a novel approach to determine reliable estimates of the moments of the steady-state resonant response of a randomly mistuned bladed disk is presented, and the use of these moments to accurately predict the corresponding distribution of the amplitude of blade vibration is described. The estimation of the moments of the response is accomplished first by relying on a “joint cumulant closure” strategy that expresses higher order moments in terms of lower order ones. A simple modeling of the error terms of these approximations is also suggested that allows the determination of an improved, or accelerated, estimate of the required moments. The evaluation of the distribution of the amplitude of blade response is then accomplished by matching the moments computed by the cumulant closure with those derived from a three-parameter model recently derived. A first order approximation of the moments obtained for a simple structural model of a bladed disk yields a new parameter that can be used as a measure of the localization of the forced response. Then, numerical results demonstrate that the method provides extremely accurate estimates of the moments for all levels of structural coupling which in turn lead to a description of the amplitude of blade response that closely matches simulation results. Finally, a comparison with existing perturbation techniques clearly shows the increased accuracy obtained with the proposed joint cumulant closure formulation.

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23

Xu, Kunpeng, Wei Sun, and Xianfei Yan. "A structural damping identification technique for coatings on blisks based on improved component mode mistuning model." Thin-Walled Structures 151 (June 2020): 106737. http://dx.doi.org/10.1016/j.tws.2020.106737.

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24

Yang, M. T., and J. H. Griffin. "A Reduced-Order Model of Mistuning Using a Subset of Nominal System Modes." Journal of Engineering for Gas Turbines and Power 123, no. 4 (March 1, 1999): 893–900. http://dx.doi.org/10.1115/1.1385197.

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Reduced-order models have been reported in the literature that can be used to predict the harmonic response of mistuned bladed disks. It has been shown that in many cases they exhibit structural fidelity comparable to a finite element analysis of the full bladed disk system while offering a significant improvement in computational efficiency. In these models the blades and disk are treated as distinct substructures. This paper presents a new, simpler approach for developing reduced-order models in which the modes of the mistuned system are represented in terms of a subset of nominal system modes. It has the following attributes: the input requirements are relatively easy to generate; it accurately predicts mistuning effects in regions where frequency veering occurs; as the number of degrees-of-freedom increases it converges to the exact solution; it accurately predicts stresses as well as displacements; and it accurately models the deformation and stresses at the blades’ bases.

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25

Zhou, Biao, Jingchao Zhao, and Teresa Maria Berruti. "Exploration of blade detuning tests for mistuning identification of blisks." Mechanical Systems and Signal Processing 175 (August 2022): 109118. http://dx.doi.org/10.1016/j.ymssp.2022.109118.

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26

Figaschewsky, F., A. Kühhorn, B. Beirow, T. Giersch, and S. Schrape. "Analysis of mistuned forced response in an axial high-pressure compressor rig with focus on Tyler–Sofrin modes." Aeronautical Journal 123, no. 1261 (March 2019): 356–77. http://dx.doi.org/10.1017/aer.2018.163.

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ABSTRACTThis paper aims at contributing to a better understanding of the effect of Tyler–Sofrin Modes (TSMs) on forced vibration responses by analysing a 4.5-stage research axial compressor rig. The first part starts with a brief review of the involved physical mechanisms and necessary prerequisites for the generation of TSMs in multistage engines. This review is supported by unsteady CFD simulations of a quasi 2D section of the studied engine. It is shown that the amplitude increasing effect due to mistuning can be further amplified by the presence of TSMs. Furthermore, the sensitivity with respect to the structural coupling of the blades and the damping as well as the shape of the expected envelope is analysed.The second part deals with the Rotor 2 blisk of the research compressor rig. The resonance of a higher blade mode with the engine order of the upstream stator is studied in two different flow conditions realised by different variable stator vane (VSV) schedules which allows to separate the influence of TSMs from the impact of mistuning. A subset of nominal system modes representation of the rotor is used to describe its mistuned vibration behaviour, and unsteady CFD simulations are used to characterise the present strength of the TSMs in the particular operating conditions. Measured maximum amplitude vs blade pattern and frequency response functions are compared against the predictions of the aeromechanical models in order to assess the strength of the TSMs as well as its influence on vibration levels.

