Iwan, W.D., A distributed-element model for hysteresis and its steady-state dynamic response. J Appl Mech 33:4 (1966), 893–900, 10.1115/1.3625199 URL http://appliedmechanics.asmedigitalcollection.asme.org/article.aspx?articleid=1397974.
Segalman, D.J., A four-parameter iwan model for lap-type joints. J Appl Mech 72:5 (2005), 752–760, 10.1115/1.1989354 URL http://www.appliedmechanics.asmedigitalcollection.asme.org/article.aspx%3farticleid=1415458%7b%%7d5Cn http://www.prod.sandia.gov/techlib/access-control.cgi/2002/023828.pdf.
Menq, C., Bielak, J., Griffin, J.H., The influence of microslip on vibratory response, Part I: a new microslip model. Tech Rep, 2, 1986.
Yang, B.D., Menq, C.H., Characterization of 3D contact kinematics and prediction of resonant response of structures having 3D frictional constraint. J Sound Vib 217:5 (1998), 909–925.
Jenkins, G., Analysis of the stress-strain relationships in reactor grade graphite. Br J Appl Phys 13:1 (1962), 30–32, 10.1088/0508-3443/13/1/307.
Griffin, J.H., Friction damping of resonant stresses in gas turbine engine airfoils. Journal of Engineering for Power 102:2 (1980), 329–333, 10.1115/1.3230256 URL https://doi.org/10.1115/1.3230256.
Valanis, K.C., Fundamental consequences of a new intrinsic time measure: plasticity as a limit of the endochronic theory. Arch Mech Stosow 32 (1980), 171–191.
Canudas de Wit, C., Olsson, H., Astrom, K., Lischinsky, P., A new model for control of systems with friction. IEEE Trans Autom Control 40:3 (1995), 419–425, 10.1109/9.376053 URL http://ieeexplore.ieee.org/document/376053/.
Bouc, R., A mathematical model for hysteresis. Acustica 24:1 (1971), 16–25.
Wen, Y.-K., Method for random vibration of hysteretic systems. Nanotechnology 8287 (1976), 142–145, 10.1002/mop.
Brake, M., A reduced Iwan model that includes pinning for bolted joint mechanics. Nonlinear Dynam 87:2 (2017), 1335–1349, 10.1007/s11071-016-3117-2.
Petrov, E.P., Ewins, D.J., State-of-the-art dynamic analysis for non-linear gas turbine structures. Proc IME G J Aero Eng 218:3 (2004), 199–211, 10.1243/0954410041872906.
Cardona, A., Coune, T., Lerusse, A., Geradin, M., A multiharmonic method for non-linear vibration analysis. Int J Numer Methods Eng 37:9 (1994), 1593–1608.
Sanliturk, K., Ewins, D., Modelling two-dimensional friction contact and its application using harmonic balance method. J Sound Vib 193:2 (1996), 511–523, 10.1006/jsvi.1996.0299 URL http://www.sciencedirect.com/science/article/pii/S0022460X96902990.
Zucca, S., Firrone, C.M., Nonlinear dynamics of mechanical systems with friction contacts: coupled static and dynamic Multi-Harmonic Balance Method and multiple solutions. J Sound Vib 333:3 (2014), 916–926, 10.1016/j.jsv.2013.09.032.
C. Gastaldi, A. Fantetti, T. Berruti, Forced response prediction of turbine blades with flexible dampers: the impact of engineering modelling choices, Appl Sci 8 (1). doi:10.3390/app8010034. URL http://www.mdpi.com/2076-3417/8/1/34.
Lacayo, R., Pesaresi, L., Gross, J., Fochler, D., Armand, J., Salles, L., Schwingshackl, C.W., Allen, M.S., Brake, M., Nonlinear modeling of structures with bolted joints: a comparison of two approaches based on a time-domain and frequency-domain solver. Mech Syst Signal Process 114 (2019), 413–438.
Newmark, N.M., A method of computation for structural dynamics. J Eng Mech Div 85:3 (1959), 67–94.
Balaji, N.N., Brake, M.R., The surrogate system hypothesis for joint mechanics. Mech Syst Signal Process 126 (2019), 42–64, 10.1016/j.ymssp.2019.02.013.
Schwingshackl, C.W., Di Maio, D., Sever, I., Green, J.S., Modeling and validation of the nonlinear dynamic behavior of bolted flange joints. J Eng Gas Turbines Power 135:122504 (2013), 1–8, 10.1115/1.4025076.
