“Multi-scale simulation of nonlinear thin-shell sound with wave turbulence” by Cirio, Qu, Drettakis, Grinspun and Zheng
Conference:
Type:
Entry Number: 110
Title:
- Multi-scale simulation of nonlinear thin-shell sound with wave turbulence
Session/Category Title: Sounds Good!
Presenter(s)/Author(s):
Moderator(s):
Abstract:
Thin shells — solids that are thin in one dimension compared to the other two — often emit rich nonlinear sounds when struck. Strong excitations can even cause chaotic thin-shell vibrations, producing sounds whose energy spectrum diffuses from low to high frequencies over time — a phenomenon known as wave turbulence. It is all these nonlinearities that grant shells such as cymbals and gongs their characteristic “glinting” sound. Yet, simulation models that efficiently capture these sound effects remain elusive.We propose a physically based, multi-scale reduced simulation method to synthesize nonlinear thin-shell sounds. We first split nonlinear vibrations into two scales, with a small low-frequency part simulated in a fully nonlinear way, and a high-frequency part containing many more modes approximated through time-varying linearization. This allows us to capture interesting nonlinearities in the shells’ deformation, tens of times faster than previous approaches. Furthermore, we propose a method that enriches simulated sounds with wave turbulent sound details through a phenomenological diffusion model in the frequency domain, and thereby sidestep the expensive simulation of chaotic high-frequency dynamics. We show several examples of our simulations, illustrating the efficiency and realism of our model.
References:
1. Steven S. An, Theodore Kim, and Doug L. James. 2008. Optimizing Cubature for Efficient Integration of Subspace Deformations. In ACM Transactions on Graphics (Proceedings of SIGGRAPH Asia 2008) (SIGGRAPH Asia ’08). ACM, New York, NY, USA, 165:1–165:10. Google ScholarDigital Library
2. David Baraff and Andrew Witkin. 1998. Large steps in cloth simulation. In Proceedings of SIGGRAPH (SIGGRAPH ’98). ACM, New York, NY, USA, 43–54. Google ScholarDigital Library
3. Jernej Barbič and Doug L. James. 2005. Real-Time Subspace Integration for St. Venant-Kirchhoff Deformable Models. ACM Transactions on Graphics (Proceedings of SIGGRAPH 2005) 24, 3 (2005), 982–990. Google ScholarDigital Library
4. K.J. Bathe. 2007. Finite Element Procedures. Prentice-Hall, Boston, Mass.Google Scholar
5. Miklos Bergou, Max Wardetzky, David Harmon, Denis Zorin, and Eitan Grinspun. 2006. A Quadratic Bending Model for Inextensible Surfaces. In Proceedings of the Eurographics Symposium on Geometry Processing (SGP ’06). Eurographics Association, Aire-la-Ville, Switzerland, Switzerland, 227–230. http://dl.acm.org/citation.cfm?id=1281957.1281987 Google ScholarDigital Library
6. Stefan Bilbao. 2008. A family of conservative finite difference schemes for the dynamical von Karman plate equations. Numerical Methods for Partial Differential Equations 24, 1 (Jan. 2008), 193–216.Google ScholarCross Ref
7. S. Bilbao. 2010. Percussion Synthesis Based on Models of Nonlinear Shell Vibration. IEEE Transactions on Audio, Speech, and Language Processing 18, 4 (May 2010), 872–880.Google ScholarCross Ref
8. R. Bridson, S. Marino, and R. Fedkiw. 2003. Simulation of clothing with folds and wrinkles. In Proceedings of the 2003 ACM SIGGRAPH/Eurographics symposium on Computer animation (SCA ’03). Eurographics Association, Aire-la-Ville, Switzerland, Switzerland, 28–36. http://dl.acm.org/citation.cfm?id=846276.846281 Google ScholarDigital Library
9. Olivier Cadot, M Ducceschi, T Humbert, Benjamin Miquel, N Mordant, C Josserand, and Cyril Touzé. 2016. Wave turbulence in vibrating plates. In Handbook of applications of chaos theory, Charilaos Skiadas Christos H. Skiadas (Ed.). Chapman and Hall/CRC.Google Scholar
10. Jeffrey N. Chadwick, Steven S. An, and Doug L. James. 2009. Harmonic shells: a practical nonlinear sound model for near-rigid thin shells. ACM Transactions on Graphics (Proceedings of SIGGRAPH Asia 2009) 28, 5 (2009). Google ScholarDigital Library
11. Antoine Chaigne, Cyril Touzé, and Olivier Thomas. 2005. Nonlinear vibrations and chaos in gongs and cymbals. Acoustical Science and Technology 26, 5 (2005), 403–409.Google ScholarCross Ref
