Nonlinear vibrations of rectangular plates with different boundary conditions: theory and experiments, Computers & Structures, vol.82, issue.31-32, pp.2587-2605, 2004. ,
DOI : 10.1016/j.compstruc.2004.03.077
Nonlinear Vibrations and Stability of Shells and Plates, 2008. ,
DOI : 10.1017/CBO9780511619694
Nonlinear vibrations of a simply supported rectangular metallic plate subjected to transverse harmonic excitation in the presence of a one-to-one internal resonance, Nonlinear Dynamics, vol.30, issue.1, pp.1-28, 2002. ,
DOI : 10.1023/A:1020362725706
SPATIO-TEMPORAL CHAOS AND SOLITONS EXHIBITED BY VON K??RM??N MODEL, International Journal of Bifurcation and Chaos, vol.12, issue.07, pp.1465-1513, 2002. ,
DOI : 10.1142/S021812740200525X
A family of conservative finite difference schemes for the dynamical von Karman plate equations, Numerical Methods for Partial Differential Equations, vol.194, issue.1, pp.193-216, 2008. ,
DOI : 10.1002/num.20260
Numerical Sound Synthesis Finite Difference Schemes and Simulation in Musical Acoustics, 2009. ,
Percussion Synthesis Based on Models of Nonlinear Shell Vibration, IEEE Transactions on Audio, Speech, and Language Processing, vol.18, issue.4, pp.872-880, 2010. ,
DOI : 10.1109/TASL.2009.2029710
On the numerical computation of nonlinear normal modes for reduced-order modelling of conservative vibratory systems, Mechanical Systems and Signal Processing, vol.36, issue.2, pp.520-539, 2013. ,
DOI : 10.1016/j.ymssp.2012.10.016
URL : https://hal.archives-ouvertes.fr/hal-00772317
Observation of Wave Turbulence in Vibrating Plates, Physical Review Letters, vol.100, issue.23, p.234504, 2008. ,
DOI : 10.1103/PhysRevLett.100.234504
URL : https://hal.archives-ouvertes.fr/hal-00326634
Nonlinear forced vibration of damped plates by an asymptotic numerical method, Computers & Structures, vol.87, issue.23-24, pp.1508-1515, 2009. ,
DOI : 10.1016/j.compstruc.2009.07.005
URL : https://hal.archives-ouvertes.fr/hal-00494489
Time-domain simulation of damped impacted plates. I. Theory and experiments, The Journal of the Acoustical Society of America, vol.109, issue.4, pp.1422-1432, 2001. ,
DOI : 10.1121/1.1354200
URL : https://hal.archives-ouvertes.fr/hal-00830699
Nonlinear vibrations and chaos in gongs and cymbals, Acoustical Science and Technology, vol.26, issue.5, pp.403-409, 2005. ,
DOI : 10.1250/ast.26.403
URL : https://hal.archives-ouvertes.fr/hal-01135295
Nonlinear oscillations of a fluttering plate, AIAA J, vol.4, pp.1267-1275, 1966. ,
Non-Linear vibrations and chaos in harmonically excited rectangular plates with one-to-one internal resonance, Nonlinear Dynamics, vol.25, issue.5, pp.433-460, 1993. ,
DOI : 10.1007/BF00053690
On free vibration of a functionally graded piezoelectric rectangular plate, Acta Mechanica, vol.32, issue.3-4, pp.207-216, 2002. ,
DOI : 10.1007/BF01177452
Nonlinear Analysis of Plates, 1980. ,
Influence of large amplitudes on free flexural vibrations of rectangular elastic plates, J. Appl. Mech, vol.23, 1956. ,
Piezoelectric coupling in energy-harvesting fluttering flexible plates: linear stability analysis and conversion efficiency, Journal of Fluids and Structures, vol.27, issue.8, pp.1357-1375, 2011. ,
DOI : 10.1016/j.jfluidstructs.2011.04.008
Auto2000: Continuation and Bifurcation Software for Ordinary Differential Equations (with HomCont), Canada, 2002. ,
Weak Turbulence for a Vibrating Plate: Can One Hear a Kolmogorov Spectrum?, Physical Review Letters, vol.97, issue.2, p.25503, 2006. ,
DOI : 10.1103/PhysRevLett.97.025503
Nonlinear bending and vibration of symmetrically laminated orthotropic elliptical plate with simply supported edge, Acta Mechanica, vol.62, issue.2, pp.155-170, 1988. ,
DOI : 10.1007/BF01194348
Electromagneto-thermo-mechanical behaviors of conductive circular plate subject to time-dependent magnetic fields, Acta Mechanica, vol.91, issue.4, pp.99-116, 2010. ,
