Applied Mathematics and Mechanics >
A novel scaling method for the elastic ring supporting structure of an aero-engine rotor system: analytical and experimental investigations
Received date: 2025-06-03
Revised date: 2025-10-12
Online published: 2025-12-30
Supported by
Project supported by the National Natural Science Foundation of China (Nos. 52405095, 12272089, and 92360305), the Guangdong Basic and Applied Basic Research Foundation of China (No. 2023A1515110557), the Natural Science Foundation of Liaoning Province of China (No. 2023-BSBA-102), the Open Fund of National Key Laboratory of Particle Transport and Separation Technology of China (No. WZKF-2024-6), the Open Project of Guangxi Key Laboratory of Automobile Components and Vehicle Technology of China (Nos. 2024GKLACVTKF07 and 2024GKLACVTKF06), the Basic Research Projects of Liaoning Provincial Department of Education of China (No. JYTQN2023162), and the Fundamental Research Funds for the Central Universities of China (No. N2403022)
Copyright
The testing of large structures is limited by high costs and long cycles, making scaling methods an attractive solution. However, the scaling process of elastic rings introduces complexities in multi-parameter geometric distortions, leading to a diminution in the predictive accuracy of the distorted similitude. To address this challenge, this study formulates a novel set of scaling laws, tailored to account for the intricate geometric distortions associated with elastic rings. The proposed scaling laws are formulated based on the intrinsic deformation characteristics of elastic rings, rather than the traditional systemic governing equations. Numerical and experimental cases are conducted to assess the efficacy and precision of the proposed scaling laws, and the obtained results are compared with those achieved by traditional methods. The outcomes demonstrate that the scaling laws put forth by this study significantly enhance the predictive capabilities for deformations of elastic rings.
Key words： rotor system; aero-engine; elastic ring; scaling method; supporting structure
Lei LI , Tianyue MA , Zhong LUO , Dongwu GAO , Xiangdong GE , Hui MA , Shibin WANG . A novel scaling method for the elastic ring supporting structure of an aero-engine rotor system: analytical and experimental investigations[J]. Applied Mathematics and Mechanics, 2026 , 47(1) : 1 -18 . DOI: 10.1007/s10483-026-3331-6
| [1] | ZHANG, W. and DING, Q. Elastic ring deformation and pedestal contact status analysis of elastic ring squeeze film damper. Journal of Sound and Vibration, 346, 314–327 (2015) |
| [2] | HAN, Z. F., DING, Q., and ZHANG, W. Dynamical analysis of an elastic ring squeeze film damper-rotor system. Mechanism and Machine Theory, 131, 406–419 (2019) |
| [3] | HAN, Z. F., MA, Z. S., ZHANG, W., HAN, B. B., and DING, Q. Dynamic analysis of an elastic ring squeeze film damper supported rotor using a semi-analytic method. Engineering Applications of Computational Fluid Mechanics, 14, 1263–1278 (2020) |
| [4] | CHEN, W. T., CHEN, S. Y., HU, Z. H., TANG, J. Y., and LI, H. N. A novel dynamic model for the spiral bevel gear drive with elastic ring squeeze film dampers. Nonlinear Dynamics, 98, 1081–1105 (2019) |
| [5] | YANG, X. M., JIANG, B. Z., LI, Y., ZHAO, Q., DENG, S. E., ZHANG, W. H., and CUI, Y. C. Dynamic characteristics of elastic ring squeeze film damper coupled high-speed ball bearings. Journal of Sound and Vibration, 537, 117186 (2022) |
