مروری بر روش‌های مدل‌سازی اتصالات پیچی در تحلیل‌های ارتعاشی

نوع مقاله: مقاله علمی ترویجی

نویسندگان

دانشگاه صنعتی مالک اشتر

چکیده

مدل‌سازی دقیق برای پیش‌بینی رفتار دینامیکی سازه‌ها یک ابزار ضروری در هر دو مرحله طراحی و عملیات است. مدل‌سازی خواص اتصال مشکل بزرگی در تحلیل‌های ارتعاشی بوده و یکی از موانع کلیدی برای پیش‌بینی دینامیک سازه‌‌ها، عدم توانایی برای دخیل کردن اثر اتصالات مکانیکی بر روی پاسخ‌های سازه‌ای است. هدف از این مقاله بررسی و مطالعه روش‌های مختلف مدل‌سازی اتصالات مکانیکی جهت استفاده در تحلیل‌های ارتعاشی است. در این راستا تلاش‌های محققین مختلف در خلال‌ سال‌های گذشته مرور شده است. عملکرد و کارآیی هر روش‌ به همراه نقاط ضعف و قوت مورد بررسی و بحث قرار گرفته است تا جایگاه و پتانسیل هر یک جهت استفاده در سازه‌های بزرگ صنعتی مورد ارزیابی قرار گیرد. با ارزیابی روش‌های مرسوم برای مدل‌سازی اتصالات، این نتیجه حاصل گردید که روش‌های مدل‌سازی سطوح نقطه-به-نقطه نظیر المان‌های فنر پتانسیل استفاده در سازه‌های بزرگ را ندارند و باید به سمت روش‌های مدل‌‌سازی پیوسته سطح‌-به-سطح با دیدگاه ماکرو نظیر لایه واسط و لایه رابط رفت.

کلیدواژه‌ها

موضوعات


[1] R.A. Ibrahim, C.L. Pettit. Uncertainties and dynamic problemsof boltedjoints andotherfasteners. Journal of Sound and Vibration 2005. 279 p. 857936.

[2] J.V.Ferreira. DynamicResponseAnalysisofStructures with Nonlinear Components, in Department of Mechanical Engineering. 1998 Imperial College of Science, Technology and Medicine.

 [3] M.B. Levine, C. White Microdynamic Analysis for Establishing Nanometric Stability Requirements of Jointed Precision Space Structures, in 19th International Modal Analysis Conference. 2001: Kissimmee, FL.

 [4] Jalali, H. Updating of Structural Joint Model Using Modal Test Results (In Persian)n Mechanical Engineering Department. Microdynamic Analysis for Establishing Nanometric StabilityRequirements of Jointed Precision Space Structures, in 19th International Modal Analysis Conference 2003, Iran University of Science and Technology: Tehran.

 [5] D.J. Segalman, et al. Modelling joint friction in structural dynamics. Structural Control and Health Monitoring. 2006. 13: p. 430-453.

[6] D.J. Segalman, et al. Handbook on Dynamics of Jointed Structures (Tech. Rep. SAND2009- 4164), Sandia National Laboratories.. 2009, Sandia National Laboratories, Albuquerque, NM.

[7] U. Parlitz, et al. Identification of pre-sliding friction dynamics. Chaos 2004. 14(2): p. 420- 430.

[8] M. Hanss, S. Oexl, and L. Gaul. Identification of a bolted-jointmodelwithfuzzyparametersloadednormal to the contact interface, Mechanics Research Communications 2002.. 29(2/3): p. 177-187.

[9] J. Montgomery. Methods for Modeling Bolts in the Bolted Joint in 38th ANSYS Conference. 2002

[10] E. Baumann. Finite element analysis of advanced composite structures containing mechanically fastened joints, Nuclear Engineering and Design. 1982. 70 p. 67-83.

[11] Ekh, J. and J. Schon. Finite element modeling and optimization of load transfer in multifastener joints using structural elements Composite Structures 2008. 82: p. 245-256.