DOI : 10.1007/s00707-009-0196-x
Nonlinear normal modes of a full-scale aircraft, 29th International Modal Analysis Conference, 2011. ,
Development of a three-dimensional viscous aeroelastic solver for nonlinear panel flutter, Fluids 2000 Conference and Exhibit, pp.497-527, 2002. ,
DOI : 10.2514/6.2000-2337
Vibrations and Waves in Continuous Mechanical Systems, p.232, 2007. ,
DOI : 10.1002/9780470518434
Nonlinear normal modes, Part I: A useful framework for the structural dynamicist, Mechanical Systems and Signal Processing, vol.23, issue.1, pp.170-194, 2009. ,
DOI : 10.1016/j.ymssp.2008.04.002
URL : https://hal.archives-ouvertes.fr/hal-01357931
Nonlinear Flexural Vibrations of a Clamped Circular Plate, Journal of Applied Mechanics, vol.39, issue.4, pp.1050-1054, 1972. ,
DOI : 10.1115/1.3422827
Nonlinearity, chaos, and the sound of shallow gongs, The Journal of the Acoustical Society of America, vol.86, issue.6, pp.2439-2443, 1989. ,
DOI : 10.1121/1.398451
Vibration of Plates, 1993. ,
Vibration analysis of rectangular plates with general elastic boundary supports, Journal of Sound and Vibration, vol.273, issue.3, pp.619-635, 2003. ,
DOI : 10.1016/S0022-460X(03)00562-5
Analytical solutions for asymmetric periodic motions to chaos in a hardening Duffing oscillator, Nonlinear Dynamics, vol.22, issue.2, pp.417-438, 2013. ,
DOI : 10.1007/s11071-012-0725-3
A consistent deduction of von K???rm???n-type plate theories from three-dimensional nonlinear continuum mechanics, Acta Mechanica, vol.37, issue.1, pp.1-17, 2001. ,
DOI : 10.1007/BF01182348
Are There Waves in Elastic Wave Turbulence?, Physical Review Letters, vol.100, issue.23, p.234505, 2008. ,
DOI : 10.1103/PhysRevLett.100.234505
URL : https://hal.archives-ouvertes.fr/hal-00712175
Fourier analysis of wave turbulence in a thin elastic plate, The European Physical Journal B, vol.2, issue.4, pp.537-545, 2010. ,
DOI : 10.1140/epjb/e2010-00197-y
URL : https://hal.archives-ouvertes.fr/hal-00712159
Non-linear dynamic thermomechanical behaviour of shape memory alloys, Journal of Intelligent Material Systems and Structures, vol.23, issue.14, pp.1593-1611, 2012. ,
DOI : 10.1177/1045389X12448446
URL : https://hal.archives-ouvertes.fr/hal-00838865
CHARACTERIZING THE DYNAMIC RESPONSE OF A THERMALLY LOADED, ACOUSTICALLY EXCITED PLATE, Journal of Sound and Vibration, vol.196, issue.5, pp.635-658, 1996. ,
DOI : 10.1006/jsvi.1996.0506
Linear and Nonlinear Structural Mechanics, 2004. ,
DOI : 10.1002/9783527617562
Superstructure in the bifurcation set of the Duffing equation, Physics Letters A, vol.107, issue.8, pp.351-355, 1985. ,
DOI : 10.1016/0375-9601(85)90687-5
Nonlinear normal modes, Part II: Toward a practical computation using numerical continuation techniques, Mechanical Systems and Signal Processing, vol.23, issue.1, pp.195-216, 2009. ,
DOI : 10.1016/j.ymssp.2008.04.003
Nonlinear vibrations of simply-supported plates by the p-version finite element method, Finite Elements in Analysis and Design, vol.41, issue.9-10, pp.911-924, 2005. ,
DOI : 10.1016/j.finel.2004.12.002
GEOMETRICAL NON-LINEAR, STEADY STATE, FORCED, PERIODIC VIBRATION OF PLATES, PART I: MODEL AND CONVERGENCE STUDIES, Journal of Sound and Vibration, vol.226, issue.5, pp.955-983, 1999. ,
DOI : 10.1006/jsvi.1999.2306
GEOMETRICAL NON-LINEAR, STEADY STATE, FORCED, PERIODIC VIBRATION OF PLATES, PART II: STABILITY STUDY AND ANALYSIS OF MULTI-MODAL RESPONSE, Journal of Sound and Vibration, vol.226, issue.5, pp.985-1010, 1999. ,
DOI : 10.1006/jsvi.1999.2336
Nonlinear Vibrations of Plates: An Update of Recent Research Developments, Applied Mechanics Reviews, vol.49, issue.10S, pp.55-62, 1996. ,
DOI : 10.1115/1.3101977
Geometrically nonlinear flexural vibrations of plates: In-plane boundary conditions and some symmetry properties, Journal of Sound and Vibration, vol.315, issue.3, pp.569-590, 2008. ,