| [6] | LUO, Z., SUN, K., GE, X. D., ZHOU, G. Z., and CUI, Z. W. Dynamic analysis of the rotor system with elastic ring squeeze film damper considering oil film temperature. Nonlinear Dynamics, 111, 15981–16002 (2023) |
| [7] | SUN, K., LUO, Z., LI, L., LIU, J. X., and WU, F. Y. Dynamic analysis of the variable stiffness support rotor system with elastic rings. Nonlinear Dynamics, 110, 201–217 (2022) |
| [8] | YANG, Y., ZHANG, Y. X., ZENG, J., MA, H., YANG, Y. R., and CAO, D. Q. Insight on uncertainty of geometrically nonlinear rotor with rub-impact under maneuvering motion. Journal of Sound and Vibration, 570, 118018 (2024) |
| [9] | MA, Y. H., SHI, C. L., WANG, Y. F., ZHOU, Y., and HONG, J. Gyroscopic effect evaluation and resonance speed prediction of complex high-speed rotor system based on energy. Mechanical Systems and Signal Processing, 198, 110423 (2023) |
| [10] | LI, Y. N., DING, J. Y., DING, H., and CHEN, L. Q. Natural vibration and critical velocity of translating Timoshenko beam with non-homogeneous boundaries. Applied Mathematics and Mechanics (English Edition), 45(9), 1523–1538 (2024) https://doi.org/10.1007/s10483-024-3148-7 |
| [11] | ZHAO, L., LU, Z. Q., DING, H., and CHEN, L. Q. A viscoelastic metamaterial beam for integrated vibration isolation and energy harvesting. Applied Mathematics and Mechanics (English Edition), 45(7), 1243–1260 (2024) https://doi.org/10.1007/s10483-024-3159-7 |
| [12] | ZHANG, C., CAO, P., ZHU, R. P., CHEN, W. F., and WANG, D. Dynamic modeling and analysis of the spline joint-flexible coupling-rotor system with misalignment. Journal of Sound and Vibration, 554, 117696 (2023) |
| [13] | LI, M. and DING, H. A vertical track nonlinear energy sink. Applied Mathematics and Mechanics (English Edition), 45(6), 931–946 (2024) https://doi.org/10.1007/s10483-024-3127-6 |
| [14] | WEI, S., CHEN, Y. F., DING, H., and CHEN, L. Q. An improved interval model updating method via adaptive Kriging models. Applied Mathematics and Mechanics (English Edition), 45(3), 497–514 (2024) https://doi.org/10.1007/s10483-024-3093-7 |
| [15] | LI, Y. Q., ZHU, Z. M., WEN, C. M., LIU, K., LUO, Z., and LONG, T. L. Rub-impact dynamic analysis of a dual-rotor system with bolted joint structure: theoretical and experimental investigations. Mechanical Systems and Signal Processing, 209, 111144 (2024) |
| [16] | LI, Y. Q., LONG, T. L., LUO, Z., WEN, C. M., ZHU, Z. M., JIN, L., and LI, B. Numerical and experimental investigations on dynamic behaviors of a bolted joint rotor system with pedestal looseness. Journal of Sound and Vibration, 571, 118036 (2024) |
| [17] | DU, D. X., SUN, W., CUI, B. B., LIU, H. H., MA, H. W., LIU, X. F., and LI, H. Traveling-wave vibrations of disc-drum rotors with PSC under mistuning-coupled conditions. International Journal of Mechanical Sciences, 250, 108326 (2023) |
| [18] | WANG, J., ZHANG, X. N., LIU, Y. F., QIN, Z. Y., MA, L., HONG, F. F., and CHU, F. L. Dynamic analysis of magnetorheological damper incorporating elastic ring in coupled multi-physical fields. Mechanical Systems and Signal Processing, 208, 111040 (2024) |
| [19] | QIN, Z. Y., QIN, L. C., ZHU, Q. Y., WANG, P., ZHANG, F. B., and CHU, F. L. An ultrasensitive self-powered smart bearing pedestal with fault locating capability. Mechanical Systems and Signal Processing, 235, 112924 (2025) |
| [20] | SONG, Z. H., HONG, J., YANG, Z. F., CAO, Y. T., and MA, Y. H. Dynamical analysis of propeller rotors whirl flutter considering complex blade geometries and induced velocities. Mechanical Systems and Signal Processing, 230, 112621 (2025) |
