M. Abramowitz and I. A. Stegun, Handbook of mathematical functions. T. 55, pp.17-74, 1966.

S. Adhikari and M. I. Et, Random matrix eigenvalue problems in structural dynamics, International Journal for Numerical Methods in Engineering, vol.11, issue.3, pp.562-591, 2007.
DOI : 10.1007/978-94-011-2430-0_1

H. Ahmadian and H. Jalali, Generic element formulation for modelling bolted lap joints, Mechanical Systems and Signal Processing 21.5, pp.2318-2334, 2007.
DOI : 10.1016/j.ymssp.2006.10.006

K. F. Alvin, Efficient Computation of Eigenvector Sensitivities for Structural Dynamics, AIAA Journal, vol.3511, pp.1760-1766, 1997.

N. M. Ames, Handbook on dynamics of jointed structures. Rapp. tech. Sandia National Laboratories (cf, pp.20-41, 2009.

A. L. Andrew, R. C. Et, and . Tan, Computation of mixed partial derivatives of eigenvalues and eigenvectors by simultaneous iteration, Communications in Numerical Methods in Engineering, vol.23, issue.9, pp.641-649, 1999.
DOI : 10.1145/279232.279234

H. Andriambololona, Calcul de sensibilité en dynamique, pp.95-96, 2009.

E. Balmes, High Modal Density, Curve Veering, Localization: A Different Perspective On The Structural Response, Journal of Sound and Vibration, vol.161, issue.2, pp.358-363, 1993.
DOI : 10.1006/jsvi.1993.1078

C. F. Beards, The Damping of Structural Vibration by Controlled Interfacial Slip in Joints, Journal of Vibration Acoustics Stress and Reliability in Design, vol.105, issue.3, pp.369-373, 1983.
DOI : 10.1115/1.3269115

C. Beards, J. Et, and . Williams, The damping of structural vibration by rotational slip in joints, Journal of Sound and Vibration, vol.53, issue.3, pp.333-340, 1977.
DOI : 10.1016/0022-460X(77)90418-7

A. D. Belegundu, B. G. Et, and . Yoon, Iterative methods for design sensitivity analysis, AIAA Journal, vol.97, issue.11, pp.1413-1415, 1988.
DOI : 10.2514/3.9793

C. Belly, Active washer for smart mechanical linkage, VIII ECCOMAS Thematic Conference on Smart Structures and Materials (cf, p.124, 2017.

K. W. Bibliographie-belvin, Modeling of joints for the dynamic analysis of truss structures, DC : School of Engineering et Applied Science, vol.40, pp.33-36, 1987.

R. Besançon, The encyclopedia of physics. T. p 498, p.62, 1990.

C. Blanzé, Stratégie de calcul de structures en présence de paramètres incertains. LMT (Cachan) Laboratoire de mécanique et technologie (cf, p.38, 2003.

C. Blanzé, L. Et, and . Champaney, A computational strategy for the random response of assemblies of structures, International Journal of Solids and Structures, vol.41, issue.22-23, pp.22-23, 2004.
DOI : 10.1016/j.ijsolstr.2004.05.003

C. Blanzé, P. Et, and . Rouch, ANALYSIS OF STRUCTURES WITH STOCHASTIC INTERFACES IN THE MEDIUM-FREQUENCY RANGE, Journal of Computational Acoustics, vol.10, issue.04, pp.711-729, 2005.
DOI : 10.1016/S0045-7825(03)00352-9

S. Bograd, Modeling the dynamics of mechanical joints, Mechanical Systems and Signal Processing 25, pp.2801-2826, 2011.
DOI : 10.1016/j.ymssp.2011.01.010

M. Böswald, M. Et, and . Link, Identification of non-linear joint parameters by using frequency response residuals, International Conference on Noise and Vibration Engineering, pp.3121-3140, 2004.