DOI : 10.1016/j.jsv.2008.04.014
Non-linear vibrations of free-edge thin spherical shells: modal interaction rules and 1:1:2 internal resonance, International Journal of Solids and Structures, vol.42, issue.11-12, pp.3339-3373, 2005. ,
DOI : 10.1016/j.ijsolstr.2004.10.028
URL : https://hal.archives-ouvertes.fr/hal-00830689
Vibrations and Stability, 2003. ,
DOI : 10.1007/978-3-662-10793-5
Transition scenario to turbulence in thin vibrating plates, Journal of Sound and Vibration, vol.331, issue.2, pp.412-433, 2011. ,
DOI : 10.1016/j.jsv.2011.09.016
Transition to chaotic vibrations for harmonically forced perfect and imperfect circular plates, International Journal of Non-Linear Mechanics, vol.46, issue.1, pp.234-246, 2011. ,
DOI : 10.1016/j.ijnonlinmec.2010.09.004
Hardening/softening behaviour in non-linear oscillations of structural systems using non-linear normal modes, Journal of Sound and Vibration, vol.273, issue.1-2, pp.77-101, 2004. ,
DOI : 10.1016/j.jsv.2003.04.005
Asymptotic non-linear normal modes for large-amplitude vibrations of continuous structures, Computers & Structures, vol.82, issue.31-32, pp.2671-2682, 2004. ,
DOI : 10.1016/j.compstruc.2004.09.003
NON-LINEAR NORMAL MODES (NNMs) AND THEIR APPLICATIONS IN VIBRATION THEORY: AN OVERVIEW, Mechanical Systems and Signal Processing, vol.11, issue.1, pp.3-22, 1997. ,
DOI : 10.1006/mssp.1996.9999
URL : https://hal.archives-ouvertes.fr/hal-01354037
Influence of Large Amplitudes on Flexural Vibrations of Elastic Plates, Zeitschrift für Angewandte Mathematik und Mechanik 41, pp.501-510, 1961. ,
DOI : 10.1002/zamm.19610411204
Local and global bifurcations in parametrically excited vibrations of nearly square plates, Series in Nonlinear Dynamics, pp.199-220, 1991. ,
DOI : 10.1016/0020-7462(91)90052-U
Wave turbulence and intermittency, Physica D: Nonlinear Phenomena, vol.152, issue.153, pp.152-153, 2001. ,
DOI : 10.1016/S0167-2789(01)00192-0
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.522.8443
Energy spectrum for stochastic oscillations of surface of a liquid, J. Appl. Mech. Tech. Phys, vol.8, issue.37, 1967. ,
Turbulence of Capillary Waves, Physical Review Letters, vol.76, issue.18, pp.3320-3323, 1996. ,
DOI : 10.1103/PhysRevLett.76.3320
Energy spectrum for stochastic oscillations of surface of a liquid, Sov. Phys. Dokl, vol.11, pp.881-883, 1967. ,
Freely Decaying Weak Turbulence for Sea Surface Gravity Waves, Physical Review Letters, vol.89, issue.14, p.89, 2002. ,
DOI : 10.1103/PhysRevLett.89.144501
Observation of Gravity-Capillary Wave Turbulence, Physical Review Letters, vol.98, issue.9, pp.98-094503, 2007. ,
DOI : 10.1103/PhysRevLett.98.094503
URL : https://hal.archives-ouvertes.fr/hal-00134723
A weak turbulence theory for incompressible magnetohydrodynamics, Journal of Plasma Physics, vol.63, issue.5, pp.447-488, 2000. ,
DOI : 10.1017/S0022377899008284
Anisotropic Turbulence of Shear-Alfv??n Waves, The Astrophysical Journal, vol.564, issue.1, pp.49-52, 2002. ,
DOI : 10.1086/338791
Classical character of turbulence in a quantum liquid, Physical Review B, vol.61, issue.2, pp.1410-1420, 2000. ,
DOI : 10.1103/PhysRevB.61.1410
Decay of superfluid turbulence at a very low temperature: The radiation of sound from a Kelvin wave on a quantized vortex, Physical Review B, vol.64, issue.13, 2001. ,
DOI : 10.1103/PhysRevB.64.134520
Weak Turbulence for a Vibrating Plate: Can One Hear a Kolmogorov Spectrum?, Physical Review Letters, vol.97, issue.2, pp.97-025503, 2006. ,
DOI : 10.1103/PhysRevLett.97.025503
Geometrically nonlinear flexural vibrations of plates: In-plane boundary conditions and some symmetry properties, Journal of Sound and Vibration, vol.315, issue.3, pp.315-569, 2008. ,
DOI : 10.1016/j.jsv.2008.04.014