| [21] | XU, Z., YU, X. C., LI, H., XU, P. Y., GU, D. W., HAN, Q. K., and WEN, B. C. Nonlinear vibration characteristics of fiber-reinforced composite thin-walled conical-cylindrical coupled shells under partial bolt looseness. Thin-Walled Structures, 209, 112874 (2025) |
| [22] | CASABURO, A., PETRONE, G., FRANCO, F., and DE ROSA, S. A review of similitude methods for structural engineering. Applied Mechanics Reviews, 71, 30802 (2019) |
| [23] | COUTINHO, C. P., BAPTISTA, A. J., and RODRIGES, J. D. Reduced scale models based on similitude theory: a review up to 2015. Engineering Structures, 119, 81–94 (2016) |
| [24] | UNGBHAKORN, V. and SINGHATANADGID, P. Similitude invariants and scaling laws for buckling experiments on anti-symmetrically laminated plates subjected to biaxial loading. Composite Structures, 59, 455–465 (2003) |
| [25] | KASIVITAMNUAY, J. and SINGHATANADGID, P. Scaling laws for displacement of elastic beam by energy method. International Journal of Mechanical Sciences, 128-129, 361–367 (2017) |
| [26] | DE ROSA, S. and FRANCO, F. A scaling procedure for the response of an isolated system with high modal overlap factor. Mechanical Systems and Signal Processing, 22, 1549–1565 (2008) |
| [27] | DE ROSA, S., FRANCO, F., and POLITO, T. Structural similitudes for the dynamic response of plates and assemblies of plates. Mechanical Systems and Signal Processing, 25, 969–980 (2011) |
| [28] | DE ROSA, S. and FRANCO, F. On the use of the asymptotic scaled modal analysis for time-harmonic structural analysis and for the prediction of coupling loss factors for similar systems. Mechanical Systems and Signal Processing, 24, 455–480 (2010) |
| [29] | DE ROSA, S., FRANCO, F., and POLITO, T. Partial scaling of finite element models for the analysis of the coupling between short and long structural wavelengths. Mechanical Systems and Signal Processing, 52-53, 722–740 (2015) |
| [30] | FRANCO, F., ROBIN, O., CIAPPI, E., DE ROSA, S., BERRY, A., and PETRONE, G. Similitude laws for the structural response of flat plates under a turbulent boundary layer excitation. Mechanical Systems and Signal Processing, 129, 590–613 (2019) |
| [31] | LUO, Z., ZHU, Y. P., ZHAO, X. Y., and WANG, D. Y. Determining dynamic scaling laws of geometrically distorted scaled models of a cantilever plate. Journal of Engineering Mechanics, 142, 04015108 (2016) |
| [32] | ADAMS, C., B?S, J., SLOMSKI, E. M., and MELZ, T. Scaling laws obtained from a sensitivity analysis and applied to thin vibrating structures. Mechanical Systems and Signal Processing, 110, 590–610 (2018) |
| [33] | ADAMS, C., B?S, J., and MELZ, T. Performance of similitude methods for structural vibration analyses of rectangular plates. Mechanical Systems and Signal Processing, 162, 108074 (2022) |
| [34] | LI, L., LUO, Z., HE, F. X., ZHAO, X. Y., and LIU, J. R. A partial similitude method considering variable powers in scaling laws and applied to rotor-bearing systems. International Journal of Mechanical Sciences, 186, 105892 (2020) |
| [35] | ASL, M. E., NIEZRECKI, C., SHERWOOD, J., and AVITABILE, P. Experimental and theoretical similitude analysis for flexural bending of scaled-down laminated I-beams. Composite Structures, 176, 812–822 (2017) |
| [36] | ASL, M. E., NIEZRECKI, C., SHERWOOD, J., and AVITABILE, P. Vibration prediction of thin-walled composite I-beams using scaled models. Thin-Walled Structures, 113, 151–161 (2017) |
