Nonlinear experiments of tuning curve resonances for the vibrational modes of a weakly stretched circular membrane

Nonlinear oscillations of a pre-stretched 11.5 cm diameter latex circular membrane clamped rigidly around the boundary were investigated. The relaxed membrane thickness was 0.4 mm. An 8 cm diameter loud speaker drove the membrane from below using a swept sinusoidal tone. Low drive tuning curve sweeps demonstrated resonant frequencies corresponded to the first three radially symmetric linear drum modes (56, 147.6, and 240.5 Hz) sweeping from 50 to 300 Hz. Regression yielded a transverse wave speed of 10.6 m/s. Incrementally increasing the speaker amplitude (after each sweep) showed the lowest resonant frequency at first decreases, then increases with increasing acoustic drive pressure. Higher modes exhibited frequency increases with drive level. Tuning curve responses were measured using a 6 mm diameter microphone 5 mm above the center of the membrane. Nonlinear tuning curves hysteresis effects occur for higher drive levels sweeping between 50 and 70 Hz. Here, the amplitude sharply falls from a high to a low microphone response at fa = 59 Hz. With the same drive level, a sweep tone starting from 70 Hz to 50 Hz exhibits at fa = 57.5 Hz, a jump from a lower to a higher microphone response. [Goncalves et al., J. Vib. Sound 327, 231 (2009).]