Observation of Wave Turbulence in Vibrating Plates, Physical Review Letters, vol.100, issue.23, p.234504, 2008. ,
DOI : 10.1103/PhysRevLett.100.234504
URL : https://hal.archives-ouvertes.fr/hal-00326634
Are There Waves in Elastic Wave Turbulence?, Physical Review Letters, vol.100, issue.23, p.234505, 2008. ,
DOI : 10.1103/PhysRevLett.100.234505
URL : https://hal.archives-ouvertes.fr/hal-00712175
Nonlinear dynamics of flexural wave turbulence, Physical Review E, vol.84, issue.6, p.66607, 2011. ,
DOI : 10.1103/PhysRevE.84.066607
URL : https://hal.archives-ouvertes.fr/hal-00712156
Nonstationary Wave Turbulence in an Elastic Plate, Physical Review Letters, vol.107, issue.3, p.34501, 2011. ,
DOI : 10.1103/PhysRevLett.107.034501
Wave turbulence in vibrating plates: The effect of damping, EPL (Europhysics Letters), vol.102, issue.3, 2013. ,
DOI : 10.1209/0295-5075/102/30002
URL : https://hal.archives-ouvertes.fr/hal-01134801
Weak and Strong Wave Turbulence Spectra for Elastic Thin Plate, Physical Review Letters, vol.110, issue.10, 2013. ,
DOI : 10.1103/PhysRevLett.110.105501
Role of dissipation in flexural wave turbulence: From experimental spectrum to Kolmogorov-Zakharov spectrum, Physical Review E, vol.89, issue.6, 2014. ,
DOI : 10.1103/PhysRevE.89.062925
URL : https://hal.archives-ouvertes.fr/hal-01009490
Free Flexural Vibration of Initially Imperfect Thin Plates with Large Elastic Amplitudes, ZAMM - Zeitschrift f??r Angewandte Mathematik und Mechanik, vol.27, issue.1, pp.423-428, 1976. ,
DOI : 10.1002/zamm.19760560905
Non-linear vibrations of imperfect free-edge circular plates and shells, European Journal of Mechanics - A/Solids, vol.28, issue.3, pp.500-515, 2009. ,
DOI : 10.1016/j.euromechsol.2008.11.005
URL : https://hal.archives-ouvertes.fr/hal-01089556
Transition to chaotic vibrations for harmonically forced perfect and imperfect circular plates, International Journal of Non-Linear Mechanics, vol.46, issue.1, pp.234-246, 2011. ,
DOI : 10.1016/j.ijnonlinmec.2010.09.004
Transition scenario to turbulence in thin vibrating plates, Journal of Sound and Vibration, vol.331, issue.2, pp.412-433, 2012. ,
DOI : 10.1016/j.jsv.2011.09.016
A family of conservative finite difference schemes for the dynamical von Karman plate equations, Numerical Methods for Partial Differential Equations, vol.194, issue.1, pp.193-216, 2008. ,
DOI : 10.1002/num.20260
Geometric Numerical Integration, Structure- Preserving Schemes for Ordinary Differential Equations, 2006. ,
Nonstationary wave turbulence, Journal of Nonlinear Science, vol.25, issue.4, pp.457-480, 1991. ,
DOI : 10.1007/BF02429849
Non-stationary spectra of local wave turbulence, Physica D: Nonlinear Phenomena, vol.184, issue.1-4, pp.64-85, 2003. ,
DOI : 10.1016/S0167-2789(03)00213-6
URL : https://hal.archives-ouvertes.fr/hal-00000319
Non-stationary regimes of surface gravity wave turbulence, JETP Letters, vol.97, issue.8, pp.459-465, 2013. ,
DOI : 10.1134/S0021364013080055
Quasiadiabatic Decay of Capillary Turbulence on the Charged Surface of Liquid Hydrogen, Physical Review Letters, vol.93, issue.7, pp.93-074501, 2004. ,
DOI : 10.1103/PhysRevLett.93.074501
Decay of capillary wave turbulence, Physical Review E, vol.85, issue.6, p.66311, 2012. ,
DOI : 10.1103/PhysRevE.85.066311
URL : https://hal.archives-ouvertes.fr/hal-00717642
Decay of capillary turbulence on the surface of a viscous liquid, JETP Letters, vol.83, issue.2, pp.58-63, 2006. ,
DOI : 10.1134/S0021364006020032
Effects of initial geometric imperfections on dynamic behaviour of rectangular plates, Nonlinear Dynam, pp.165-181, 1992. ,
Nonlinear dynamics of rectangular plates: investigation of modal interaction in free and forced vibrations, Acta Mechanica, vol.26, issue.1, pp.213-232, 2014. ,
DOI : 10.1007/s00707-013-0931-1
URL : https://hal.archives-ouvertes.fr/hal-01134793