H. Bouaziz, Contrôle vibratoire des structures assemblées, Thèse de doct. Cotutelle entre l'Ecole Nationale des Inénieurs de Sfax et l'Ecole Centrale Paris (cf, pp.50-153, 2017.

R. Bouc, Forced vibration of mechanical systems with hysteresis, Abstract of proceedings of the fourth conference on nonlinear oscillations, p.30, 1967.

M. R. Brake, The Mechanics of Jointed Structures. Recent Research and Open Challenges for Developing Predictive Models for Structural Dynamics, p.20, 2017.

A. Caignot, Prédiction par essais virtuels de l'amortissement dans les structures spatiales, Thèse de doct., 1 vol. (117 p.) (Cf, pp.33-158, 2009.

T. M. Cameron and J. H. Griffin, An Alternating Frequency/Time Domain Method for Calculating the Steady-State Response of Nonlinear Dynamic Systems, Journal of Applied Mechanics, vol.56, issue.1, pp.149-154, 1989.
DOI : 10.1115/1.3176036

URL : https://hal.archives-ouvertes.fr/hal-01333697

C. Canudas-de-wit, A new model for control of systems with friction, IEEE Transactions on Automatic Control, vol.40, issue.3, pp.419-425, 1995.
DOI : 10.1109/9.376053

T. Chen, Design sensitivity analysis for repeated eigenvalues in structural design, AIAA Journal, vol.26, issue.12, pp.2347-2350, 1993.
DOI : 10.2514/3.48905

M. Claeys, Experiments and numerical simulations of nonlinear vibration responses of an assembly with friction joints ??? Application on a test structure named ???Harmony???, Mechanical Systems and Signal Processing 70-71, pp.1097-1116, 2016.
DOI : 10.1016/j.ymssp.2015.08.024

J. D. Collins, W. T. Et, and . Thomson, The eigenvalue problem for structural systems with statistical properties, AIAA Journal, vol.74, pp.642-648, 1969.

E. F. Crawley, A. C. Et, and . Aubert, Identification of nonlinear structural elements by force-state mapping, AIAA Journal, vol.241, issue.33, pp.155-162, 1986.

E. F. Crawley and K. J. Et, Force-state mapping identification of nonlinear joints, AIAA Journal, vol.9, issue.2, pp.1003-1010, 1987.
DOI : 10.2514/3.9213

A. Crocombe, Estimating the energy dissipated in a bolted spacecraft at resonance, Computers & Structures, vol.84, issue.5-6, pp.5-6, 2006.
DOI : 10.1016/j.compstruc.2005.09.024

P. Dahl, A solid friction model, p.29, 1968.
DOI : 10.21236/ADA041920

R. L. Dailey, Eigenvector derivatives with repeated eigenvalues, AIAA Journal, vol.27, issue.4, pp.486-491, 1989.
DOI : 10.2514/3.7211

S. Daouk, Propagation d'incertitudes à travers des modèles dynamiques d'assemblages de structures mécaniques, Thèse de doct. École Normale Supérieure de Cachan (cf, pp.38-41, 2016.

J. Didier, J. Sinou, and B. Faverjon, Nonlinear vibrations of a mechanical system with non-regular nonlinearities and uncertainties, Communications in Nonlinear Science and Numerical Simulation, vol.18, issue.11, pp.3250-3270, 2013.
DOI : 10.1016/j.cnsns.2013.03.005

URL : https://hal.archives-ouvertes.fr/hal-00831862

D. Bois, J. L. , S. Adhikari, and N. A. Lieven, On the quantification of eigenvalue curve veering : a veering index, Journal of applied mechanics 78, pp.41007-41008, 2011.