| [37] | KASIVITAMNUAY, J. and SINGHATANADGID, P. Scaling laws for static displacement of linearly elastic cracked beam by energy method. Theoretical and Applied Fracture Mechanics, 98, 157–166 (2018) |
| [38] | EL-BORGI, S., ALRUMAIHI, A., RAJENDRAN, P., YAZBECK, R., FERNANDES, R., BOYD, J. G., and LAGOUDAS, D. C. Model updating of a scaled piping system and vibration attenuation via locally resonant bandgap formation. International Journal of Mechanical Sciences, 194, 106211 (2021) |
| [39] | REZAEEPAZHAND, J., SIMITSES, G. J., REZAEEPAZHAND, J., and SIMITSES, G. J. Use of scaled-down models for predicting vibration response of laminated plates. Composite Structures, 30, 419–426 (1995) |
| [40] | REZAEEPAZHAND, J. and WISNOM, M. R. Scaled models for predicting buckling of delaminated orthotropic beam-plates. Composite Structures, 90, 87–91 (2009) |
| [41] | REZAEEPAZHAND, J. and YAZDI, A. A. Similitude requirements and scaling laws for flutter prediction of angle-ply composite plates. Composites Part B-Engineering, 42, 51–56 (2011) |
| [42] | REZAEEPAZHAND, J., SIMITSES, G. J., and STARNES, J. H. Design of scaled down models for predicting shell vibration response. Journal of Sound and Vibration, 195, 301–311 (1996) |
| [43] | REZAEEPAZHAND, J. and SIMITSES, G. J. Structural similitude for vibration response of laminated cylindrical shells with double curvature. Composites Part B-Engineering, 28, 195–200 (1997) |
| [44] | YAZDI, A. A. and REZAEEPAZHAND, J. Accuracy of scale models for flutter prediction of cross-ply laminated plates. Journal of Reinforced Plastics and Composites, 30, 45–52 (2011) |
| [45] | YAZDI, A. A. Prediction flutter boundaries of laminated cylindrical shells using scaling laws. Journal of Aerospace Engineering, 27, 86–92 (2014) |
| [46] | SINGHATANADGID, P. and UNGBHAKORN, V. Scaling laws for buckling of polar orthotropic annular plates subjected to compressive and torsional loading. Thin-Walled Structures, 43, 1115–1129 (2005) |
| [47] | UNGBHAKORN, V. and SINGHATANADGID, P. A scaling law for vibration response of laminated doubly curved shallow shells by energy approach. Mechanics of Advanced Materials and Structures, 16, 333–344 (2009) |
| [48] | SINGHATANADGID, P. and SONGKHLA, A. N. An experimental investigation into the use of scaling laws for predicting vibration responses of rectangular thin plates. Journal of Sound and Vibration, 311, 314–327 (2008) |
| [49] | DE ROSA, S., FRANCO, F., and MERUANE, V. Similitudes for the structural response of flexural plates. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 230, 174–188 (2016) |
| [50] | CASABURO, A., PETRONE, G., MERUANE, V., FRANCO, F., and DE ROSA, S. The vibroacoustic behaviour of aluminium foam sandwich panels in similitude. Journal of Sandwich Structures & Materials, 23, 4170–4195 (2021) |
| [51] | LI, H., LIU, Y., ZHANG, H. Y., QIN, Z. Y., WANG, Z. Y., DENG, Y. C., XIONG, J., WANG, X. P., and HA, S. K. Amplitude-dependent damping characteristics of all-composite sandwich plates with a foam-filled hexagon honeycomb core. Mechanical Systems and Signal Processing, 186, 109845 (2023) |
| [52] | LI, H., LI, Z. L., XIAO, Z. Y., XIONG, J., WANG, X. P., HAN, Q. K., ZHOU, J., and GUAN, Z. W. Vibro-impact response of FRP sandwich plates with a foam core reinforced by chopped fiber rods. Composites Part B-Engineering, 242, 110077 (2022) |