12. Dominique Chapelle and Klaus-Jurgen Bathe. 2010. The Finite Element Analysis of Shells – Fundamentals (2nd ed. 2011 edition ed.). Springer, Berlin; New York.Google ScholarCross Ref
13. Chuen-Yuan Chia. 1980. Nonlinear analysis of plates. McGraw-Hill International Book Company.Google Scholar
14. Gabriel Cirio, Dingzeyu Li, Eitan Grinspun, Miguel A. Otaduy and Changxi Zheng. 2016. Crumpling Sound Synthesis. ACM Trans. Graph. 35, 6 (Nov. 2016), 181:1–181:11. Google ScholarDigital Library
15. Lothar Cremer and Manfred Heckl. 2013. Structure-borne sound: structural vibrations and sound radiation at audio frequencies. Springer Science & Business Media.Google Scholar
16. Michele Ducceschi, Olivier Cadot, Cyril Touzé, and Stefan Bilbao. 2014. Dynamics of the wave turbulence spectrum in vibrating plates: A numerical investigation using a conservative finite difference scheme. Physica D: Nonlinear Phenomena 280–281, Supplement C (July 2014), 73–85.Google Scholar
17. M. Ducceschi and C. Touzé. 2015. Modal approach for nonlinear vibrations of damped impacted plates: Application to sound synthesis of gongs and cymbals. Journal of Sound and Vibration 344, Supplement C (May 2015), 313–331.Google Scholar
18. S. Dyachenko, A. C. Newell, A. Pushkarev, and V. E. Zakharov. 1992. Optical turbulence: weak turbulence, condensates and collapsing filaments in the nonlinear Schrödinger equation. Physica D: Nonlinear Phenomena 57, 1 (June 1992), 96–160. Google ScholarDigital Library
19. Gustavo Düring, Christophe Josserand, and Sergio Rica. 2006. Weak turbulence for a vibrating plate: can one hear a Kolmogorov spectrum? Physical Review Letters 97, 2 (July 2006), 025503.Google ScholarCross Ref
20. Éric Falcon, Claude Laroche, and Stéphan Fauve. 2007. Observation of Gravity-Capillary Wave Turbulence. Physical Review Letters 98, 9 (March 2007), 094503.Google Scholar
21. G. E. Falkovich and A. V. Shafarenko. 1991. Nonstationary wave turbulence. Journal of Nonlinear Science 1, 4 (Dec. 1991), 457–480.Google ScholarCross Ref
22. J. R. Fienup. 1982. Phase retrieval algorithms: a comparison. Applied Optics 21, 15 (Aug. 1982), 2758–2769.Google ScholarCross Ref
23. Akash Garg, Eitan Grinspun, Max Wardetzky, and Denis Zorin. 2007. Cubic Shells. In Proceedings of ACM SIGGRAPH/Eurographics Symposium on Computer Animation. Eurographics Association, 91–98. Google ScholarDigital Library
24. Yotam Gingold, Adrian Secord, Jefferson Y. Han, Eitan Grinspun, and Denis Zorin. 2004. A Discrete Model for Inelastic Deformation of Thin Shells. Technical Report. Courant Institute of Mathematical Sciences, New York University.Google Scholar
25. Eitan Grinspun, Anil N. Hirani, Mathieu Desbrun, and Peter Schröder. 2003. Discrete Shells. In Proceedings of ACM SIGGRAPH/Eurographics Symposium on Computer Animation. Eurographics Association, 62–67. Google ScholarDigital Library
26. T. Humbert, C. Josserand, C. Touzé, and O. Cadot. 2016. Phenomenological model for predicting stationary and non-stationary spectra of wave turbulence in vibrating plates. Physica D: Nonlinear Phenomena 316, Supplement C (Feb. 2016), 34–42.Google Scholar
27. Christophe Josserand, Yves Pomeau, and Sergio Rica. 2006. Self-similar Singularities in the Kinetics of Condensation. Journal of Low Temperature Physics 145, 1–4 (Nov. 2006), 231–265.Google ScholarCross Ref
28. Theodore Kim, Nils Thürey, Doug James, and Markus Gross. 2008. Wavelet Turbulence for Fluid Simulation. ACM Transactions on Graphics (Proceedings of SIGGRAPH 2008) (2008), 50:1–50:6. Google ScholarDigital Library
29. P. Krysl, S. Lall, and J. E. Marsden. 2001. Dimensional model reduction in non-linear finite element dynamics of solids and structures. Internat. J. Numer. Methods Engrg. 51, 4 (June 2001), 479–504.Google ScholarCross Ref
30. C. E. Leith. 1967. Diffusion Approximation to Inertial Energy Transfer in Isotropic Turbulence. The Physics of Fluids 10, 7 (July 1967), 1409–1416.Google ScholarCross Ref
31. F. Moussaoui and R. Benamar. 2002. Nonlinear vibrations of shell type structures: A review with bibliography. Journal of Sound and Vibration 255, 1 (Aug. 2002), 161–184.Google ScholarCross Ref
32. Sam L. Musher, Alexander M. Rubenchik, and Vladimir E. Zakharov. 1995. Weak Langmuir turbulence. Physics Reports 252, 4 (Feb. 1995), 177–274.Google ScholarCross Ref