J. Ducarne, O. Thomas, and J. Deü, Placement and dimension optimization of shunted piezoelectric patches for vibration reduction, Journal of Sound and Vibration, vol.331, issue.14, pp.3286-3303, 2012.
DOI : 10.1016/j.jsv.2012.03.002

M. Eriten, Nonlinear system identification of frictional effects in a beam with a bolted joint connection, Mechanical Systems and Signal Processing 39.1-2, pp.245-264, 2013.
DOI : 10.1016/j.ymssp.2013.03.003

J. Esteban, C. A. Et, and . Rogers, Energy dissipation through joints: theory and experiments, Computers & Structures, vol.75, issue.4, pp.347-359, 2000.
DOI : 10.1016/S0045-7949(99)00096-6

D. J. Ewins, Modal testing -Theory and practice. T. ch 3, Mechanical engineering research studies (cf, pp.158-168, 1984.

J. V. Ferreira, Dynamic Response Analysis of Structures with Nonlinear Components Imperial college of science, technology et medecine, Thèse de doct, pp.34-40, 1998.

A. A. Ferri, A. C. Et, and . Bindemann, Damping and Vibration of Beams With Various Types of Frictional Support Conditions, Journal of Vibration and Acoustics, vol.1143, pp.289-296, 1992.

H. Festjens, Identification and modeling of jointed structures for dynamic analysis, pp.27-28, 2014.
URL : https://hal.archives-ouvertes.fr/tel-01081475

R. L. Fox, M. P. Et, and . Kapoor, Rates of change of eigenvalues and eigenvectors., AIAA Journal, vol.2, issue.12, pp.2426-2429, 1968.
DOI : 10.2514/3.4587

M. Friswell, The Derivatives of Repeated Eigenvalues and Their Associated Eigenvectors, Journal of Vibration and Acoustics, vol.31, issue.3, pp.390-397, 1996.
DOI : 10.1115/1.2888195

M. I. Friswell, Calculation of second and higher order eigenvector derivatives, Journal of Guidance, Control, and Dynamics, vol.18, issue.4, pp.919-921, 1995.
DOI : 10.2514/3.21170

F. Gant, Modeling and simulation strategy of aeronautical assemblies in an uncertain context " . Theses. École normale supérieure de Cachan -ENS Cachan (cf, p.41, 2011.
URL : https://hal.archives-ouvertes.fr/tel-00675741

L. Gaul, J. Et, and . Lenz, Nonlinear dynamics of structures assembled by bolted joints, Acta Mechanica, vol.32, issue.1-4, pp.169-181, 1997.
DOI : 10.1007/BF01177306

L. Gaul, J. Lenz, and D. Sachau, Active Damping of Space Structures by Contact Pressure Control in Joints???, Mechanics of Structures and Machines 26, pp.81-100, 1998.
DOI : 10.1007/978-3-642-50995-7_16

L. Gaul, R. Et, and . Nitsche, FRICTION CONTROL FOR VIBRATION SUPPRESSION, Mechanical Systems and Signal Processing 14, pp.139-150, 2000.
DOI : 10.1006/mssp.1999.1285

L. Gaul, R. Et, and . Nitsche, The Role of Friction in Mechanical Joints, Applied Mechanics Reviews, vol.54, issue.2, pp.93-106, 2001.
DOI : 10.1115/1.3097294

R. Ghanem, Modal properties of a space-frame with localized system uncertainties, 8th ASCE Specialty Conference of Probabilistic Mechanics and Structural Reliability, p.41, 2000.

R. Ghanem, D. Et, and . Ghosh, Eigenvalue analysis of a random frame, pp.341-380, 2002.

R. Ghanem, P. D. Et, and . Spanos, Polynomial Chaos in Stochastic Finite Elements, Journal of Applied Mechanics, vol.57, issue.1, pp.197-202, 1990.
DOI : 10.1115/1.2888303

R. G. Ghanem, P. D. Et, and . Spanos, Stochastic Finite Elements : A Spectral Approach, p.39, 2003.
DOI : 10.1007/978-1-4612-3094-6

M. Ghienne, C. Et, and . Blanzé, Caractérisation robuste du comportement vibratoire d'une structure en présence de paramètres incertains, Actes du 22ème Congrès Français de Mécanique, CFM 2015, p.156, 2015.