| [53] | HUI, L., ZHAO, S. Q., SHI, X. J., WU, H. H., QIN, Z. Y., LU, P. X., WANG, X. P., and GUAN, Z. W. Thermal-vibration aging of fiber-reinforced polymer cylindrical shells with polyurea coating: theoretical and experimental studies. Mechanics of Advanced Materials and Structures, 30, 1368–1383 (2023) |
| [54] | DU, D. X., YAN, X. F., LIU, H. H., LIU, X. F., SUN, W., and LI, H. Veering of frequency loci and nonlinear coupling vibration analysis between traveling waves of rotational hard-coated cylindrical shells. Journal of Sound and Vibration, 536, 117152 (2022) |
| [55] | DU, D. X., SUN, W., YAN, X. F., LIU, H. H., XU, K. P., and QIN, Z. Y. Modelling and analysis of nonlinear vibrations for a coupling hard-coated ring disc-cylindric shell structure under piecewise-continuous coupling conditions. International Journal of Mechanical Sciences, 215, 106940 (2022) |
| [56] | PETRONE, G., MANFREDONIA, M., DE ROSA, S., and FRANCO, F. Structural similitudes of stiffened cylinders. Mathematics and Mechanics of Solids, 24, 527–541 (2019) |
| [57] | ZHOU, L. L. A new structural similitude method for laminated composite cylinders. Thin-Walled Structures, 164, 107920 (2021) |
| [58] | LIU, P. T., WANG, X. P., WANG, Y. Q., and MAO, F. R. Research on coupling distorted similitude method of coupled cylindrical-conical shells. Thin-Walled Structures, 179, 109734 (2022) |
| [59] | YU, W. and LI, Z. L. Structural similitude for prestressed vibration and buckling of eccentrically stiffened circular cylindrical panels and shells by energy approach. International Journal of Structural Stability and Dynamics, 16, 1550074 (2016) |
| [60] | WANG, J. C., LI, Z. L., and YU, W. Structural similitude for the geometric nonlinear buckling of stiffened orthotropic shallow spherical shells by energy approach. Thin-Walled Structures, 138, 430–457 (2019) |
| [61] | DE ROSA, S., FRANCO, F., LI, X., and POLITO, T. A similitude for structural acoustic enclosures. Mechanical Systems and Signal Processing, 30, 330–342 (2012) |
| [62] | DE ROSA, S., FRANCO, F., PETRONE, G., CASABURO, A., and MARULO, F. A versatile offset operator for the discrete observation of objects. Journal of Sound and Vibration, 500, 116019 (2021) |
| [63] | COUTINHO, C. P., BAPTISTA, A. J., and RODRIGES, J. D. Modular approach to structural similitude. International Journal of Mechanical Sciences, 135, 294–312 (2018) |
| [64] | SONG, Y. Y., WU, J., YU, G., and HUANG, T. Dynamic characteristic prediction of a 5-DOF hybrid machine tool by using scale model considering the geometric distortion of bearings. Mechanism and Machine Theory, 145, 103679 (2020) |
| [65] | YOU, C., YASAEE, M., and DAYYANI, I. Structural similitude design for a scaled composite wing box based on optimised stacking sequence. Composite Structures, 226, 111255 (2019) |
| [66] | WU, J. J. Prediction of lateral vibration characteristics of a full-size rotor-bearing system by using those of its scale models. Finite Elements in Analysis and Design, 43, 803–816 (2007) |
| [67] | LUO, Z., LI, L., HE, F. X., and YAN, X. L. Partial similitude for dynamic characteristics of rotor systems considering gravitational acceleration. Mechanism and Machine Theory, 156, 104142 (2021) |
| [68] | LI, L., LUO, Z., WU, F. Y., HE, F. X., and SUN, K. Experimental and numerical studies on partial similitude of rotor system considering the vibration consistency. Mechanism and Machine Theory, 183, 105270 (2023) |