[12] P.J. Gray, C.T. McCarthy. A global bolted joint model for finite element analysis of load distributions in multi-bolt composite joints. Composites: Part B 2010. 41 p. 317-325.

 [13] M.A.McCarthy. Bolted joints in composite aircraft structures, in COMPOSIT Workshop on Joining and Assembling Technologies. 2003: Turin, Italy.

[14] J.E. Mottershead, et al. Experience in Mechanical Joint Model Updating, in 19th International Seminar on Modal Analysis. 1994: Leuven, Belgium.

[15] J.E. Mottershead, et al. Geometric Parameters for Finite Element Model Updating of Joints and Constraints. . Mechanical Systems and Signal Processing 1996. 10(2): p. 171-182.

[16] H.Ahmadian., J.E.Mottershead, andM.I.Friswell Joint Modelling for Finite Element Model Updating,inProceedingsof14thIMAC..1996: Dearborn, Michigan. p. 591-596.

 [17] C.B. Horton, et al Finite-element model updating of the welded joints in a tubular hframe. in Proceedings of the 17th international modal analysis conference. 1999. Orlando, USA.

 [18] J.E. Mottershead, et al. Selection and updating of parameters for an aluminium space-frame model, Mechanical Systems and Signal Processing 2000. . 114(6): p. 923-944.

 [19] Mottershead, J.E. and S. James Updating Parameters for the Model of a Three Storey Aluminium Frame, in Proceedings of the 16th International Modal Analysis Conference. 1998. p. 8-11.

[20] O.A.-S Duque, et al. A methodology for the choice of the initial conditions in the model updating of welded joints using the fuzzy finite element method, Computers and Structures. 2007. 85 p. 1534-1546.

[21] C.Stocchi, P.Robinson, andS.T.Pinho A detailed finite element investigation of composite bolted joints with countersunk fasteners. . Composites: Part A 2013. 52 p. 143- 150.

 [22] J. Kim, J.-C. Yoon, and B.-S. Kang Finite element analysis and modeling of structure with bolted joints. Applied Mathematical Modelling 2007. 31: p. 895-911.

 [23] D.J. Segalman, et al. Handbook on Dynamics of Jointed Structures, SAND2009-4164. 2009. ASandia National Laboratories.

[24] Y.-D. Kwon, et al. Finite Element Modeling for Static and Dynamic Analysis of Structures with BoltedJoint.KeyEngineeringMaterials2006. 306308: p. 547-552.

 [25] Ireman, T. Three-dimensional stress analysis of bolted single-lap composite joints.. 3Composite Structutes, 1998. 43(3): p. 195-216.

 [26] McCarthy, M.A., et al. Three-dimensional finite element analysis of single-bolt, singlelap composite bolted joints: part I – model development and validation. Composite Structures 2005. Threedimensional finite element analysis of single-bolt, singlelap composite bolted joints: part I – model development and validation. Composite Structures 2005

[27] McCarthy, C.T. and M.A. McCarthy Threedimensional finite element analysis of singlebolt, singlelap composite bolted joints: part II - effects of bolthole clearance. Composite Structures, 2005. 71(2): p. 159-175.

[28] McCarthy, C.T., et al. Experiences with modelling frictionincompositeboltedjoints.Experienceswith modelling friction in composite bolted joints

[29] Padhi, G.S., M.A. McCarthy, and C.T McCarthy, BOLJAT: a tool for designing composite bolted joints using threedimensional finite element analysis. Composite Part A 2002. 33(11): p. 1573-1584.

[30] McCarthy, C.T., M.A. McCarthy, and V.P.Lawlor Progressive damage analysis of multibolt composite joints with variable bolthole clearances. Composite Part B, 2005. 36(4): p. 290-305.

 [31] Camanho, P.P. and F.L. Matthews A progressive damage model for mechanically fastened joints in composite laminates. Journal of Composite Materials 1999. 33(24): p. 2248- 2280.

