Tonal Innovation Center (TONIC) hosted the second annual International Musical Instruments Seminar in Joensuu, Finland on 14th September- 16th September 2011.

1. Virtual Guitar Pasi Marttila COMSOL Oy +358 9 2510 4051

2. Outline Introduction Tuning Fork: Validate and Verify Virtual Guitar: Design and Innovate Conclusion Q & A

3. Introduction What do we understand with ”Virtual Guitar”? Synthesizer vs. Physical simulation model Modeling and simulation Some key terms: model, simulation model and analysis What information these models can tell us? What else we can do with such virtual models?

4. Let’s Tune Our Instruments First! http://www.ultimate-guitar-tuner.com/standard-tuning/

5. Tuning Fork: Validate and Verify Classical example: Tuning Fork Eigenmode analysis to verify the design: Here we compute the fundamental eigenfrequency and eigenmode of a tuning fork. When correctly designed, the tuning fork vibrates at 440 Hz, a frequency known as standard concert pitch. Forced responce analysis to hear the tone and fine tune the model: Here we excite the structure with a known frequency and study the response of the structure both visually and tonally. Acoustic-structure interaction: Final step is to study the acoustic pressure field generated by the vibrations of the prongs.

6. Tuning Fork: Validate and Verify Tuning Fork: Eigenmode analysis Analysis is used to verify the dimensions of the fork (length of the prongs) to meet the design parameters ... to verify the material properties for this specific design (mechanical) ... to verify the numerical accuracy ... to validate the chosen simulation method so that we can rely on the results

7. Tuning Fork: Validate and Verify In frequency response analysis the structure will be excited with harmonical load at given frequency Air domain over the fork has also been simulated while acoustical pressure field created by vibrating prongs can be identified

8. Tuning Fork: Validate and Verify And it sounds like this ...

9. Virtual Guitar http://www.publicdomainpictures.net/

10. Virtual Guitar: Design and Innovate Three different analysis has been made Eigenfrequency analysis to find the eigenmodes and shapes of the guitar Forced responce analysis with acoustic coupling to study the structural and acoustic response of the guitar in a harmonically loaded case Time-dependent analysis to produce the sound of the guitar while all the dynamics and damping effects has been taken into account Simulation assumptions: We imitate the vibrating string by applying the surface load to the bridge Vibration has been modeled as a damped time-dependent load case

11. Virtual Guitar: Eigenfrequency Analysis First guitar model: Eigenfrequency and mode analysis Only structural effects are in the simulation With such model we can find eigenfrequencies (resonance) of the structure As an output we get both the actual frequencies and the shape how structure vibrates

12. Virtual Guitar: Eigenfrequency Analysis

13. Virtual Guitar: Frequency Response Analysis Second guitar model: Forced response analysis in frequency domain Both acoustical and structural effects are in the simulation With such model we can simulate single frequencies and frequency sweeps while certain components are harmonically loaded (bridge in this case) As an output we get both the structucal response of the guitar and the acoustic pressure field of the simulated air domain

14. Virtual Guitar: Frequency Response Analysis

15. Virtual Guitar: Frequency Response Analysis

16. Virtual Guitar: Transient analysis Third guitar model: Time-dependent simulation with sampling frequency in audio range (22050Hz in this case) Both acoustical and structural effects are in the simulation Critical design parameters for simulation are material settings including the damping effects With such model we can study how guitar structure behaves and what kind of sound it produces Simulations are ”time hungry” and requires lots of wall clock time to run

17. Virtual Guitar: Transient analysis

18. Virtual Guitar: Transient analysis

19. Virtual Guitar: Transient analysis And it sounds like this ...

20. Conclusion Modern simulation and modeling techniques are useful while designing musical instruments Material knowledge acts key role when producing reliable simulation results Eigenfrequency and frequency response analysis can be run in minutes while full transient simulations might take days Machinery is already available, computing power is cheap and simulation knowledgeistaughtat universities = Virtual Guitar is reality today! THANK YOU!

21. Q & A