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27

Pichot, F., D. Laxalde, J. J. Sinou, F. Thouverez, and J. P. Lombard. "Mistuning identification for industrial blisks based on the best achievable eigenvector." Computers & Structures 84, no. 29-30 (November 2006): 2033–49. http://dx.doi.org/10.1016/j.compstruc.2006.08.022.

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28

Mignolet, M. P., A. J. Rivas-Guerra, and J. P. Delor. "Identification of Mistuning Characteristics of Bladed Disks From Free Response Data—Part I." Journal of Engineering for Gas Turbines and Power 123, no. 2 (June 9, 1999): 395–403. http://dx.doi.org/10.1115/1.1338949.

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The focus of the present two-part investigation is on the estimation of the dynamic properties, i.e., masses, stiffnesses, natural frequencies, mode shapes and their statistical distributions, of turbomachine blades to be used in the accurate prediction of the forced response of mistuned bladed disks. As input to this process, it is assumed that the lowest natural frequencies of the blades alone have been experimentally measured, for example, in a broach block test. Since the number of measurements is always less than the number of unknowns, this problem is indeterminate in nature. In this first part of the investigation, two distinct approaches will be investigated to resolve the shortfall of data. The first one relies on the imposition of as many constraints as needed to ensure a unique solution to this identification problem. Specifically, the mode shapes and modal masses of the blades are set to their design/tuned counterparts while the modal stiffnesses are varied from blade to blade to match the measured natural frequencies. The second approach, based on the maximum likelihood principle, yields estimates of all the structural parameters of the blades through the minimization of a specified “cost function.” The accuracy of these two techniques in predicting the forced response of mistuned bladed disks will be assessed on simple dynamic models of the blades.

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29

Rivas-Guerra, A. J., M. P. Mignolet, and J. P. Delor. "Identification of Mistuning Characteristics of Bladed Disks From Free Response Data— Part II." Journal of Engineering for Gas Turbines and Power 123, no. 2 (June 9, 1999): 404–11. http://dx.doi.org/10.1115/1.1338950.

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The focus of the present two-part investigation is on the estimation of the dynamic properties, i.e., masses, stiffnesses, natural frequencies, mode shapes and their statistical distributions, of turbomachine blades to be used in the accurate prediction of the forced response of mistuned bladed disks. As input to this process, it is assumed that the lowest natural frequencies of the blades alone have been experimentally measured, for example in a broach block test. Since the number of measurements is always less than the number of unknowns, this problem is indeterminate in nature. In this second part of the investigation, the maximum likelihood method (ML) will first be revisited and a thorough assessment of its reliability in a wide variety of conditions, including the presence of measurement noise, different distributions of blade structural properties, etc., will be conducted. Then, a technique that provides a bridge between the two identification methods introduced in Part I, i.e., the random modal stiffnesses (RMS) and maximum likelihood (ML) approaches, will be presented. This technique, termed the improved random modal stiffnesses (IRMS) method is based on the maximum likelihood concepts but yields a mistuning model similar to that of the random modal stiffnesses technique. Finally, the accuracy of the RMS, ML, and IRMS methods in predicting the forced response statistics of mistuned bladed disks will be investigated in the presence of close blade alone natural frequencies.

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30

Píštěk, Václav, Pavel Kučera, Oleksij Fomin, Alyona Lovska, and Aleš Prokop. "Acoustic Identification of Turbocharger Impeller Mistuning—A New Tool for Low Emission Engine Development." Applied Sciences 10, no. 18 (September 14, 2020): 6394. http://dx.doi.org/10.3390/app10186394.

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At present, exhaust gas turbochargers not only form the basis for the economical operation of petrol, diesel or gas engines of all power categories, but also have an irreplaceable role on reducing their emissions. In order to reduce emissions from internal combustion engines, various systems are being developed, all of which have a turbocharger as an important component. Demands on turbocharger system durability and reliability keep growing, which requires the application of increasingly advanced computational and experimental methods at the development beginning of these systems. The design of turbochargers starts with a mathematical description of their rotationally cyclic impellers. However, mistuning, i.e., a slight individual blade property deviation from the intended design parameters, leads to a disturbance of the rotational cyclic symmetry. This article deals with the effects of manufacturing-related deviations on the structural dynamic behaviour of real turbine rotors. As opposed to methods exploiting expensive scanning vibrometers for experimental modal analysis or time-consuming accurate measurement of the geometry of individual blades using 3D optical scanners. A suitable microphone and a finite element rotor wheel model are the basis of this new method. After comparing the described acoustic approach with the laser vibrometer procedure, the results seemed to be practically identical. In comparison with the laser technique the unquestionable added value of this new method is the fact that it brings a significant reduction in the financial requirements for laboratory equipment. Another important benefit is that the measuring process of bladed wheel mistuning is significantly less time-consuming.

