Mechanisms Of Subharmonic And Chaos In Loudspeaker Shells

The loudspeaker is generally known as the weakest link in the high-fidelity sound-reproduction chain. China is the largest loudspeaker manufacturer country; however it is far from a great power country producing quality loudspeakers. The subharmonics and chaos caused by the nonlinearity of loudspeaker shells will significantly affect the sound quality. Main studies are listed as follows:1. The nonlinear vibration mode equations of loudspeaker shells are derived, in which an axisymmetric mode and an asymmetric mode of the loudspeaker shell are selected to analyze the subharmonics and chaos in loudspeakers. The axisymmetric mode is driven resonantly, and the asymmetric mode and the axisymmetric mode are in the internal resonances of 2:1. Analytic solutions of the equations are obtained by the harmonic balance method.2. The bifurcation of the above equations is studied by using the software AUTO. The frequency response and driving force response are presented, the bifurcation points of the system are located, and the types of the bifurcations are determined. The bifurcation sets obtained agree basically with the existing experiment results. The typical time histories of the two modes obtained from the Runge-Kutta method are exhibited to verify the bifurcation results. The analyses show that in the case of the axisymmetric mode driven resonantly, and the two modes in the internal resonances of 2:1, the occurrence of the subharmonics in loudspeakers is due to the autoparametric resonance.3. The time histories in the region of no stable periodic solutions in bifurcation sets are analyzed with the Lyapunov exponent, the fractal dimension and the power spectrum, and the results verify the occurrence of the chaotic vibration there. The system undergoes the path of period-doubling to chaos. Therefore in the case considered not only the subharmonics but also the chaos can take place in loudspeakers under some certain conditions. The numerical results of chaos coincide with the existing experiment ones.