Cigeroglu, E., An, N., Menq, C.-H., Forced response prediction of constrained and unconstrained structures coupled through frictional contacts. J Eng Gas Turbines Power, 131(022505), 2009, 1, 10.1115/1.2940356.
Petrov, E.P., Method for sensitivity analysis of resonance forced response of bladed disks with nonlinear contact interfaces. J Eng Gas Turbines Power 126 (2009), 654–662, 10.1115/1.2969094.
Zucca, S., Firrone, C.M., Gola, M., Modeling underplatform dampers for turbine blades: a refined approach in the frequency domain. JVC/Journal of Vibration and Control 19:7 (2013), 1087–1102, 10.1177/1077546312440809.
Pesaresi, L., Salles, L., Jones, A., Green, J.S., Schwingshackl, C.W., Modelling the nonlinear behaviour of an underplatform damper test rig for turbine applications. Mech Syst Signal Process 85 (2017), 662–679, 10.1016/j.ymssp.2016.09.007.
Fantetti, A., Gastaldi, C., Berruti, T., Modelling and testing flexible friction dampers: challenges and peculiarities. Exp Tech 42:4 (2018), 407–419.
Siewert, C., Panning, L., Schmidt-fellner, A., Kayser, A., The estimation of the contact stiffness for directly and indirectly coupled turbine blading. Proceedings of ASME turbo expo 2006: power for land, 2006, Sea and Air.
Schwingshackl, C.W., Petrov, E.P., Ewins, D.J., Effects of contact interface parameters on vibration of turbine bladed disks with underplatform dampers. J Eng Gas Turbines Power, 134(3), 2012, 032507, 10.1115/1.4004721 URL http://gasturbinespower.asmedigitalcollection.asme.org/article.aspx?articleid=1429804.
Schwingshackl, C.W., Measurement of friction contact parameters for nonlinear dynamic analysis. Topics in Modal Analysis I 5 (2012), 167–177, 10.1007/978-1-4614-2425-3_16.
Lavella, M., Botto, D., Gola, M.M., Design of a high-precision, flat-on-flat fretting test apparatus with high temperature capability. Wear 302:1–2 (2013), 1073–1081, 10.1016/j.wear.2013.01.066 URL https://doi.org/10.1016/j.wear.2013.01.066.
Kartal, M.E., Mulvihill, D.M., Nowell, D., Hills, D.A., Measurements of pressure and area dependent tangential contact stiffness between rough surfaces using digital image correlation. Tribol Int 44:10 (2011), 1188–1198, 10.1016/j.triboint.2011.05.025 URL https://doi.org/10.1016/j.triboint.2011.05.025.
Pesaresi, L., Armand, J., Schwingshackl, C.W., Salles, L., Wong, C., An advanced underplatform damper modelling approach based on a microslip contact model. J Sound Vib 436 (2018), 327–340, 10.1016/j.jsv.2018.08.014.
Greenwood, J., Williamson, J., Contact of nominally flat surfaces. Proc Roy Soc Lond 1442:295 (1966), 300–319.
Medina, S., Nowell, D., Dini, D., Analytical and numerical models for tangential stiffness of rough elastic contacts. Tribol Lett 49:1 (2013), 103–115, 10.1007/s11249-012-0049-y.
Hertz, H., Uber die Beruhrung fester elasticher Korper. Jnl. reine und angewandte Mathematik 92 (1882), 156–171.
Mindlin, R.D., Deresiewicz, H., Elastic spheres in contact under varying oblique forces. J Appl Mech 20 (1953), 327–344.
O'Connor, J.J., Johnson, K.L., The role of surface asperities in transmitting tangential forces between metals. Wear 6:2 (1963), 118–139, 10.1016/0043-1648(63)90125-X.
Botto, D., Lavella, M., High temperature tribological study of cobalt-based coatings reinforced with different percentages of alumina. Wear 318:1–2 (2014), 89–97, 10.1016/j.wear.2014.06.024.
Lavella, M., Botto, D., Fretting wear characterization by point contact of nickel superalloy interfaces. Wear 271:9–10 (2011), 1543–1551, 10.1016/j.wear.2011.01.064 URL https://doi.org/10.1016/j.wear.2011.01.064.