M. Ghienne, C. Blanzé, and L. Laurent, Réduction de Modèle Stochastique pour la caractérisation robuste du comportement vibratoire des structures assemblées, Actes du 13ème Colloque National en Calcul des Structures, pp.2017-156, 2017.

M. Ghienne, C. Et, and . Blanzé, A simplified method for random vibration analysis of structures with random parameters, Journal of Physics : Conference Series 744.1, pp.12174-156, 2016.
DOI : 10.1088/1742-6596/744/1/012174

D. Ghosh, R. Ghanem, and C. Petit, Stochastic buckling of a joined wing, Stochastic Dynamics Conference, p.40, 2003.

L. E. Goodman and J. H. Klumpp, Analysis of slip damping with reference to turbine blade vibration, Journal of Applied Mechanics, vol.23, pp.421-448, 1956.

J. Guillot, Modélisation et calcul des assemblages vissés. Généralités " . In : Techniques de l'ingénieur Assemblages et fixations mécaniques base documentaire : TIB177DUO.ref. article : bm5560 (cf, p.49, 2007.

L. Heller, E. Foltête, and J. Piranda, Experimental identification of nonlinear dynamic properties of built-up structures, Journal of Sound and Vibration, vol.327, issue.1-2, pp.183-196, 2009.
DOI : 10.1016/j.jsv.2009.06.008

URL : https://hal.archives-ouvertes.fr/hal-00441023

C. Hewlett-packard, The fundamentals of modal testing : application note 243-3. Application note : Hewlett-Packard Company, pp.55-56, 1986.

I. Hirai, M. Et, and . Kashiwaki, Derivatives of eigenvectors of locally modified structures, International Journal for Numerical Methods in Engineering, vol.6, issue.11, pp.1769-1773, 1977.
DOI : 10.1002/nme.1620111110

R. Ibrahim, C. Et, and . Pettit, Uncertainties and dynamic problems of bolted joints and other fasteners, Journal of Sound and Vibration, vol.279, issue.3-5, pp.3-5, 2005.
DOI : 10.1016/j.jsv.2003.11.064

W. D. Iwan, A Distributed-Element Model for Hysteresis and Its Steady-State Dynamic Response, Journal of Applied Mechanics, vol.33, issue.4, pp.393-900, 1966.
DOI : 10.1115/1.3625199

H. Jalali, H. Ahmadian, and J. E. Mottershead, Identification of nonlinear bolted lap-joint parameters by force-state mapping, International Journal of Solids and Structures, vol.44, issue.25-26, pp.25-26, 2007.
DOI : 10.1016/j.ijsolstr.2007.06.003

M. S. Jankovic, Exact nth derivatives of eigenvalues and eigenvectors, Journal of Guidance, Control, and Dynamics, vol.13, issue.2, pp.136-144, 1994.
DOI : 10.1002/nme.1620280704

Y. Karim, Caractérisation robuste de liaisons amortissantes avec dispositifs piézoélectriques pour la réduction de vibrations de structures, Theses. Conservatoire national des arts et metiers -CNAM (cf, pp.41-137, 2013.

W. Kimm, Y. Et, and . Park, Non-linear joint parameter identification by applying the force-state mapping technique in the frequency domain, Mechanical Systems and Signal Processing 8.5, pp.519-529, 1994.
DOI : 10.1006/mssp.1994.1037

P. Ladevèze, G. Puel, and T. Romeuf, Lack of knowledge in structural model validation, Computer Methods in Applied Mechanics and Engineering, vol.195, issue.37-40, pp.4697-4710, 0195.
DOI : 10.1016/j.cma.2005.10.017

I. Lee, D. Kim, and G. Jung, Natural frequency and mode shape sensitivites of damped systems : Part I, Distinct natural frequencies, In : Journal of Sound and Vibration, vol.2233, pp.399-412, 1999.