[32] Vogt, F. The load distribution in bolted or riveted joints in light-alloy structures. Report No. SME3300 (or NACA TM 1135). 1944, Royal Aircraft Establishment.

[33] Tate, M.R. and S.J. Rosenfeld Preliminary investigation of the loads carries by individual bolts in bolted joints, NACA TN-1051. 1946. National Advisory Committee for Aeronautics

 [34] Rosenfeld, S.J. Analytical and experimental investigation of bolted joints, NACA TN- 1458. 1947, National Advisory Committee for Aeronautics.

[35] Nelson, W.D., B.L. Bunin, and L.J. HartSmith Critical Joints in Large Composite Aircraft Structure, NASA CR-3710. 1983. Nelson, W.D., B.L. Bunin, and L.J. HartSmith

 [36] Alley, V.L. and S.A. Leadbetter, Prediction and Measurement of Natural Vibrations of Multistage Launch Vehicles. AIAA Journal, 1963. 1(2): p. 374-379.

[37] Maloney, J.G., M.T. Shelton, and D.a. Underhill SStructural dynamic properties of tactical missile joints-phase1, GeneralDynamicsReportNo. CR6-384-945-001. 1970

[38] Maloney, J.G. and M.T. Shelton Structural dynamic properties of tactical missile joints phase 2. General Dynamics Report No. CR-6- 384-945-002. 1971.

[39] Lasker, G., et al. Structural dynamic properties of tactical missile joints - phase 3. General Dynamics Report No. CR-6-384-945- 003. 1974.

[40] Yoshimura, M. Measurement of Dynamic Rigidity and Damping Property for Simplified Joint Models and Simulation by Computer. Annals of the CIRP, 1977. 25(1): p. 193-198.

 [41] Wang, J.H. and C.M. Liou Experimental Identification of Mechanical Joint Parameters. Journal of Vibration and Acoustics, 1991. 113.

 [42] Witek, A. Stiffness and Damping Identification of Vibroisolation Pads in Machine Elements Joints. inContactmechanicsIII :third InternationalConference on Contact Mechanics, A.S. editors: M.H. Aliabadi, Editor. 1997.

[43] Wang, J. and P. Sas A Method for Identifying Parameters of Mechanical Joints. Trans. of ASME, Journal of Applied Mechanics. i1990. 57: p. 337342

 [44] Ahmadian, H. and H. Jalali dentification of bolted lap joints parameters in assembled structures. Mechanical Systems and Signal Processing 2007. 21 p. 1041-1050.

[45] Gant, F., et al. Definition and updating of simplified models of joint stiffness. International Journal of Solids and Structures 2011. 48 p. 775-784

[46] Guo,T.,etal. Alternativemethodforidentification ofthedynamicpropertiesofboltedjoints.Journalof Mechanical Science and Technology, 2012. 26(10): p. 3017-3027.

 [47] Wang, L., et al. Analysis and modeling for flexible joint interfaces under micro and macro scale. Precision Engineering. 2013. 37(7): p. 817-824.

[48] McCarthy, M.A., C.T. McCarthy, and G.S. Padhi Asimplemethodfordeterminingtheeffectsofbolt– hole clearance on load distribution in single-column multi-bolt composite joints. Composite Structures 2006. 73 p. 78-87.

[49] McCarthy, C.T.andP.J.Gray An analytical model for the prediction of load distribution in highly torqued multi-bolt composite joints. Composite Structures, 2011. 93 p. 287-298.

[50] Gray, P.J.andC.T.McCarthy An analytical model for the prediction of through-thickness stiffness in tension-loaded composite bolted joints. . Composite Structures, 2012. 94 p. 2450- 2459.

[51] Bois, C., et al. An analytical model for the strength prediction of hybrid (bolted/bonded) composite joints. Composite Structures, 2013. 97 p. 252-260.