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31

Moyroud, F., T. Fransson, and G. Jacquet-Richardet. "A Comparison of Two Finite Element Reduction Techniques for Mistuned Bladed Disks." Journal of Engineering for Gas Turbines and Power 124, no. 4 (September 24, 2002): 942–52. http://dx.doi.org/10.1115/1.1415741.

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The high performance bladed disks used in today’s turbomachines must meet strict standards in terms of aeroelastic stability and resonant response level. One structural characteristic that can significantly impact on both these areas is that of bladed disk mistuning. To predict the effects of mistuning, computational efficient methods are much needed to make free-vibration and forced-response analyses of full assembly finite element (FE) models feasible in both research and industrial environments. Due to the size and complexity of typical industrial bladed disk models, one must resort to robust and systematic reduction techniques to produce reduced-order models of sufficient accuracy. The objective of this paper is to compare two prevalent reduction methods on representative test rotors, including a modern design industrial shrouded bladed disk, in terms of accuracy (for frequencies and mode shapes), reduction order, computational efficiency, sensitivity to intersector elastic coupling, and ability to capture the phenomenon of mode localization. The first reduction technique employs a modal reduction approach with a modal basis consisting of mode shapes of the tuned bladed disk which can be obtained from a classical cyclic symmetric modal analysis. The second reduction technique uses Craig and Bampton substructure modes. The results show a perfect agreement between the two reduced-order models and the nonreduced finite element model. It is found that the phenomena of mode localization is equally well predicted by the two reduction models. In terms of computational cost, reductions from one to two orders of magnitude are obtained for the industrial bladed disk, with the modal reduction method being the most computationally efficient approach.

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32

Tan, Yuanqiu, Chaoping Zang, and E. P. Petrov. "Mistuning sensitivity and optimization for bladed disks using high-fidelity models." Mechanical Systems and Signal Processing 124 (June 2019): 502–23. http://dx.doi.org/10.1016/j.ymssp.2019.02.002.

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33

Liu, Honghao, Wei Sun, Dongxu Du, Xiaofeng Liu, and Hongwei Ma. "Nonlinear vibration of mistuning bolted composite plates considering stick-slip-separation characteristics." International Journal of Mechanical Sciences 245 (May 2023): 108126. http://dx.doi.org/10.1016/j.ijmecsci.2023.108126.

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34

Xu, Kunpeng, Wei Sun, and Junnan Gao. "Mistuning identification and model updating of coating blisk based on modal test." Mechanical Systems and Signal Processing 121 (April 2019): 299–321. http://dx.doi.org/10.1016/j.ymssp.2018.11.029.

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35

Sall, A. C., F. Thouverez, L. Blanc, and P. Jean. "Stochastic Behaviour of Mistuned Stator Vane Sectors: An Industrial Application." Shock and Vibration 19, no. 5 (2012): 1041–50. http://dx.doi.org/10.1155/2012/798610.

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Stator vanes which are found in axial compressors are subject to vibratory fatigue. Their division into monoblock sectors makes the prediction of their vibratory behaviour difficult by deterministic methods due to the loss of the cyclic symmetry properties and also to a high sensitivity to mistuning. The purpose is to present a robust calculation strategy based on a stochastic modelisation of the structure. The methodology has been developed first on a simplified model and then applied to an industrial case. Polynomial chaos based results are in good agreement with reference Monte Carlo simulations.

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36

Yan, Xianfei, Dongxu Du, Honghao Liu, Kunpeng Xu, and Wei Sun. "Nonlinear vibration analysis of coated blisks in the presence of stiffness mistuning identification." Mechanical Systems and Signal Processing 165 (February 2022): 108338. http://dx.doi.org/10.1016/j.ymssp.2021.108338.

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37

Baek, Seunghun, and Bogdan Epureanu. "Damping mistuning effects on the amplification factor and statistical investigation of vane packet." Mechanical Systems and Signal Processing 120 (April 2019): 117–32. http://dx.doi.org/10.1016/j.ymssp.2018.10.011.

