Chaotic State in an Electrodynamic Loudspeaker

An electrodynamic loudspeaker has been operated in a nonlinear regime with driving currents I ₀ = 2–4 A. At I ₀ = 4 A an amplitude cut-off was observed at frequency ƒ = 46 Hz. In the next step driving frequencies have been selected in the interval 45–55 Hz, and driving current was then swept until vibration amplitude produced sequences of subharmonics which terminated in the chaotic state. An attempt to explain the chaotic phenomena in terms of forced anharmonic oscillator with elastic stiffness derived from static stress-strain measurement and entering Duffing equation failed. Viscoelastic model proposed by Bennewitz and Rötger was applied, when membrane viscoelasticity and corresponding intrinsic friction term enhance the restoring force of the vibrating system. Such a model supplemented with system parameters and transferred to simulation procedure resulted in a period doubling and bifurcation diagram, which might be brought within the loudspeaker technical performances and qualitative agreements such as would be indicated by observations and measurements.