Schwingshackl, C.W., Petrov, E.P., Ewins, D.J., Measured and estimated friction interface parameters in a nonlinear dynamic analysis. Mech Syst Signal Process 28 (2012), 574–584, 10.1016/j.ymssp.2011.10.005 URL https://doi.org/10.1016/j.ymssp.2011.10.005.
Lavella, M., Contact properties and wear behaviour of nickel based superalloy rené 80. Metals, 6(7), 2016, 159, 10.3390/met6070159 URL www.mdpi.com/journal/metals.
Fouvry, S., Duó, P., Perruchaut, P., A quantitative approach of Ti-6Al-4V fretting damage: friction, wear and crack nucleation. Wear 257:9–10 (2004), 916–929, 10.1016/j.wear.2004.05.011.
Toumi, S., Fouvry, S., Salvia, M., Prediction of sliding speed and normal force effects on friction and wear rate evolution in a dry oscillating-fretting PTFE Ti-6Al-4V contact. Wear 376–377 (2017), 1365–1378, 10.1016/j.wear.2017.02.021 URL https://doi.org/10.1016/j.wear.2017.02.021.
Van Peteghem, B., Fouvry, S., Petit, J., Effect of variable normal force and frequency on fretting wear response of Ti-6Al-4V contact. Wear 271:9–10 (2011), 1535–1542, 10.1016/j.wear.2011.01.060 URL https://doi.org/10.1016/j.wear.2011.01.060.
Mohd Tobi, A.L., Sun, W., Shipway, P.H., Evolution of plasticity-based wear damage in gross sliding fretting of a Ti-6Al-4V non-conforming contact. Tribol Int 113 (2017), 474–486, 10.1016/j.triboint.2017.01.010.
Lee, H., Mall, S., Effect of dissimilar mating materials and contact force on fretting fatigue behavior of Ti-6Al-4V. Tribol Int 37:1 (2004), 35–44, 10.1016/S0301-679X(03)00112-9.
Mohd Tobi, A.L., Ding, J., Bandak, G., Leen, S.B., Shipway, P.H., A study on the interaction between fretting wear and cyclic plasticity for Ti-6Al-4V. Wear 267 (2009), 270–282, 10.1016/j.wear.2008.12.039.
Navas, C., Cadenas, M., Cuetos, J.M., de Damborenea, J., Microstructure and sliding wear behaviour of Tribaloy T-800 coatings deposited by laser cladding. Wear 260:7–8 (2006), 838–846, 10.1016/j.wear.2005.04.020.
Hager, C.H., Sanders, J.H., Sharma, S., Characterization of mixed and gross slip fretting wear regimes in Ti6Al4V interfaces at room temperature. Wear 257:1–2 (2004), 167–180, 10.1016/j.wear.2003.10.023.
Huang, X., Neu, R.W., High-load fretting of Ti-6Al-4V interfaces in point contact. Wear 265:7–8 (2008), 971–978, 10.1016/j.wear.2008.02.018.
Berthier, Y., Godet, M., Brendle, M., Velocity accommodation in friction. Wear 125 (1988), 25–38, 10.1080/10402008908981917.
Ding, J., Bandak, G., Leen, S.B., Williams, E.J., Shipway, P.H., Experimental characterisation and numerical simulation of contact evolution effect on fretting crack nucleation for Ti-6Al-4V. Tribol Int 42 (2009), 1651–1662, 10.1016/j.triboint.2009.04.040.
N. M. Everitt, J. Ding, G. Bandak, P. H. Shipway, S. B. Leen, E. J. Williams, Characterisation of fretting-induced wear debris for Ti-6Al-4 V, Weardoi:10.1016/j.wear.2008.12.032.
Kartal, M.E., Mulvihill, D.M., Nowell, D., Hills, D.A., Determination of the frictional properties of titanium and nickel alloys using the digital image correlation method. Exp Mech 51:3 (2011), 359–371, 10.1007/s11340-010-9366-y.
Kubiak, K.J., Liskiewicz, T., Mathia, T., Surface morphology in engineering applications Inuence of roughness on sliding and wear in dry fretting. Tribol Int 44 (2011), 1427–1432.
Hintikka, J., Mäntylä, A., Vaara, J., Frondelius, T., Lehtovaara, A., Stable and unstable friction in fretting contacts. Tribol Int 131 (2019), 73–82, 10.1016/j.triboint.2018.10.014.