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38

Zhou, Biao, and Teresa Maria Berruti. "A novel model reduction approach for blisks with blend repairs and small mistuning." Mechanical Systems and Signal Processing 195 (July 2023): 110308. http://dx.doi.org/10.1016/j.ymssp.2023.110308.

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39

Yan, Xianfei, Wei Sun, Jinpeng Su, and Qiang Zhang. "Optimization-based vibration suppression method of deterministic blisks by nonlinear coatings with mistuning identification." Structures 53 (July 2023): 986–99. http://dx.doi.org/10.1016/j.istruc.2023.04.121.

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40

Schwerdt, Lukas, Niklas Maroldt, Lars Panning-von Scheidt, Joerg Wallaschek, and Joerg Seume. "An improved reduced order model for bladed disks including multistage aeroelastic and structural coupling." Journal of the Global Power and Propulsion Society 7 (April 25, 2023): 140–52. http://dx.doi.org/10.33737/jgpps/161707.

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To assess the influence of mistuning on the vibration amplitudes of turbomachinery rotors, reduced order models (ROMs) are widely used. A variety of methods are available for single-stage configurations and mostly aeroelastic effects can be taken into account. More recent research focusses on extending these methods to include multiple stages. However, due to the significantly increased computational effort of the aeroelastic simulations when adding more stages to the models, these ROMs are rarely applied with the inclusion of multistage aeroelastic effects. It is therefore desirable to develop reduction methods which minimize the number of these simulations to reduce the computational cost and thereby enable analyses of rotors with multiple stages including aeroelastic effects. In this paper, a cyclic Craig-Bampton reduction method with an a priori interface reduction for multistage rotors is extended with an additional a posteriori interface reduction to reduce the number of aeroelastic simulations necessary for a given accuracy level of the ROM. The interface degrees of freedom between stages are reduced using a modified version of Characteristic Constraint Modes, to yield a more efficient representation of their displacements while retaining their monoharmonic nature. The method is applied to a two-stage axial compressor with full aeroelastic coupling between the stages and its reduced computational effort is demonstrated. Additionally, two sorting methods for the degrees of freedom (DOFs) of the ROM are compared.

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41

Tacher, Anthony, Fabrice Thouverez, and Jason Armand. "Modelling and analysis of a bladed drum subject to the Coriolis and mistuning effects." International Journal of Mechanical Sciences 218 (March 2022): 106994. http://dx.doi.org/10.1016/j.ijmecsci.2021.106994.

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42

Fitzner, Colin, Bogdan I. Epureanu, and Sergio Filippi. "Nodal energy weighted transformation: A mistuning projection and its application to FLADE™ turbines." Mechanical Systems and Signal Processing 42, no. 1-2 (January 2014): 167–80. http://dx.doi.org/10.1016/j.ymssp.2013.08.027.

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43

Xu, Kunpeng, Xianfei Yan, Dalu Xu, Dongxu Du, and Wei Sun. "Detection of blade substrate crack parameters of hard-coated blisk based on mistuning identification technology." Mechanical Systems and Signal Processing 165 (February 2022): 108381. http://dx.doi.org/10.1016/j.ymssp.2021.108381.

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44

Yan, Xianfei, Wei Sun, Kunpeng Xu, and Dongxu Du. "Modelling method and mistuning amplification analysis of the forced response for coated blisks in the presence of coatings-material nonlinearity." Thin-Walled Structures 154 (September 2020): 106850. http://dx.doi.org/10.1016/j.tws.2020.106850.

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45

Wang, Weimin, Dongfang Hu, Qihang Li, and Xulong Zhang. "An improved non-contact dynamic stress measurement method for turbomachinery rotating blades based on fundamental mistuning model." Mechanical Systems and Signal Processing 144 (October 2020): 106851. http://dx.doi.org/10.1016/j.ymssp.2020.106851.

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46

Xiao, Congzhen, Zhenhong Wu, Kai Chen, Yi Tang, and Yalin Yan. "Development of a Water Supplement System for a Tuned Liquid Damper under Excitation." Buildings 13, no. 5 (April 22, 2023): 1115. http://dx.doi.org/10.3390/buildings13051115.