Time-domain simulation of damped impacted plates. I. Theory and experiments, The Journal of the Acoustical Society of America, vol.109, issue.4, pp.1422-1432, 2001. ,
DOI : 10.1121/1.1354200
URL : https://hal.archives-ouvertes.fr/hal-00830699
Numerical Sound Synthesis: Finite Difference Schemes and Simulation in Musical Acoustics, 2009. ,
DOI : 10.1002/9780470749012
Statistics of power injection in a plate set into chaotic vibration, The European Physical Journal B, vol.66, issue.3, pp.399-407, 2008. ,
DOI : 10.1140/epjb/e2008-00431-3
URL : https://hal.archives-ouvertes.fr/hal-00326633
Linear versus nonlinear response of a forced wave turbulence system, Physical Review E, vol.82, issue.4, p.46211, 2010. ,
DOI : 10.1103/PhysRevE.82.046211
URL : https://hal.archives-ouvertes.fr/hal-00838873
Non-linear behaviour of free-edge shallow spherical shells: Effect of the geometry, International Journal of Non-Linear Mechanics, vol.41, issue.5, pp.41-678, 2006. ,
DOI : 10.1016/j.ijnonlinmec.2005.12.004
Effect of imperfections and damping on the type of non-linearity of circular plates and shallow spherical shells, Math. Probl. Eng, p.2008, 2008. ,
Theory and experiments for nonlinear vibrations of imperfect rectangular plates with free edges, Journal of Sound and Vibration, vol.332, issue.14, pp.3564-3588, 2013. ,
DOI : 10.1016/j.jsv.2013.02.015
Nonlinear vibrations of rectangular plates with different boundary conditions: theory and experiments, Computers and Structures, vol.82, pp.31-32, 2004. ,
A TECHNIQUE FOR THE SYSTEMATIC CHOICE OF ADMISSIBLE FUNCTIONS IN THE RAYLEIGH???RITZ METHOD, Journal of Sound and Vibration, vol.224, issue.3, pp.519-539, 1999. ,
DOI : 10.1006/jsvi.1999.2198
Nonlinear vibrations of a simply supported rectangular metallic plate subjected to transverse harmonic excitation in the presence of a one-to-one internal resonance, Nonlinear Dynamics, vol.30, issue.1, pp.1-28, 2002. ,
DOI : 10.1023/A:1020362725706
Simulation numérique d'un réverbérateurréverbérateurà plaque, 2009. ,
Natural frequencies of rectangular plates using characteristic orthogonal polynomials in rayleigh-ritz method, Journal of Sound and Vibration, vol.102, issue.4, pp.493-499, 1985. ,
DOI : 10.1016/S0022-460X(85)80109-7
A family of conservative finite difference schemes for the dynamical von Karman plate equations, Numerical Methods for Partial Differential Equations, vol.194, issue.1, pp.193-216, 2008. ,
DOI : 10.1002/num.20260
Numerical sound synthesis, 2008. ,
DOI : 10.1002/9780470749012
URL : https://hal.archives-ouvertes.fr/hal-01354779
Modeling of Complex Geometries and Boundary Conditions in Finite Difference/Finite Volume Time Domain Room Acoustics Simulation, IEEE Transactions on Audio, Speech, and Language Processing, vol.21, issue.7, pp.1524-1533, 2013. ,
DOI : 10.1109/TASL.2013.2256897
Large scale physical modeling synthesis, Proceedings of the Stockholm Musical Acoustics Conference/Sound and Music Computing Conference, 2013. ,
Observation of Wave Turbulence in Vibrating Plates, Physical Review Letters, vol.100, issue.23, p.234504, 2008. ,
DOI : 10.1103/PhysRevLett.100.234504
URL : https://hal.archives-ouvertes.fr/hal-00326634
THE VIBRATION OF A RECTANGULAR PLATE WITH EDGES ELASTICALLY RESTRAINED AGAINST ROTATION, The Quarterly Journal of Mechanics and Applied Mathematics, vol.12, issue.1, pp.29-42, 1959. ,
DOI : 10.1093/qjmam/12.1.29
Modélisation et simulation numérique d'un piano par modéles physiques, 2012. ,
Modeling and simulation of a grand piano, The Journal of the Acoustical Society of America, vol.134, issue.1, p.648, 2013. ,
DOI : 10.1121/1.4809649
URL : https://hal.archives-ouvertes.fr/hal-00768234
On the use of finite differences for musical synthesis. application to plucked string instruments, Journal d'Acoustique, vol.5, issue.2, pp.181-211, 1992. ,
