Collisions play an important role in manyaspects of the physics of musical instruments. The striking action of ah ammer or mallet in keyboard and percussion instruments is perhaps the most important example, buto thers include reed-beating effects in wind instruments, the string/neck interaction in fretted instruments such as the guitar as well as in the sitar and the wire/membrane interaction in the snare drum. From asimulation perspective, whether the eventual goal is the validation of musical instrument models or sound synthesis, such highly nonlinear problems pose various difficulties, not the least of which is the risk of numerical instability.Inthis article, anovel finite difference time domain simulation framework for such collision problems is developed, where numerical stability follows from strict numerical energy conservation or dissipation, and where ap ower lawf ormulation for collisions is employed, as ap otential function within ap assive formulation. The power laws erves both as amodel of deformable collision, and as amathematical penalty under perfectly rigid, non-deformable collision. Va rious numerical examples, illustrating the unifying features of such methods across awide variety of systems in musical acoustics are presented, including numerical stability and energy conservation/dissipation, bounds on spurious penetration in the case of rigid collisions, as well as various aspects of musical instrument physics.

We fabricate a MEMS microphone that incorporates a graphene-based membrane that vibrates in response to acoustic forcing. We employ a novel fabrication process, where a graphene/PMMA bilayer membrane is transferred over a cavity on a separate chip before being affixed to the surface of another chip containing an electrode, resulting in the fabrication of a moveable capacitor with a membrane-to-electrode gap of 8 µm. The gap, which is less than half the size of other reported graphene membrane-based audio transducers, allows for the device to operate with low DC bias voltages of about 1 V and, when integrated with a custom-designed readout circuit, demonstrates a sensitivity to sound pressure between 0.1 mV/Pa and 10 mV/Pa across the range 100 Hz to 20 kHz. As well as a sensitivity that is comparable to previous work, the flat frequency response is stable when the sound pressure is varied between 70 dB SPL and 80 dB SPL , with the sensitivity value not varying by more than 0.2 mV/Pa.

This letter reports an experimental study of an electrothermal actuator made from an ultra-large graphene-based bilayer thin film with a diameter to thickness aspect ratio of ∼10 000. Suspended thin films consisting of multilayer graphene and 350–500 nm-thick Poly(methyl methacrylate) have been transferred over circular cavities with a diameter of 3.5 mm. The use of bilayer materials with different mechanical and thermal properties results in thin film structures that can be induced to vibrate mechanically under the electrothermal transduction mechanism. The dynamic response of the bilayer has been investigated electrothermally by driving the structures with a combination of alternating current and direct current actuation voltages (Vac and Vdc) and characterizing their resonant frequencies. It has been found that the bilayer thin film structure behaves as a membrane. In addition, the actuation configurations affect not only the amplitude of vibration but also the tuning of the resonant frequency of the vibrating membranes. The existence of Joule heating-induced tension lowers the mechanical stiffness of the membrane and hence shifts the resonant frequency downwards by −108187 ppm. A resonant frequency of 3.26 kHz with a vibration amplitude of 4.34 nm has been achieved for 350 nm-thick membranes under actuation voltages of 1 V of Vac and 8 V of Vdc.

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