有内共振时的扬声器分谐波和混沌

研究了当轴对称模态由驱动力共振激发,并且轴对称模态和非轴对称模态存在2:1内共振时的扬声器辐射体薄壳的分谐波和昆沌。采用多尺度法分析了非线性模态方程的稳态解及其稳定性,由此进一步确定了驱动频率和驱动力平面上的分岔集。给出了所考虑情形下扬声器分谐波的阈值电压公式,该阈值电压低于无内共振时的阈值电压。除出现非轴对称模态的1/2分谐波振动外,2个模态的振幅经Hopf分岔后作极限环运动,并经倍周期分岔进入混沌运动。混沌出现是由于2个模态间能量的强烈交换。理论结果和实验结果基本吻合,该一致性表明了所建扬声器非线性薄壳模型的正确性。 

Subharmonics and chaos in loudspeakers with internal resonance

The Subharmonics and chaos in a loudspeaker shell are investigated when the axisymmetric mode is excited resonantly by the driven force,and the internal resonance of 2:1 exists between the axisymmetric mode and the asymmetric mode.The method of multiple scales is used to obtain the first-order approximations to the nonlinear modal equations,then to analyze their stabilities,and furthermore to determine the bifurcation sets on the driving frequency and force plane.The formula of the threshold voltage of the subharmonics is given in the case considered,which is lower than the one in the case without internal resonance.Besides the presence of the 1/2 subharmonics of the asymmetric mode,the amplitudes of the two modes undergo Hopf bifurcation to limit cycle motions,and then undergo perioddoubling bifurcations to chaos.The occurrence of the chaos is due to the strong energy interchange between the two modes.The experimental results agree with the theoretical ones.This agreement verifies the correctness in modeling the nonlinearity of the loudspeaker shell.