Numerical simulations of piano strings. I. A physical model for a struck string using finite difference methods, The Journal of the Acoustical Society of America, vol.95, issue.2, pp.1112-1118, 1994. ,
DOI : 10.1121/1.408459
Nonlinear oscillations of a fluttering plate Non-linear vibrations and chaos in harmonically excited rectangular plates with one-toone internal resonance, AIAA Journal Nonlinear Dynamics, vol.4, issue.4, pp.1267-1275, 1966. ,
On free vibration of a functionally graded piezoelectric rectangular plate, Acta Mechanica, vol.32, issue.3-4, pp.3-4, 2002. ,
DOI : 10.1007/BF01177452
Influence of large amplitudes on free flexural vibrations of rectangular elastic plates, Journal of Applied Mechanics, vol.23, pp.532-540, 1956. ,
???ber die partiellen Differenzengleichungen der mathematischen Physik, Mathematische Annalen, vol.98, issue.6, pp.32-74, 1928. ,
DOI : 10.1007/BF01448839
The vibration of rectangular plates treated using simply supported plate functions in the Rayleigh???Ritz method, The Journal of the Acoustical Society of America, vol.69, issue.S1, pp.87-87, 1981. ,
DOI : 10.1121/1.386053
NATURAL FREQUENCIES OF RECTANGULAR PLATES USING A SET OF STATIC BEAM FUNCTIONS IN RAYLEIGH-RITZ METHOD, Journal of Sound and Vibration, vol.189, issue.1, pp.81-87, 1996. ,
DOI : 10.1006/jsvi.1996.0006
Piezoelectric coupling in energy-harvesting fluttering flexible plates: linear stability analysis and conversion efficiency, Journal of Fluids and Structures, vol.27, issue.8, pp.1357-1375, 2011. ,
DOI : 10.1016/j.jfluidstructs.2011.04.008
Rectangular, thin plate vibration: A modal approach, Master's thesis, 2010. ,
Dynamics of the wave turbulence spectrum in vibrating plates: A numerical investigation using a conservative finite difference scheme, Physica D: Nonlinear Phenomena, vol.280, issue.281, pp.280-281, 2014. ,
DOI : 10.1016/j.physd.2014.04.008
URL : https://hal.archives-ouvertes.fr/hal-01135260
Nonlinear plate vibrations: A modal approach with application to cymbals and gongs Bibliography 151 30. , Sound synthesis of gongs obtained from nonlinear thin plates vibrations: comparison between a modal approach and a finite difference scheme, Proceedings of Acoustics 2012 Proceedings of the Stockholm Musical Acoustics Conference/Sound and Music Computing Conference, 2012. ,
Nonlinear dynamics of rectangular plates: investigation of modal interaction in free and forced vibrations, Acta Mechanica, vol.26, issue.1, pp.213-232, 2014. ,
DOI : 10.1007/s00707-013-0931-1
URL : https://hal.archives-ouvertes.fr/hal-01134793
Weak Turbulence for a Vibrating Plate: Can One Hear a Kolmogorov Spectrum?, Physical Review Letters, vol.97, issue.2, pp.97-025503, 2006. ,
DOI : 10.1103/PhysRevLett.97.025503
Sound synthesis by physical modeling with Modalys, Proceedings of the International Symposium on Musical Acoustics, p.1195 ,
ARBITRARY PRECISION FREQUENCIES OF A FREE RECTANGULAR THIN PLATE, Journal of Sound and Vibration, vol.230, issue.3, pp.521-539, 2000. ,
DOI : 10.1006/jsvi.1999.2629
Nonlinear bending and vibration of symmetrically laminated orthotropic elliptical plate with simply supported edge, Acta Mechanica, vol.62, issue.2, pp.155-170, 1988. ,
DOI : 10.1007/BF01194348
Vibrations of a Beam Carrying a Concentrated Mass, Journal of Applied Mechanics, vol.40, issue.3, pp.821-822, 1973. ,
DOI : 10.1115/1.3423102
Free vibration analysis of the completely free rectangular plate by the method of superposition, Journal of Sound and Vibration, vol.57, issue.3, pp.437-447, 1978. ,
DOI : 10.1016/0022-460X(78)90322-X
A review of the superposition method for computing free vibration eigenvalues of elastic structures, Computers & Structures, vol.104, issue.105, pp.27-37, 2012. ,
DOI : 10.1016/j.compstruc.2012.02.018
Wave motion in elastic solids, 1975. ,