Juoksukangas, J., Nurmi, V., Hintikka, J., Vippola, M., Lehtovaara, A., Mäntylä, A., Vaara, J., Frondelius, T., Characterization of cracks formed in large flat-on-flat fretting contact. Int J Fatigue 124 (2019), 361–370, 10.1016/j.ijfatigue.2019.03.004.
Hager, C.H., Sanders, J., Sharma, S., Voevodin, A., Gross slip fretting wear of CrCN, TiAlN, Ni, and CuNiIn coatings on Ti6Al4V interfaces. Wear 263 (2007), 430–443, 10.1016/j.wear.2006.12.085 1-6 SPEC. ISS.
Hirsch, M.R., Neu, R.W., A simple model for friction evolution infretting. Wear 301 (2013), 517–523, 10.1016/j.wear.2013.01.036.
Hintikka, J., Lehtovaara, A., Mäntylä, A., Fretting-induced friction and wear in large flat-on-flat contact with quenched and tempered steel. Tribol Int 92 (2015), 191–202, 10.1016/j.triboint.2015.06.008.
Milestone, W.D., Janeczko, J.T., Friction between steel surfaces during fretting. Wear 18 (1971), 29–40, 10.1016/0043-1648(71)90062-7.
McColl, I.R., Ding, J., Leen, S.B., Finite element simulation and experimental validation of fretting wear. Wear 256 (2004), 1114–1127, 10.1016/j.wear.2003.07.001.
Shen, Y., Zhang, D., Ge, S., Effect of fretting amplitudes on fretting wear behavior of steel wires in coal mines. Min Sci Technol 20 (2010), 803–808, 10.1016/S1674-5264(09)60285-4.
Hurricks, P.I., The mechanism of fretting - a review. Wear 15 (1970), 389–409.
Zhang, D.K., Ge, S.R., Qiang, Y.H., Research on the fatigue and fracture behavior due to the fretting wear of steel wire in hoisting rope. Wear 255 (2003), 1233–1237, 10.1016/S0043-1648(03)00161-3.
Yue, T., Abdel Wahab, M., Finite element analysis of fretting wear under variable coefficient of friction and different contact regimes. Tribol Int 107 (2017), 274–282, 10.1016/j.triboint.2016.11.044.
Fouvry, S., Liskiewicz, T., Kapsa, P., Hannel, S., Sauger, E., An energy description of wear mechanisms and its applications to oscillating sliding contacts. Wear 255:1–6 (2003), 287–298, 10.1016/S0043-1648(03)00117-0.
Meng, H.C., Ludema, K.C., Wear models and predictive equations: their form and content. Wear 181–183 (1995), 443–457.
Jareland, M.H., Csaba, G., Friction damper mistuning of a bladed disk and optimization with respect to wear. Proceedings of ASME turbo expo, vol. 2000, 2000 URL http://proceedings.asmedigitalcollection.asme.org.
Petrov, E.P., Analysis of nonlinear vibrationd upon wear-induced loss of friction dampers in tuned and mistuned bladed discs. Proceedings of ASME turbo expo 2013: turbine technical conference and exposition, 2013 URL https://proceedings.asmedigitalcollection.asme.org.
Salles, L., Blanc, L., Thouverez, F., Gouskov, A.M., Jean, P., Dynamic analysis of a bladed disk with friction and fretting-wear in blade attachments. Proceedings of ASME turbo expo 2009: power for land, sea and air, 2009, 465, 10.1115/GT2009-60151 URL http://proceedings.asmedigitalcollection.asme.org/proceeding.aspx?articleid=1647364.
Salles, L., Blanc, L., Thouverez, F., Gouskov, A.M., Dynamic analysis of fretting-wear in friction contact interfaces. Int J Solids Struct 48 (2011), 1513–1524, 10.1016/j.ijsolstr.2011.01.035.
Armand, J., Pesaresi, L., Salles, L., Schwingshackl, C.W., A multi-scale Approach for nonlinear dynamic response predictions with fretting wear. J Eng Gas Turbines Power 139:022505 (2017), 1–7, 10.1115/GT2016-56201 URL http://proceedings.asmedigitalcollection.asme.org/proceeding.aspx?doi=10.1115/GT2016-56201.
Armand, J., Pesaresi, L., Salles, L., Wong, C., Schwingshackl, C.W., A modelling approach for the nonlinear dynamics of assembled structures undergoing fretting wear. Proc. R. Soc. A, 475(2223), 2019, 20180731 URL http://creativecommons.org/licenses/by/4.0/,whichpermitsunrestricteduse,providedtheoriginalauthorandsourcearecredited.