I. Lee, G. Et, and . Jung, An efficient algebraic method for the computation of natural frequency and mode shape sensitivities???Part I. Distinct natural frequencies, Computers & Structures, vol.62, issue.3, pp.429-435, 1997.
DOI : 10.1016/S0045-7949(96)00206-4

U. Lee, Dynamic Characterization of the Joints in a Beam Structure by Using Spectral Element Method, Shock and Vibration 8.6 (cf, pp.35-40, 2001.
DOI : 10.1155/2001/254020

R. Lin, Z. Wang, and M. Lim, A practical algorithm for the efficient computation of eigenvector sensitivities, Computer Methods in Applied Mechanics and Engineering, vol.130, issue.3-4, pp.3-4, 1996.
DOI : 10.1016/0045-7825(95)00929-9

K. Liu, J. Et, and . Liu, The damped dynamic vibration absorbers: revisited and new result, Journal of Sound and Vibration, vol.284, issue.3-5, pp.284-1181, 2005.
DOI : 10.1016/j.jsv.2004.08.002

E. Lund, N. Et, and . Olhoff, Shape design sensitivity analysis of eigenvalues using ???exact??? numerical differentiation of finite element matrices, Structural optimization 8.1, pp.52-59, 1994.
DOI : 10.1007/BF01742934

C. S. Manohar, A. J. Et, and . Keane, Statistics of Energy Flows in Spring-Coupled One-Dimensional Subsystems, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.346, issue.1681, pp.525-542, 1681.
DOI : 10.1098/rsta.1994.0034

L. Martini, Développement et évaluation de l'hypothèse de stabilité modal pour la variabilité du comportement vibratoire des structures minces modélisées par élélements finis, Thèse de doct, p.84, 2008.

G. Masing, Eigenspannungen und verfestigung beim messing, Proceedings of the 2nd International Congress of Applied Mechanics, pp.332-335, 1926.

H. C. Mateus, Sensitivity analysis and optimization of thin laminated structures with a nonsmooth eigenvalue based criterion, Structural optimization 14, pp.219-224, 1997.
DOI : 10.1007/978-3-642-83051-8_2

M. Mayer, L. Et, and . Gaul, Segment-to-segment contact elements for modelling joint interfaces in finite element analysis, Mechanical Systems and Signal Processing 21, pp.724-734, 2007.
DOI : 10.1016/j.ymssp.2005.10.006

M. A. Mccarthy, Measurement of Bolt Pre-load in Torqued Composite Joints, Strain, vol.32, issue.3, pp.109-112, 2005.
DOI : 10.1111/j.1475-1305.2005.00201.x

A. F. Metherell, S. V. Et, and . Diller, Instantaneous Energy Dissipation Rate in a Lap Joint???Uniform Clamping Pressure, Journal of Applied Mechanics, vol.35, issue.1, pp.123-128, 1968.
DOI : 10.1115/1.3601124

M. P. Mignolet, P. Song, and X. Wang, A stochastic Iwan-type model for joint behavior variability modeling, Journal of Sound and Vibration, vol.349, issue.43, pp.289-298, 2015.
DOI : 10.1016/j.jsv.2015.03.032

W. C. Mills-curran, Calculation of eigenvector derivatives for structures with repeated eigenvalues, AIAA Journal, vol.267, pp.867-871, 1988.