Transverse vibrations of orthotropic rectangular plates with thickness varying in two directions and with edges elastically restrained against rotation, Fibre Science and Technology, vol.14, issue.4, pp.311-317, 1981. ,
DOI : 10.1016/0015-0568(81)90022-1
Vibrations and waves in continuous mechanical systems, 2007. ,
DOI : 10.1002/9780470518434
Geometric numerical integration, structure-preserving schemes for ordinary differential equations, 2006. ,
Numerical methods for scientists and engineers, second edition, 1973. ,
Wave turbulence in vibrating plates: The effect of damping, EPL (Europhysics Letters), vol.102, issue.3, p.30002, 2013. ,
DOI : 10.1209/0295-5075/102/30002
URL : https://hal.archives-ouvertes.fr/hal-01134801
AN EXACT SERIES SOLUTION FOR CALCULATING THE EIGENFREQUENCIES OF ORTHOTROPIC PLATES WITH COMPLETELY FREE BOUNDARY, Journal of Sound and Vibration, vol.244, issue.5 ,
DOI : 10.1006/jsvi.2000.3541
Die Eigenschwingungen und Klangfiguren der vierseitig freien rechteckigen Platte, Ingenieur-Archiv, vol.21, issue.5-6, pp.5-6, 1953. ,
DOI : 10.1007/BF00535853
On the flexural vibration of rectangular plates approached by using simple polynomials in the Rayleigh-Ritz method, Journal of Sound and Vibration, vol.143, issue.3, pp.379-394, 1990. ,
DOI : 10.1016/0022-460X(90)90730-N
Dynamics response of cantilevers with attached masses, no. EMS, pp.695-706, 1975. ,
Nonlinear Flexural Vibrations of a Clamped Circular Plate, Journal of Applied Mechanics, vol.39, issue.4, pp.1050-1054, 1972. ,
DOI : 10.1115/1.3422827
Modèle temporel pour la simulation numerique de plaques vibrantes. application a la synthèse sonore, 1997. ,
Time-domain simulation of damped impacted plates. II. Numerical model and results, The Journal of the Acoustical Society of America, vol.109, issue.4, pp.1433-1447, 2001. ,
DOI : 10.1121/1.1354201
URL : https://hal.archives-ouvertes.fr/hal-00830699
Theory of elasticity, 1986. ,
Vibration of plates, 1993. ,
FREE VIBRATIONS OF BEAMS WITH GENERAL BOUNDARY CONDITIONS, Journal of Sound and Vibration, vol.237, issue.4, pp.709-725, 2000. ,
DOI : 10.1006/jsvi.2000.3150
Vibration frequencies for a uniform beam with one end spring-hinged and subjected to a translational restraint at the other end, Journal of Sound and Vibration, vol.48, issue.4, pp.565-568, 1976. ,
DOI : 10.1016/0022-460X(76)90559-9
Computational methods in structural dynamics, Sijthoff and Noordhoff, 1980. 62. , Fundamentals of vibration, 2001. ,
Role of dissipation in flexural wave turbulence: From experimental spectrum to Kolmogorov-Zakharov spectrum, Physical Review E, vol.89, issue.6, 2008. ,
DOI : 10.1103/PhysRevE.89.062925
URL : https://hal.archives-ouvertes.fr/hal-01009490
The finite difference method in partial differential equations, 1980. ,
Bounded eigenvalues of fully clamped and completely free rectangular plates, Master's thesis, The University of Waikato, 2007. ,
Transient vibration analysis of a completely free plate using modes obtained by Gorman's superposition method, Journal of Sound and Vibration, vol.329, issue.10, pp.1890-1900, 2010. ,
DOI : 10.1016/j.jsv.2009.11.029
Are There Waves in Elastic Wave Turbulence?, Physical Review Letters, vol.100, issue.23, p.234505, 2008. ,
DOI : 10.1103/PhysRevLett.100.234505
URL : https://hal.archives-ouvertes.fr/hal-00712175
MOSAIC: A Framework for Modal Synthesis, Computer Music Journal, vol.17, issue.1, pp.45-56, 1993. ,
DOI : 10.2307/3680569
Asymmetric non-linear forced vibrations of free-edge circular plates. Part II: experiments, Journal of Sound and Vibration, vol.265, issue.5, pp.1075-1101, 2003. ,
DOI : 10.1016/S0022-460X(02)01564-X
URL : https://hal.archives-ouvertes.fr/hal-00830696
Theoretical and experimental modal analysis of nonlinear vibrating stuctures using Nonlinear Normal Modes, 2010. ,
Viscous damping identification in linear vibration, Journal of Sound and Vibration, vol.303, issue.35, pp.475-500, 2007. ,
