Computation and investigation of mode characteristics in nonlinear system with tuned/mistuned contact interface

Abstract

This study derived a novel computation algorithm for a mechanical system with multiple friction contact interfaces that is well-suited to the investigation of nonlinear mode characteristic of a coupling system. The procedure uses the incremental harmonic balance method to obtain the nonlinear parameters of the contact interface. Thereafter, the computed nonlinear parameters are applied to rebuild the matrices of the coupling system, which can be easily solved to calculate the nonlinear mode characteristics by standard iterative solvers. Lastly, the derived method is applied to a cycle symmetry system, which represents a shaft–disk–blade system subjected to dry friction. Moreover, this study analyzed the effects of the tuned and mistuned contact features on the nonlinear mode characteristics. Numerical results prove that the proposed method is particularly suitable for the study of nonlinear characteristics in such nonlinear systems.

Keywords

coupling vibration / nonlinear mode / original algorithm / contact interface

References

[1] Chun S B, Lee C W. Vibration analysis of shaft-bladed disk system by using substructure synthesis and assumed modes method. Journal of Sound and Vibration, 1996, 189(5): 587–608

[2] Yang C H, Huang S C. The influence of disk’s flexibility on coupling vibration of shaft–disk–blades systems. Journal of Sound and Vibration, 2007, 301(1–2): 1–17

[3] Chiu Y J, Huang S C. The influence on coupling vibration of a rotor system due to a mistuned blade length. International Journal of Mechanical Sciences, 2007, 49(4): 522–532

[4] Wang F, Zhang W. Stability analysis of a nonlinear rotating blade with torsional vibrations. Journal of Sound and Vibration, 2012, 331(26): 5755–5773

[5] She H X, Li C F, Tang Q S, The investigation of the coupled vibration in a flexible-disk blades system considering the influence of shaft bending vibration. Mechanical Systems and Signal Processing, 2018, 111: 545–569

[6] Li C F, She H X, Tang Q S, The coupling vibration characteristics of a flexible shaft-disk-blades system with mistuned features. Applied Mathematical Modelling, 2019, 67: 557–572

[7] Yao M H, Chen Y P, Zhang W. Nonlinear vibrations of blade with varying rotating speed. Nonlinear Dynamics, 2012, 68(4): 487–504

[8] Yao M H, Zhang W, Chen Y P. Analysis on nonlinear oscillations and resonant responses of a compressor blade. Acta Mechanica, 2014, 225(12): 3483–3510

[9] Cao D X, Liu B Y, Yao M H, Free vibration analysis of a pre-twisted sandwich blade with thermal barrier coatings layers. Science China Technological Sciences, 2017, 60(11): 1747–1761

[10] Yang X D, Wang S W, Zhang W, Model formulation and modal analysis of a rotating elastic uniform Timoshenko beam with setting angle. European Journal of Mechanics-A/Solids, 2018, 72: 209–222

[11] Petrov E P, Ewins D J. Effects of damping and varying contact area at blade-disk joints in forced response analysis of bladed disk assemblies. Journal of Turbomachinery, 2006, 128(2): 403–410

[12] Petrov E P. Explicit finite element models of friction dampers in forced response analysis of bladed disks. Journal of Engineering for Gas Turbines and Power, 2008, 130(2): 022502

[13] Ciğeroğlu E, Özgüven H N. Nonlinear vibration analysis of bladed disks with dry friction dampers. Journal of Sound and Vibration, 2006, 295(3–5): 1028–1043

[14] Georgiades F, Peeters M, Kerschen G, Modal analysis of a nonlinear periodic structure with cyclic symmetry. AIAA Journal, 2009, 47(4): 1014–1025

[15] Peeters M, Viguié R, Sérandour G, et al. Nonlinear normal modes, Part II: Toward a practical computation using numerical continuation techniques. Mechanical Systems and Signal Processing, 2009, 23(1): 195–216

[16] Zucca S, Firrone C M, Gola M M. Numerical assessment of friction damping at turbine blade root joints by simultaneous calculation of the static and dynamic contact loads. Nonlinear Dynamics, 2012, 67(3): 1943–1955

[17] Lassalle M, Firrone C M. A parametric study of limit cycle oscillation of a bladed disk caused by flutter and friction at the blade root joints. Journal of Fluids and Structures, 2018, 76: 349–366

[18] Li C F, Shen Z C, Zhong B F, Study on the nonlinear characteristics of a rotating flexible blade with dovetail interface feature. Shock and Vibration, 2018, 2018: 4923898

[19] Joannin C, Thouverez F, Chouvion B. Reduced-order modelling using nonlinear modes and triple nonlinear modal synthesis. Computers & Structures, 2018, 203: 18–33

[20] Joannin C, Chouvion B, Thouverez F, Nonlinear modal analysis of mistuned periodic structures subjected to dry friction. Journal of Engineering for Gas Turbines and Power, 2016, 138(7): 072504

[21] Joannin C, Chouvion B, Thouverez F, A nonlinear component mode synthesis method for the computation of steady-state vibrations in non-conservative systems. Mechanical Systems and Signal Processing, 2017, 83: 75–92

[22] Petrov E P, Ewins D J. Advanced modeling of underplatform friction dampers for analysis of bladed disk vibration. Journal of Turbomachinery, 2007, 129(1): 143–150

[23] Firrone C M, Zucca S, Gola M M. The effect of underplatform dampers on the forced response of bladed disks by a coupled static/dynamic harmonic balance method. International Journal of Non-linear Mechanics, 2011, 46(2): 363–375

[24] Berruti T, Firrone C M, Gola M M. A test rig for noncontact traveling wave excitation of a bladed disk with underplatform dampers. Journal of Engineering for Gas Turbines and Power, 2011, 133(3): 032502

[25] Zhang D, Fu J, Zhang Q, An effective numerical method for calculating nonlinear dynamics of structures with dry friction: Application to predict the vibration response of blades with underplatform dampers. Nonlinear Dynamics, 2017, 88(1): 223–237

[26] Pesaresi L, Salles L, Jones A, Modelling the nonlinear behaviour of an underplatform damper test rig for turbine applications. Mechanical Systems and Signal Processing, 2017, 85: 662–679

[27] Pesaresi L, Armand J, Schwingshackl C W, An advanced underplatform damper modelling approach based on a microslip contact model. Journal of Sound and Vibration, 2018, 436: 327–340

[28] Zucca S, Firrone C M. Nonlinear dynamics of mechanical systems with friction contacts: Coupled static and dynamic Multi-Harmonic Balance Method and multiple solutions. Journal of Sound and Vibration, 2014, 333(3): 916–926

Acknowledgements

This research was supported by the National Natural Science Foundation of China (Grant No. 51575093) and the Fundamental Research Funds for the Central Universities (Grant Nos. N180313008, N170308028, and N170302001).Open AccessƒThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.ƒThe images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.ƒTo view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

RIGHTS & PERMISSIONS

2019 The Author(s) 2019. This article is published with open access at link.springer.com and journal.hep.com.cn