R. Mindlin, Compliance of Elastic Bodies in Contact, Journal of Applied Mechanics, vol.16, pp.259-268, 1949.
DOI : 10.1007/978-1-4613-8865-4_24

P. Nair, A. Et, and . Keane, An approximate solution scheme for the algebraic random eigenvalue problem, Journal of Sound and Vibration, vol.260, issue.1, pp.45-65, 2003.
DOI : 10.1016/S0022-460X(02)00899-4

B. Nanda, Study of the effect of bolt diameter and washer on damping in layered and jointed structures, Journal of Sound and Vibration, vol.290, issue.3-5, pp.3-5, 2006.
DOI : 10.1016/j.jsv.2005.05.027

R. B. Nelson, Simplified calculation of eigenvector derivatives, AIAA Journal, vol.149, pp.1201-1205, 1976.

E. Oberg, Machinery's Handbook. Sous la dir. de H. H. Ryffel, 2016.

I. U. Ojalvo, Efficient computation of mode-shape derivatives for large dynamic systems, AIAA Journal, vol.2510, pp.1386-1390, 1987.

M. Oldfield, H. Ouyang, and J. E. Mottershead, Simplified models of bolted joints under harmonic loading, Computers & Structures, vol.84, issue.1-2, pp.25-33, 2005.
DOI : 10.1016/j.compstruc.2005.09.007

N. Olhoff, E. Lund, and A. P. Seyranian, Sensitivity Analysis and optimization of Multiple eigenvaues in structural design problems, Structural optimization 8.4, pp.207-227, 1994.

C. Pan, T. Yamaguchi, and Y. Suzuki, Evaluation of the Bolt Axial Force in High Strength Bolted Joints by Using Strain Gauges, p.50, 2011.

M. Papadrakakis and . Et-kotsopulos, Parallel solution methods for stochastic finite element analysis using Monte Carlo simulation, Computer Methods in Applied Mechanics and Engineering, vol.168, issue.1-4, pp.305-320, 1999.
DOI : 10.1016/S0045-7825(98)00147-9

N. Perkins, C. Et, and . Mote, Comments on curve veering in eigenvalue problems, Journal of Sound and Vibration, vol.106, issue.3, pp.451-463, 1986.
DOI : 10.1016/0022-460X(86)90191-4

N. Peyret, Dissipation de l'énergie mécanique dans les assemblages : effet du frottement en sollicitation dynamique, Thèse de doct, pp.25-47, 2012.

N. Peyret, G. Chevallier, and J. Dion, Dynamic Damping in Joints: Multiscale Model Taking into Account Defects in a Nominally Plane Surface, International Journal of Applied Mechanics, vol.331, issue.1, pp.1650097-157, 2016.
DOI : 10.1006/jsvi.1996.0572

URL : https://hal.archives-ouvertes.fr/hal-01589621

R. H. Plaut, K. Et, and . Huseyin, Derivatives of eigenvalues and eigenvectors in non-self-adjoint systems., AIAA Journal, vol.98, issue.2, pp.250-251, 1973.
DOI : 10.2514/3.50271

Y. Ren, T. M. Lim, and M. K. Lim, Identification of Properties of Nonlinear Joints Using Dynamic Test Data, Journal of Vibration and Acoustics, vol.172, issue.2, pp.324-330, 1998.
DOI : 10.1115/1.2893834

B. R. Resor, M. J. Et, and . Starr, Influence of Misfit Mechanisms on Jointed Structure Response, tech. Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States) (cf, p.62, 2007.

L. C. Rogers, Derivatives of eigenvalues and eigenvectors, AIAA Journal, vol.3, issue.2, pp.943-944, 1970.
DOI : 10.2514/3.5008

L. Rouleau, Modélisation vibro-acoustique de structures sandwich munies de matériaux viscoélastiques, Thèse de doct. Conservatoire National des Arts et Métiers (cf, p.59, 2013.

C. A. Schenk and G. I. Schüller, Uncertainty Assessment of Large Finite Element Systems, Lecture Notes in Applied and Computational Mechanics. T. 24, pp.59-61, 2005.

