Fractional Modeling And Investigation On The Nonlinear Distortions Of Electro-Dynamic Loudspeakers

The accuracy of equivalent electrical circuit is significantly affected by the eddy currents,creep effects and time varying behaviors of loudspeakers.Putting forwards on improving the accuracy of equivalent electrical circuit both in low frequency range and high frequency range,the physical mechanism of eddy currents as well as creep effects have been lucubrated by this thesis.By expanding the derivative normal order to fractional order,the linear and nonlinear fractional equivalent circuits have been presented,and the nonlinear distortions given by nonlinear parameters as well as the time varying effects have been investigated.To get the structural nonlinear effects of spiders,a noncontact dynamic experimental system has been set up based on added-mass method.The creep effects as well as the nonlinear stiffness of spiders have been measured,and the nonlinear mechanism of the measured stiffness has been presented.The main work and innovations are summarized as follows:1.To model the eddy currents,the fractional lossy inductance(FLI)model has been introduced by expanding the integer Maxwell electromagnetic wave equation to fractional order.To model the creep effects,the fractional standard linear solid(FSLS)model has been set up by substituting the Abel dashpot for Newton dashpot in standard linear solid model.The model parameters and fitting errors were identified by fitting the measured loudspeaker electrical impedances as well as the transfer functions based on the least-mean-square(LMS)method.The results find that,the FLI model has improved the fitting accuracy in high frequency range since it gives a better modeling on the measured frequency power law of the lossy inductance.Due to an accurate description on the frequency power law of the loss factor in suspensions,the equivalent circuit accuracy at low frequencies has been improved by FSLS model.2.The fractional calculus can be adopted as the criterions on the effective of the ac-shorting devices as well as the creep effects of suspensions.The loss of the voice coil inductance increases with the fractional calculus,a higher fractional calculus gives a better frequency response spectrum at high frequencies of loudspeakers.Additionally,the lower fractional calculus of the FSLS model,the loss factor varying with frequency becomes more dramatically,and the creep effect is more significant.3.The equivalent electrical circuit of loudspeakers has been improved by adding the fractional lossy inductance model as well as the fractional creep compliance model,and the approximate solution in time domain has been given by modified Oustaloup filter method.The solved displacements have been compared with the measured data and the results show that,the approximate solution of the diaphragm displacements in time domain gives better correspondences with the measurement.Moreover,the analytical solution of the displacement in steady state under sine wave input signal has been presented.4.The fractional nonlinear equivalent electrical circuit has been presented as well as the numerical calculation method.The accuracy on calculating the nonlinear distortions of this circuit has been investigated.The results find that,this fractional circuit has a good accuracy in calculating both the harmonic distortion and the intermodulation distortion at low frequencies under high large signal.Nevertheless,for intermodulation distortion at high frequencies,the numerical results have some errors.The effects of the nonlinear parameters as well as the time varying effect on nonlinear distortions have been investigated.The results illustrate that,the nonlinear inductance has a small effect on harmonic distortions,but some influences on intermodulation distortions.The curve symmetry has almost no effect on distortions.The nonlinear force factor has a significant effect both on the harmonic distortions and the intermodulation distortions,and the curve symmetry has really small influence on nonlinear distortions.As for the nonlinear compliance,it has a large influence on harmonic distortions at low frequencies,but practically no effect on intermodulation.On the contrary of nonlinear force factor,the curve symmetry of the nonlinear compliance has a significant effect on harmonic distortions.Additionally,time varying effect brings remarkable influences on both harmonic distortions and intermodulation distortions.5.A noncontact dynamic experimental system was presented by added-mass method.The Young's moduli of the tested spiders were derived from the measured vibrating modes.The creep effects as well as the level dependent behaviors of tested spiders were investigated.The results reveal that,the creep effect of spiders is due to the coupled configurationally motion of neighboring molecules in polymer molecular chains.The molecular chains need a time to move and slide alongside each other under a harmonic stress,resulting in a time delay between the strain and the stress.The nonlinear stiffness of the tested spiders was acquired by harmonic balanced method,and the nonlinear mechanism of stiffness was investigated.The results find that,the DC displacement comes from the nonlinear behaviors of spider material such as creep effect,and the axisymmetric characteristic is ascribed to the nonlinear geometry structure of spiders.Some results of this paper can be used as theory methodology and experimental configuration for the loudspeaker design,R&D,nonlinear distortion improvement and nonlinear feedback compensation.