[52] Lecomte, J., et al. An analytical model for the prediction of load distribution in multi-bolt composite joints including hole-location errors. Composite Structures, 2014. 117 p. 354-361

 [53] Liu, F., et al. An analytical joint stiffness model for load transfer analysis in highly torqued multibolt composite joints with clearances. Composite Structures, 2015. 131 p. 625-636

[54] Visser, W.J. Updating Structural Dynamics Models Using Frequency Response Data in Department of Mechanical Engineering. 1992 Imperial College of Science, Technology and Medicine: London

[55] Iwan, W.D. A Distributed-Element Model for Hysteresis and Its Steady-State Dynamic Response. ASME Journal of Applied Mechanics, 1966. 33(4): p. 893-900.

 [56] Iwan, W.D. On a class of models for the yielding behavior of continuous and composite systems. Journal of Applied Mechanics, 1967. 34(3): p. 612617

[57] Segalman, D.J. and M.J. Starr, Iwan models and their provenance in ASME International Design Engineering Technical Conference.. 2012: Chicago, IL, USA. [58] Kashani, H. Parametric Study of Nonlinear Behavior of Jenkins Element Using Harmonic Balance Method. in 11th International Conference on Vibration Problems. 2013: Lisbon, Portugal

[59] Segalman,D.J., AnInitialOverviewofIwanModeling for Mechanical Joints (Tech. Rep. SAND20010811). Sandia National Laboratories 2001: Albuquerque

[60] Gaul, L. and J. Lenz Nonlinear dynamics of structures assembled by bolted joints. Acta Mechanica, 1997. 125: p. 169-181

[61] Peng,C.-YGeneralizedModelIdentificationofLinear and Nonlinear Dynamic Systems. 1988, California Institute of Technology: Pasadena, CA

[62] Segalman, D.J., A Four-Parameter Iwan Model forLap-TypeJoints(Tech.Rep.SAND2002-3828). Sandia National Laboratories 2002: Albuquerque.

 [63] Segalman, D.J A Four-Parameter Iwan Model for Lap-Type Joints. Transactions of the ASME, Journal of Applied Mechanics, 2005. 72: p. 752-760.

[64] Allen, M.S. and R.L. Mayes Estimating the degree of nonlinearity in transient responses with zeroed early-timefastFouriertransforms. MechanicalSystemsandSignalProcessing,2010.24: p.2049-2064.

[65] Segalman, D.J. and W. Holzmann Nonlinear Response of a Lap-Type Joint using a WholeInterface Model. n 23rd International Modal Analysis Conference. 2005: Orlando, Florida.

[66] Deaner, B.J., et al Investigation of Modal Iwan Models for Structures with Bolted Joints. in 31th International Modal Analysis Conference. 2013

 [67] Songa, Y., et al. Simulation of dynamics of beam structures with bolted joints using adjusted Iwan beam elements. Journal of Sound and Vibration, 2004. 273 p. 249-276.

 [68] Shiryayeva, O.V., et al. Parameter estimation and investigation of a bolted joint model. Journal of Sound and Vibration, 2007. 307 p. 680-697. [69] Pettit,C.L.,etal. ParameterIdentificationandInvestigation of a Bolted Joint Model, (AIAA 20052378). in 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference. 2005: Austin, Texas.

 [70] Segalman, D.J. and M.J. Starr Relation ships Among Certain Joints Constitutive Models (Tech.Rep.SAND2004-4321).SandiaNationalLaboratories, 2004, Sandia National Laboratories: Albuquerque, NM.

 [71] Sanliturk, K.Y. and D.J. Ewins Modelling twodimensional friction contact and its application using harmonic balance method. Journal of Sound and Vibration, 1996. 193: p. 511-523

[72] Ouyang, H., M.J. Oldfield, and J.E. Mottershead Experimental and theoretical studies of a bolted joint excited by a torsional dynamic load. InternationalJournalofMechanicalSciences,2006.48(12): p. 1447- 1455.

[73] Ahmadian, H., H. Jalali, and F Pourahmadian, Nonlinear model identification of a frictional contact support. Mechanical Systems and Signal Processing. 2010. 24 (8): p. 2844-2854.