D. J. Segalman, An initial overview of Iwan modeling for mechanical Joints, pp.30-31, 2001.
DOI : 10.2172/780307

D. J. Segalman, M. J. Et, and . Starr, Relationships among certain joint constitutive models. SAND2001-0811,Unlimited Release. Sandia National Laboratories (cf, pp.30-40, 2004.
DOI : 10.2172/919196

URL : https://www.osti.gov/servlets/purl/919196

D. J. Segalman, A four-parameter Iwan model for lap-type joints, Proposed for publication in Journal of Applied Mechanics. (Cf, pp.26-33, 2003.

M. Shinozuka and C. J. Et, Random Eigenvalue Problems in Structural Analysis, AIAA Journal, vol.104, pp.456-462, 1972.

D. O. Smallwood, D. L. Gregory, and R. G. Coleman, A three parameter constitutive model for a joint which exhibits a power law relationship between energy loss and relative displacement, Proceeding of the Shock and Vibration Symposium. Destin, FL. (cf, pp.30-40, 2001.

C. Bibliographie-soize, Stochastic modeling of uncertainties in computational structural dynamics -Recent theoretical advances, In : Journal of Sound and Vibration, vol.33210, issue.124, pp.2379-2395, 2013.

C. Soize, Stochastic Models of Uncertainties in Computational Mechanics, p.125, 2012.
DOI : 10.1061/9780784412237

URL : https://hal.archives-ouvertes.fr/hal-00749201

Y. Song, Simulation of dynamics of beam structures with bolted joints using adjusted Iwan beam elements, Journal of Sound and Vibration, vol.273, issue.1-2, pp.1-2, 2004.
DOI : 10.1016/S0022-460X(03)00499-1

Y. Song, Effect of Pressure Distribution on Energy Dissipation in a Mechanical Lap Joint, AIAA Journal, vol.23, issue.2, pp.420-425, 2005.
DOI : 10.1115/1.3607751

B. Sudret, A. D. Et, and . Kiureghian, Stochastic Finite Element Methods and Reliability : A State-of-the-Art Report, 2000.

O. Thomas, J. Ducarne, and J. Deü, Performance of piezoelectric shunts for vibration reduction, Smart Materials and Structures 21.1, pp.15008-15032, 2012.
DOI : 10.1088/0964-1726/21/1/015008

URL : https://hal.archives-ouvertes.fr/hal-01082925

E. Ungar, The status of engineering knowledge concerning the damping of builtup structures, Journal of Sound and Vibration, vol.261, issue.136, pp.141-154, 1973.

K. C. Valanis, A friction viscoplasticity without a yield surface, Archive Mech, vol.234, pp.517-551, 1970.

K. L. Van-buren, A case study to quantify prediction bounds caused by model-form uncertainty of a portal frame, Mechanical Systems and Signal Processing 50-51, pp.11-26, 2015.
DOI : 10.1016/j.ymssp.2014.05.001

B. Van-den-nieuwenhof, J. Et, and . Coyette, Modal approaches for the stochastic finite element analysis of structures with material and geometric uncertainties, Computer Methods in Applied Mechanics and Engineering, vol.192, issue.33-34, pp.3705-3729, 2003.
DOI : 10.1016/S0045-7825(03)00371-2

Y. K. Wen, Method of random vibration of hysteretic systems, Journal of the Engineering Mechanics Division 102, pp.249-263, 1976.

N. Wiener, The Homogeneous Chaos, American Journal of Mathematics, vol.60, issue.4, pp.897-936, 1938.
DOI : 10.2307/2371268

D. Xiu, G. E. Et, and . Karniadakis, Modeling uncertainty in flow simulations via generalized polynomial chaos, Journal of Computational Physics, vol.1871, pp.137-167, 2003.

L. Zadeh, Fuzzy sets as a basis for a theory of possibility " . In : Fuzzy Sets and Systems 100, pp.9-34, 1999.

C. Zang, M. Friswell, and J. Mottershead, A review of robust optimal design and its application in dynamics, Computers & structures 83, pp.315-326, 2005.
DOI : 10.1016/j.compstruc.2004.10.007