James H. Irwin
Elec. and Comput., Eng. and Technol. Dept., Bradley Univ., Peoria, IL 61625
James W. Beauchamp
Univ. of Illinois at Urbana-Champaign, Urbana, IL 61801
A difference equation derived from a physical model of a stiff membrane is used to simulate the acoustic signal produced by a drum head. The physical model was extended beyond the classical model by the inclusion of terms which represent viscous damping, air loading, and time-varying tension. Fixed phase vocoder and tracking spectral analysis show that the simulated sound contains correct theoretical frequencies when the damping and stiffness are set to zero. As stiffness is increased, the partial frequencies increase as predicted by plate theory. Simulations of zero (vacuum) and typical air loads show no significant changes. As a means of corroboration, measurements were made on an actual drum head mounted in a vacuum chamber. The drum signal was generated by striking the drumhead with a plastic tip mounted on a solenoid core and measured with an accelerometer mounted upon the drumhead. Spectral analysis results for this signal are qualitatively similar to the simulation measurements although they differ in some details.