[74] Ahmadian,H.andM.Rajaei IdentificationofIwan distribution density function in frictional contacts. Journal of Sound and Vibration 2014. 333 p. 33823393

[75] Smallwood, D.O., D.L. Gregory, and R.G. Coleman Damping Investigations of a Simplified Frictional Shear Joint (Tech. Rep. SAND2001-0811). Sandia National Laboratories 2000. [76] Song, Y., et al. Effect of Pressure Distribution on Energy Dissipation in a Mechanical Lap Joint. AIAA Journal. 2005. 43: p. 420-425.

[77] Quinn,D.D.andD.J.Segalman Using SeriesSeries Iwan-TypeModelsforUnderstandingJointDynamics. Transactions of the ASME. Journal of Applied Mechanics, 2005. 72.

[78] Miller, J.D. and D.D. Quinn A two-sided interface modelfordissipationinstructuralsystemswithfrictional joints Journal of Sound and Vibration. 2009. 321: p. 201-219.

[79] Deshmukh, D.V., et al. Correlation of a discrete friction (Iwan) element and continuum approaches topredictinterfaceslidingbehavior. Europeanjournal of Mechanics A - Solids 2007. 26: p. 212-224.

[80] Segalman,D.J.andM.J.Starr InversionofMasing models via continuous Iwan systems. International Journal of Non-Linear Mechanics. 2008. 43: p. 74-80.

 [81] Argatov, I.I. and E.A. Butcher, On the Iwan models for lap-type bolted joints International Journal of Non-Linear Mechanics 2011. 46 p. 347-356.

 [82] Rajaei, M. and H. Ahmadian models for lap-type bolted joints Development of generalized Iwan model to simulate frictional contacts with variable normal loads. Applied Mathematical Modelling, 2014. 38(15-16): p. 4006-4018.

[83] Li, Y. and Z. Hao A six-parameter Iwan model and its application. Mechanical Systems and Signal Processing, 2016. 68-69: p. 354-365.

[84] Ahmadian, H., G.M.L. Gladwell, and F. Ismail Families of Finite Element Models for Updating Procedures. in 12th International Modal Analysis Conference. 1994.

 [85] Gladwell, G.M.L. and H. Ahmadian Generic Elements Suitable for Finite Element Model Updating. Mechanical Systems and Signal Processing. 1995. 9(6): p. 601-614.

[86] Ahmadian, H. Dynamic model identification using modal testing data. in Department of mechanicalEngineering.1994,UniversityofWaterloo: Canada.

[87] Jalali, H. Modeling and Identification of Nonlinear Parameters in Bolted Joints (In Persian), in Department of Mechanical Engineering. in Department of Mechanical Engineering. 2007, Iran University of Science and Technology: Tehran.

 [88] Ahmadian, H. and H. Jalali Generic element formulation for modelling bolted lap joints. in Mechanical Systems and Signal Processing, 2007. 21: p. 2318-2334.

 [89] Ahmadian, H., J.E. Mottershead, and M.I Friswell Parameterisation and Identification of a Rubber Seal.inProceedingsofthe16thInternationalModal Analysis Conference. in 1998.

 [90] Ratcliffe, M.J. and N.A.J. Lieven A Generic Element-based Method for Joint Identification. Mechanical Systems and Signal Processing 2000. in 14(1): p. 3-28.

[91] Titurus, B., M.I. Friswell, and L. Starek Damage Detection Using Generic Elements - Part I. Model updating Computers and Structures. in 2003. 81 p. 2273-2286

[92] Titurus, B., M.I. Friswell, and L. Starek Damage detection using generic elements - Part II. Damage detection Computers and Structures. in 2003. 81 p. 2287-2299.

[93] H. Ahmadian, G.M.L. Gladwell, and F. Ismail Parameter Selection Strategies in Finite Element Model Updating Transactions of the ASME. in Journal of Vibration and Acoustics, 1997. 119: p. 37-45.