| [69] | ZHANG, C. P., WEI, J., PENG, B., CAO, M. F., HOU, S. S., and LIM, T. C. Investigation of dynamic similarity of gear transmission system considering machining error distortion: theoretical analysis and experiments. Mechanism and Machine Theory, 172, 104803 (2022) |
| [70] | CHEN, H. Y., ZENG, Y. C., DING, H., LAI, S. K., and CHEN, L. Q. Dynamics and vibration reduction performance of asymmetric tristable nonlinear energy sink. Applied Mathematics and Mechanics (English Edition), 45(3), 389–406 (2024) https://doi.org/10.1007/s10483-024-3095-9 |
| [71] | LI, L., LUO, Z., HE, F. X., SUN, K., and YAN, X. L. An improved partial similitude method for dynamic characteristic of rotor systems based on Levenberg-Marquardt method. Mechanical Systems and Signal Processing, 165, 108405 (2022) |
| [72] | LI, L., LUO, Z., HE, F. X., DING, Z., and SUN, K. A partial similitude method for vibration responses of rotor systems: numerical and experimental verification. International Journal of Mechanical Sciences, 208, 106696 (2021) |
| [73] | ZHAO, R. C., JIAO, Y. H., and QU, X. Q. Scaling design strategy for experimental rotor systems subjected to restricted support stiffness. Applied Mathematical Modelling, 109, 265–282 (2022) |
| [74] | JING, J., MAO, X. Y., DING, H., and CHEN, L. Q. Parametric resonance of axially functionally graded pipes conveying pulsating fluid. Applied Mathematics and Mechanics (English Edition), 45(2), 239–260 (2024) https://doi.org/10.1007/s10483-024-3083-6 |
| [75] | LI, L., LUO, Z., LIU, K. N., and ZHOU, J. L. Dynamic stiffness characteristics of aeroengine elastic support structure and its effects on rotor systems: mechanism and numerical and experimental studies. Applied Mathematics and Mechanics (English Edition), 44(2), 221–236 (2023) https://doi.org/10.1007/s10483-023-2950-8 |
| [76] | TANG, T., WANG, Y., WANG, S., ZHANG, M. Q., CHEN, Z. Y., and ZHAO, Y. H. Investigation on dynamic rubbing characteristics of a bladed rotor system with multi-mode rubbing fault. Journal of Sound and Vibration, 596, 118790 (2024) |
| [77] | LI, L., LUO, Z., WU, F. Y., HE, F. X., and SUN, K. Frequency spectrum analysis of the rotor system with bolted joint: numerical and experimental verification. Applied Mathematical Modelling, 118, 745–761 (2023) |
| [78] | ZHU, Z. M., LI, Y. Q., WEN, C. M., LUO, Z., CHEN, Y. Z., and LI, B. Rub-impact investigation of a bolted joint rotor-bearing system considering hysteresis behavior at mating interface. Mechanical Systems and Signal Processing, 224, 112072 (2025) |
| [79] | LI, L., LUO, Z., HE, F. X., ZHOU, J. L., MA, H., and LI, H. Experimental and simulation studies on similitude design method for shock responses of beam-plate coupled structure. Applied Mathematics and Mechanics (English Edition), 44(6), 917–930 (2023) https://doi.org/10.1007/s10483-023-3000-8 |
| [80] | SILVA, V. D. Mechanics and Strength of Materials, Springer, Berlin (2006) |
| [81] | EBERLE, R. and OBERGUGGENBERGER, M. A new method for estimating the bending stiffness curve of non-uniform Euler-Bernoulli beams using static deflection data. Applied Mathematical Modelling, 105, 514–533 (2022) |
| [82] | MAZZARIOL, L. M. and ALVES, M. Similarity laws of structures under impact load: geometric and material distortion. International Journal of Mechanical Sciences, 157, 633–647 (2019) |
| [83] | YAZDI, A. A. and REZAEEPAZHAND, J. Structural similitude for flutter of delaminated composite beam-plates. Composite Structures, 93, 1918–1922 (2011) |
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