33. Rahul Narain, Tobias Pfaff, and James F. O’Brien. 2013. Folding and Crumpling Adaptive Sheets. ACM Transactions on Graphics (Proceedings of SIGGRAPH 2013) 32, 4 (2013), 51:1–51:8. Google ScholarDigital Library
34. Ali H. Nayfeh and Dean T. Mook. 1995. Nonlinear Oscillations. Wiley-VCH, New York.Google Scholar
35. Alan C. Newell, Sergey Nazarenko, and Laura Biven. 2001. Wave turbulence and intermittency. Physica D: Nonlinear Phenomena 152–153 (May 2001), 520–550.Google Scholar
36. James F. O’Brien, Perry R. Cook, and Georg Essl. 2001. Synthesizing sounds from physically based motion. In Proceedings of SIGGRAPH (SIGGRAPH ’01). ACM, New York, NY, USA, 529–536. Google ScholarDigital Library
37. James F. O’Brien, Chen Shen, and Christine M. Gatchalian. 2002. Synthesizing sounds from rigid-body simulations. In The ACM SIGGRAPH 2002 Symposium on Computer Animation. ACM Press, 175–181. Google ScholarDigital Library
38. Ken Perlin. 1985. An Image Synthesizer. In Proceedings of SIGGRAPH (SIGGRAPH ’85). ACM, New York, NY, USA, 287–296. Google ScholarDigital Library
39. John R. Pierce and Scott A. Van Duyne. 1997. A passive nonlinear digital filter design which facilitates physics-based sound synthesis of highly nonlinear musical instruments. The Journal of the Acoustical Society of America 101, 2 (Feb. 1997), 1120–1126.Google ScholarCross Ref
40. Nick Rasmussen, Duc Quang Nguyen, Willi Geiger, and Ronald Fedkiw. 2003. Smoke Simulation for Large Scale Phenomena. ACM Trans. Graph. 22, 3 (July 2003), 703–707. Google ScholarDigital Library
41. Sandra Rugonyi and Klaus-Jürgen Bathe. 2003. An evaluation of the Lyapunov characteristic exponent of chaotic continuous systems. Internat. J. Numer. Methods Engrg. 56, 1 (2003), 145–163.Google ScholarCross Ref
42. Ahmed A Shabana. 2012. Theory of vibration: Volume II: discrete and continuous systems. Springer Science & Business Media.Google Scholar
43. L. Shen and Y. J. Liu. 2006. An adaptive fast multipole boundary element method for three-dimensional acoustic wave problems based on the Burton-Miller formulation. Computational Mechanics 40, 3 (Oct. 2006), 461–472.Google Scholar
44. Breannan Smith, Danny M. Kaufman, Etienne Vouga, Rasmus Tamstorf, and Eitan Grinspun. 2012. Reflections on Simultaneous Impact. ACM Transactions on Graphics (Proceedings of SIGGRAPH 2012) 31, 4 (July 2012), 106:1–106:12. Google ScholarDigital Library
45. Demetri Terzopoulos, John Platt, Alan Barr, and Kurt Fleischer. 1987. Elastically deformable models. In Proceedings of SIGGRAPH. ACM, 205–214. Google ScholarDigital Library
46. C. Touzé, S. Bilbao, and O. Cadot. 2012. Transition scenario to turbulence in thin vibrating plates. Journal of Sound and Vibration 331, 2 (Jan. 2012), 412–433.Google ScholarCross Ref
47. W. F. Vinen. 2000. Classical character of turbulence in a quantum liquid. Physical Review B 61, 2 (Jan. 2000), 1410–1420.Google ScholarCross Ref
48. Pascal Volino, Nadia Magnenat-Thalmann, and Francois Faure. 2009. A simple approach to nonlinear tensile stiffness for accurate cloth simulation. ACM Transactions on Graphics (Proceedings of SIGGRAPH 2009) 28, 4 (2009), 105:1–105:16. Google ScholarDigital Library
49. Stephen Wiggins. 2003. Introduction to Applied Nonlinear Dynamical Systems and Chaos (2nd edition ed.). Springer, New York.Google Scholar
50. Alan Wolf, Jack B. Swift, Harry L. Swinney, and John A. Vastano. 1985. Determining Lyapunov exponents from a time series. Physica D: Nonlinear Phenomena 16, 3 (July 1985), 285–317.Google ScholarCross Ref
51. V. E. Zakharov and N. N. Filonenko. 1967. Energy Spectrum for Stochastic Oscillations of the Surface of a Liquid. Soviet Physics Doklady 11 (April 1967), 881. http://adsabs.harvard.edu/abs/1967SPhD…11/…881ZGoogle Scholar
52. Vladimir E. Zakharov, Victor S. L’vov, and Gregory Falkovich. 1992. Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer.Google Scholar
53. Changxi Zheng and Doug L. James. 2010. Rigid-body Fracture Sound with Precomputed Soundbanks. ACM Trans. Graph. 29, 4 (July 2010). Google ScholarDigital Library
54. Changxi Zheng and Doug L. James. 2011. Toward High-Quality Modal Contact Sound. ACM Transactions on Graphics (Proceedings of SIGGRAPH 2011) 30, 4 (Aug. 2011). Google ScholarDigital Library