 [94] Ahmadian, H., J.E.Mottershead, andM.I.Friswell Physical Realization of Generic Element ParametersinModelUpdating.TransactionsoftheASME, Journal of Vibration and Acoustics. 2002. 124: p. 628- 633.

 [95] Jalali, H., H. Ahmadian, and J.E. Mottershead Identification of nonlinear bolted lap-joint parameters by force-state mapping. International Journal of Solids and Structures 2007. 44 p. 8087-8105.

[96] Palmonella,M.,etal. Finiteelementmodelsofspot welds in structural dynamics - review and updating Computers and Structures 2005. 83: p. 648-661.

 [97] Goodman, R.E., R.L. Taylor, and T.L. Brekke A model for the mechanics of jointed rock. Journal of the Soil Mechanics and Foundation Division. 1968. 59 p. 99-137.

[98] Heuze, F.E. and T.G. Barbour, New models for rock joints and interfaces ASCE Journal of the Geotechnical Engineering Division. 1982. 108: p. 757-766.

[99] Wang, J.G., Y. Ichikawa, and C.F. Leung A constitutive model for rock interfaces and joints. International Journal of Rock Mechanics and Mining Sciences 2003. 40: p. 41- 53.

 [100] Gaul, L. and M. Mayer Modeling of Contact Interfaces in Built-up Structures by Zero-thickness Elements. 2004.

 [101] Mayera, M.H. and L. Gaul Segment-toSegment Contact Elements for Modelling Joint Interfaces in Finite Element Analysis Mechanical Systems and Signal Processing 2007. 21 p. 724-734.

[102] Beer, G. An isoparametric joint interface element for finite element analysis. International Journal for Numerical Methods in Engineering, 1985. 21 p. 585-600.

 [103] Riahi, A., E.R. Hammah, and J.H. Curran Limits of Applicability of the Finite Element Explicit Joint Model in the Analysis of Jointed Rock Problems. in ARMA 10- 336. 2008

 [104] Sharma, K.G. and C.S. Desai Analysis and implementation of thin-layer element for interfaces and joints. JournalofEngineeringMechanics,1992.118 p. 2442-2462.

 [105] Day, R.A. and D.M. Potts Zero thickness interface elements - numerical stability and application International Journal for Numerical and Analytical Methods in Geomechanics. 1994. 18: p. 689-708.

 [106] Potts, D.M. and L. Zdravkovic ZFinite element analysis in geotechnical engineering: Theory. 1999, Thomas Telford Limited: Great Britain.

[107] C.S.,Desai, et al., Thin-layer elements for interfaces and joints International Journal for Numerical and Analytical Methods in Geomechanics. 1984. 8(1): p. 19-43.

 [108] Zaman, M.M.-u., C.S. Desai, and E.C. Drumm Interface model for dynamic soilstructure interaction Journal of Geotechnical Engineering. 1984. 110(9): p. 1257-1273.

[109] Samadhiy, N.K., M.N. Viladkar, and M.A. AlObaydi Three-Dimensional Joint-Interface Element for Rough Undulating Major Discontinuities in Rock Masses INTERNATIONAL JOURNAL OF GEOMECHANICS. 2008. 8: p. 327-335.

 [110] Ahmadian, H., et al., Identification of bolted-joint in-terface models in International Conference on Noise and Vibration Engineering (ISMA). 2002: Katholieke University, Leuven, Belgium.

 [111] H. Ahmadian, et al Modeling and updating of large surface-to-surface joints in the AWE-MACE structure. Mechanical Systems and Signal Processing, 2006. 20 p. 868-880.

[112] H. Ahmadian, et al. Dynamic modelling of spot welds using thin-layer interface theory, in 10th International Congress on Sound and Vibration (ICSV10). 2003: Stockholm, Sweden.

[113] Bograd,S.,A.Schmidt,andL.Gaul Jointdamping prediction by thin-layer elements. in 26th International Modal Analysis Conference 2008: Orlando, FL. [114] Bograd, S., A. Schmidt, and L. Gaul Integration of Damping Properties of Assembled Structures into the Finite Element Method Using Thin-Layer Elements and the Model of Constatnt Hystersis in IMAC. 2009.

