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Extensions to the 2D Waveguide Mesh for Modeling Thin Plate Vibrations
Chris Chafe
Center for Computer Research in Music and Acoustics (CCRMA) Stanford University
The 2D Waveguide Mesh computes realistic-sounding simulations of struck plates. The early 90’s saw an initial flurry of development on the model but it hasn’t yet found the greater musical use that its interesting sonic qualities suggest are possible.
The overall project goal is a synthesis instrument for real-time music performance and studio composition.
Rectilinear mesh using 4-port scattering junctions and unit delays (Julius Smith)
Adding edge filters and reflections, Synthesis Toolkit (12x12 nodes)
Enhancements which will be described (32x8 nodes)
Swinging in space simulated by wavefield synthesis
Synthesis Toolkit's Mesh2D class
The C++ implementation has been ported to many computer music languages (ChucK, SuperCollider, Csound, etc.)
Mesh size originally limited to 12x12 (probably for historical reasons related to limited CPU)
One input (dynamically adjustable location but non-interpolated ie., quantized to an integer X/Y coordinate position)
One output (upper right corner)
Excitation
noteOn
method adds a single sample impulse to the input node (with adjustable amplitude)
inputTick
method adds an external signal to the input node
noteOn
(32x8 nodes)
inputTick
External excitation signal from synthesized stikes (impulsed filters in this example)
Enhancements
Geometry scaled to speed of sound in metal
Multi-tap outputs and wavefield synthesis
Mode stretching and passive nonlinearity (allpass filters at edge nodes)
Damping at internal nodes
Rectangular interpolation (input, output and damping nodes)
Excitation "contact sound" mixed into output
Brass plate in front of 15-channel microphone array
Testing 15-channel microphone array with an impulse generator
Impulse response across mic (channel 8 muted)
Channels independently normalized (speed of sound in air visible)
Same thing for 15-channel wavefield synthesis (impulse response across array outputs)
Channels independently normalized (speed of sound in air visible)
Impulse response of mesh with 12 output taps
Mesh output (12 channels) fed through WFS array (15 outputs)
Excitation (force hammer recording) added through WFS array
Creates the two wavefronts
Edge Filters
Allpass filters for mode shifting and stretching "A Simplified Approach to Modeling Dispersion Caused by Stiffness in Strings and Plates," Scott Van Duyne and Julius Smith, 1994
no allpass, only lowpass
allpass (order 4) with stretch factor = 0
stretch factor = 0.73
signal dependent, passive nonlinearity "A Passive Nonlinear Digital Filter Design Which Facilitates Physics-based Sound Synthesis of Highly Nonlinear Musical Instruments," John Pierce and Scott Van Duyne, 1997
signal dependent stretch factor (pie pan)
Thanks for listening!
This deck available online at https://ccrma.stanford.edu/~cc/deck.js/ICSV
along with the code: https://cm-gitlab.stanford.edu/cc/waveguideMesh