Jin, O., Mall, S., Effects of independent pad displacement on fretting fatigue behavior of Ti-6Al-4V. Wear 253 (2002), 585–596.
Magaziner, R.S., Jain, V.K., Mall, S., Wear characterization of Ti-6Al-4V under fretting-reciprocating sliding conditions. Wear 264 (2008), 1002–1014, 10.1016/j.wear.2007.08.004.
Fouvry, S., Arnaud, P., Mignot, A., Neubauer, P., Contact size, frequency and cyclic normal force effects on Ti6Al4V fretting wear processes: an approach combining friction power and contact oxygenation. Tribol Int 113 (2017), 460–473, 10.1016/j.triboint.2016.12.049.
Ramalho, A., Miranda, J.C., The relationship between wear and dissipated energy in sliding systems. Wear 260 (2006), 361–367, 10.1016/j.wear.2005.02.121.
Huq, M.Z., Celis, J.P., Expressing wear rate in sliding contacts based on dissipated energy. Wear 252 (2002), 375–383, 10.1016/S0043-1648(01)00867-5.
Leonard, B.D., Head of the graduate program date an experimental and numerical investigation of the effect of coatings and the third body on fretting wear doctor of philosophy. Ph.D. thesis, 2012, Purdue University URL http://www.purdue.edu/policies/pages/teach%7b_%7dres%7b_%7doutreach/c%7b_%7d22.html.
Done, V., Kesavan, D., Krishna R, M., Chaise, T., Nelias, D., Semi analytical fretting wear simulation including wear debris. Tribol Int 109 (2017), 1–9, 10.1016/j.triboint.2016.12.012 arXiv:15334406.
Pearson, S.R., Shipway, P.H., Is the wear coefficient dependent upon slip amplitude in fretting? Vingsbo and Söderberg revisited. Wear(330–331), 2015, 93–102, 10.1016/j.wear.2014.11.005.
Stearns, S.D., Ahmed, N., Digital signal analysis. IEEE Transactions on Systems, Man, and Cybernetics(10), 1976, 724.
Feldman, M., Hilbert transform applications in mechanical vibration. 2011, John Wiley & Sons.
Sumali, H., Kellogg, R., Calculating damping from ring-down using hilbert transform and curve fitting. IOMAC, vol. 2011, 2011, 10.5285/78114093-E2BD-4601-8AE5-3551E62AEF2B 4th international operational modal analysis conference.
Sracic, M.W., Allen, M.S., Sumali, H., Identifying the modal properties of nonlinear structures using measured free response time histories from a scanning laser Doppler vibrometer. 30th international modal analysis conference (IMAC XXX), jacksonville, FL, 2012.
M. Jin, M. R. W. Brake, H. Song, Comparison of nonlinear system identification methods for free decay measurements with application to jointed structures, J Sound Vib 453, 268-293[Accepted].
Moore, K.J., Kurt, M., Eriten, M., McFarland, D.M., Bergman, L.A., Vakakis, A.F., Wavelet-bounded empirical mode decomposition for measured time series analysis. Mech Syst Signal Process 99 (2018), 14–29, 10.1016/j.ymssp.2017.06.005.
Guo, K., Zhang, X., Li, H., Hua, H., Meng, G., A new dynamical friction model. Int J Mod Phys B 22:08 (2008), 967–980, 10.1142/S0217979208039010 URL http://www.worldscientific.com/doi/abs/10.1142/S0217979208039010.
Ma, F., Zhang, H., Bockstedte, A., Foliente, G.C., Paevere, P., Parameter analysis of the differential model of hysteresis. J Appl Mech, 71(3), 2004, 342, 10.1115/1.1668082 URL http://appliedmechanics.asmedigitalcollection.asme.org/article.aspx?articleid=1415149.
Brake, M., An overview of constitutive models. Brake, M.R.W., (eds.)The mechanics of jointed structures, 2018, Springer International Publishing, Cham, 207–221, 10.1007/978-3-319-56818-8_14 URL https://doi.org/10.1007/978-3-319-56818-8{_}14.
Ismail, M., Ikhouane, F., Rodellar, J., The hysteresis Bouc-Wen model, a survey. Arch Comput Methods Eng 16:2 (2009), 161–188, 10.1007/s11831-009-9031-8.