[115] Jalali, H., A. Hedayati, and H Ahmadian, Modelling mechanical interfaces experiencing microslip/slap. Inverse Problems in Science and Engineering, 2011. 19(6): p. 751-764.

 [116] M. Iranzad, H. Ahmadian Identification of nonlinear bolted lap joint models. Computers and Structures. 2012. 96-97: p. 1-8.

[117] G. N. Pande, K. G. Sharma On joint/interface elements and associated problems of illconditionin. InternationalJournalforNumericalandAnalytical Methods in Geomechanics, 1979. 3(3): p. 293-300 س.ﺷﺮاﻟﻠﻬ،ح.اﺣﻤﺪﯾﺎن،ف.ﻋﺎدل. ﺗﻮﺳﻌﻪﯾاﻟﻮیﺟﺪﯾﺪ [١١٨]

 ﺑﺮایﺑﻪ روزرﺳﺎﻧﻣﺪلاﻟﻤﺎنﻣﺤﺪوداﺗﺼﺎﻻتﭘﯿﭽوﻣﻘﺎﯾﺴﻪﮐﺎرآﯾﯽ آنﺑﺎروﯾﺮدﻻﯾﻪواﺳﻂ،ﻣﺠﻠﻪﻣﻬﻨﺪﺳﻣﺎﻧﯿﻣﺪرس.دوره۶١، ﺷﻤﺎره٣،ص ص ۵٣ ‐ ٢۴،ﺧﺮداد۵٩٣١ . ف.ﻋﺎدل، ﺑﻪروزرﺳﺎﻧﻣﺪلاﻟﻤﺎنﻣﺤﺪودﯾﺳﺎزهﻫﻮاﻓﻀﺎﯾﯽ [١١٩]

 ﺑﺎاﺳﺘﻔﺎدهازﻧﺘﺎﯾﺞﺗﺴﺖﻣﻮدال. ررﺳﺎﻟﻪدﮐﺘﺮیﻣﻬﻨﺪﺳﻫﻮاﻓﻀﺎ، ﻣﺠﺘﻤﻊداﻧﺸﺎﻫﻫﻮاﻓﻀﺎ،داﻧﺸﺎهﺻﻨﻌﺘﻣﺎﻟاﺷﺘﺮ،آﺑﺎن۵٩٣١ .

 [120] S.Shokrollahi,F.Adel Finiteelementmodelupdating of bolted lap joints implementing identification of joint affected region parameters. Journal of Theoretical and Applied Vibration and Acoustics 2(1), 64-77, 2016.

[121] F.Adel,S.Shokrollahi,M.Jamal-Omidi,H.Ahmadian A model updating method for hybrid composite/aluminum Bolted joints using modal test data. JournalofSoundandVibration396,172–185,2017. ف.ﻋﺎدل،س.ﺷﺮاﻟﻠﻬ،س.ﺧﺪاﯾﺎریآﺑﻨﺎر ﺑﻪ روزرﺳﺎﻧﻣﺪل

[١٢٢] اﻟﻤﺎنﻣﺤﺪودﺳﺎزه ﻫﺎیﺑﺰرگﻫﻮاﯾﯽﺑﺎاﺳﺘﻔﺎدهازﯾروﯾﺮدﺳﺎده، ﺷﺎﻧﺰدﻫﻤﯿﻦ ﮐﻨﻔﺮاﻧﺲ ﺑﯿﻦ اﻟﻤﻠﻠ اﻧﺠﻤﻦ ﻫﻮاﻓﻀﺎی اﯾﺮان، ﺗﻬﺮان، داﻧﺸﺎهﺻﻨﻌﺘﺧﻮاﺟﻪﻧﺼﯿﺮاﻟﺪﯾﻦﻃﻮﺳ. ٣‐ ۵اﺳﻔﻨﺪ۵٩٣١