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Integrating existing liquid storage and supply tanks in buildings with tuned liquid dampers (TLDs) are significant for reducing the effective cost of TLDs. However, existing water supplement devices for fire-suppression liquid tanks may overfill with water, which leads to TLD mistuning. To overcome this problem, a passive liquid control system named TLD with a stable replenishment sub-tank system (TLD-SRS) is proposed. The system, which consists of an additional sub-tank connected to the main tank and a floating ball, replenishes liquid in the TLD automatically. The system can avoid vibration interference and maintain the normal operation of the passive replenishment system under usual wind loads. According to the studies of tuned liquid column dampers (TLCD), the proposed TLD with a stable replenishment sub-tank system (TLD-SRS) uses simple devices to ensure that the liquid level in the TLD is steady at the target liquid level with a floating ball. The TLD-SRS is verified on a large-scale TLD shaking table experiment. The overshoot, which is the percentage of liquid that exceeds the target volume of TLD is calculated during sloshing with wind loads. Compared with TLD installed with a regular liquid replenishment device, the proposed TLD-SRS significantly reduces the overshoot of liquid and acceleration on the roof of the building.

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47

Xu, Hailong, Zhongsheng Chen, Yongmin Yang, Limin Tao, and Xuefeng Chen. "Effects of Crack on Vibration Characteristics of Mistuned Rotated Blades." Shock and Vibration 2017 (2017): 1–18. http://dx.doi.org/10.1155/2017/1785759.

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Rotated blades are key mechanical components in turbine and high cycle fatigues often induce blade cracks. Meanwhile, mistuning is inevitable in rotated blades, which often makes it much difficult to detect cracks. In order to solve this problem, it is important and necessary to study effects of crack on vibration characteristics of mistuned rotated blades (MRBs). Firstly, a lumped-parameter model is established based on coupled multiple blades, where mistuned stiffness with normal distribution is introduced. Next, a breathing crack model is adopted and eigenvalue analysis is used in coupled lumped-parameter model. Then, numerical analysis is done and effects of depths and positions of a crack on natural frequency, vibration amplitude, and vibration localization parameters are studied. The results show that a crack causes natural frequency decease and vibration amplitude increase of cracked blade. Bifurcations will occur due to a breathing crack. Furthermore, based on natural frequencies and vibration amplitudes, variational factors are defined to detect a crack in MRBs, which are validated by numerical simulations. Thus, the proposed method provides theoretical guidance for crack detection in MRBs.

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48

Fan, Zhenfang, Hongkun Li, Jiannan Dong, Daitong Wei, Hongwei Cao, and Yugang Chen. "An improved mistuning identification and dynamic strain prediction method for rotating blades with application of blade tip timing technology." Mechanical Systems and Signal Processing 184 (February 2023): 109684. http://dx.doi.org/10.1016/j.ymssp.2022.109684.

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49

Hu, Dongfang, Weimin Wang, Xulong Zhang, and Kang Chen. "On-line real-time mistuning identification and model calibration method for rotating blisks based on blade tip timing (BTT)." Mechanical Systems and Signal Processing 147 (January 2021): 107074. http://dx.doi.org/10.1016/j.ymssp.2020.107074.

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50

Jay, R. L., and D. W. Burns. "Characteristics of the Diametral Resonant Response of a Shrouded Fan Under a Prescribed Distortion." Journal of Vibration and Acoustics 108, no. 2 (April 1, 1986): 125–31. http://dx.doi.org/10.1115/1.3269312.

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A comprehensive controlled study of the resonant vibratory structural response of a shrouded fan blade/disk due to known excitation was performed. A full circumferential definition of the inlet velocity field was obtained at five radial locations for three axial spacings and for four unique patterns of distortion and three mass flow rates. Harmonic analyses of the velocity patterns were used to establish a gust perturbation velocity normal to the blade chord. From these spanwise perturbation velocities, a normalized force parameter was established. In-vacuum, nonrotating testing of the fan assembly allowed identification of individual blade frequencies and system modes. This testing used strain gaging and holography to identify mistuning, damping and split factors for diametral patterns of the 3, 4, 5, and 6 diametral mode families. Dynamic strain signatures from rotating rig resonant responses were obtained for inlet flows having 3, 4, 5, and 6 distorted regions to simulate inlet struts. Groups of 1/4-in. rods were used to create these regions of distorted flow. System mode responses to these distortion patterns included occurrences of standing and traveling waves. Trends of gust perturbation force parameter and measured dynamic stress with varying axial gap, mass flow, and loading were established. The data collectively quantify the strong cause and effect relationship between force parameter and measured dynamic stress.

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