A note on vibrations of generally restrained beams, Journal of Sound and Vibration, vol.130, issue.3, pp.453-465, 1989. ,
DOI : 10.1016/0022-460X(89)90069-2
Time-domain modeling and numerical simulation of a kettledrum, The Journal of the Acoustical Society of America, vol.105, issue.6, pp.3545-3562, 1999. ,
DOI : 10.1121/1.424679
Theorie der Transversalschwingungen einer quadratischen Platte mit freien R??ndern, Annalen der Physik, vol.64, issue.4, pp.737-786, 1909. ,
DOI : 10.1002/andp.19093330403
The normal modes of a nonlinear n-degree-of-freedom systems Of nonlinear vibrations of systems with many degrees of freedom, Journal of Applied Mechanics Advances in Applied Mechanics, vol.30, issue.9, pp.7-14, 1962. ,
A technique for simulating the vibrations of strings with a digital computer, 1969. ,
Subharmonic responses in harmonically excited rectangular plates with one-to-one internal resonance, Chaos, Solitons and Fractals, vol.8, issue.4, pp.479-498, 1997. ,
Computational electrodynamics, Artech House Advances in computational electrodynamics, Artech House, 1995. ,
Geometrically nonlinear flexural vibrations of plates: In-plane boundary conditions and some symmetry properties, Journal of Sound and Vibration, vol.315, issue.3, pp.569-590, 2008. ,
DOI : 10.1016/j.jsv.2008.04.014
Fourier series, 1965. ,
A 3d multi-plate environment for sound synthesis, Proceedings of the 16th International Digital Audio Effects Conference, 2013. ,
Nonlinear normal modes for damped geometrically nonlinear systems: Application to reduced-order modelling of harmonically forced structures, Journal of Sound and Vibration, vol.298, issue.4-5, pp.958-981, 2006. ,
DOI : 10.1016/j.jsv.2006.06.032
Reduced-order models for large-amplitude vibrations of shells including in-plane inertia, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.21-24, pp.2030-2045, 2008. ,
DOI : 10.1016/j.cma.2008.01.002
Transition scenario to turbulence in thin vibrating plates, Journal of Sound and Vibration, vol.331, issue.2, pp.412-433, 2012. ,
DOI : 10.1016/j.jsv.2011.09.016
Asymptotic non-linear normal modes for large-amplitude vibrations of continuous structures, Computers & Structures, vol.82, issue.31-32, pp.2671-2682, 2004. ,
DOI : 10.1016/j.compstruc.2004.09.003
NON-LINEAR NORMAL MODES (NNMs) AND THEIR APPLICATIONS IN VIBRATION THEORY: AN OVERVIEW, Mechanical Systems and Signal Processing, vol.11, issue.1, pp.3-22, 1997. ,
DOI : 10.1006/mssp.1996.9999
URL : https://hal.archives-ouvertes.fr/hal-01354037
Festigkeitsprobleme im maschinenbau, Encyklopadie der Mathematischen Wissenschaften, vol.4, pp.311-385, 1910. ,
DYNAMIC ANALYSIS OF GENERALLY SUPPORTED BEAMS USING FOURIER SERIES, Journal of Sound and Vibration, vol.196, issue.3, pp.285-293, 1996. ,
DOI : 10.1006/jsvi.1996.0484
Computing virtual acoustics using the 3D Finite Difference time domain method and Kepler architecture gpus, Proceedings of the Stockholm Musical Acoustics Conference/Sound and Music Computing Conference, 2013. ,
LINEAR DAMPING MODELS FOR STRUCTURAL VIBRATION, Journal of Sound and Vibration, vol.215, issue.3, pp.547-569, 1998. ,
DOI : 10.1006/jsvi.1998.1709
Influence of Large Amplitudes on Flexural Vibrations of Elastic Plates, ZAMM - Zeitschrift f??r Angewandte Mathematik und Mechanik, vol.56, issue.12, pp.501-510, 1961. ,
DOI : 10.1002/zamm.19610411204
Numerical solutions of intial boundary value problems involving maxwell's equations in isotropic media, IEEE Transactions of Antennas and Propagation, vol.14, pp.302-307, 1966. ,
Weak and Strong Wave Turbulence Spectra for Elastic Thin Plate, Physical Review Letters, vol.110, issue.10, p.105501, 2013. ,
DOI : 10.1103/PhysRevLett.110.105501
Kolmogorov spectra of turbulence 1: Wave turbulence, Series in Nonlinear Dynamics, 1992. ,