Physical modeling of a percussion musical instrument using mass spring network system

Abstract

This work investigates physical modeling techniques for percussion instruments, with a focus on developing a practical and computationally efficient drum sound synthesis. A comparison was made between four major physical modeling approaches, which are Finite Difference Time Domain (FDTD), Delay Line, Modal Synthesis, and Mass-Spring Network. The mass-spring approach emerged as the most appropriate method, balancing feasibility with computational efficiency. Thus, two frameworks were implemented: a detailed offline model with Cartesian-grid representation, integrating complex membrane physics in the model; and an optimized polar-coordinate real-time version, which is implemented as both a VST plugin and VCV Rack module. Spectral and modal analyses confirm that the models mentioned above reproduce successfully the characteristic resonant frequencies predicted by Bessel function theory. When comparing with recordings of acoustic drums, the model cannot capture all the spectral nuances of physical drums. However, it successfully reproduces the perceptually significant modal patterns that define different drum types. The real-time implementation maintains these essential characteristics while introducing performance-responsive behaviors that are not typically achievable with sample-based instruments. This research contributes to both the theoretical understanding of percussion acoustics and practical applications in music technology, offering a methodology that fills the gap between physical accuracy and computational practicality for drum sound synthesis.