# JSV: Nonlinear viscoelastic behaviours of loudspeaker suspensions-like structures

March 3, 2018 Antonin Novak

research research_nonlinear research_electroacoustics B. Maillou, P. Lotton, A. Novak & L. Simon (2018), “Modelling nonlinear viscoelastic behaviours of loudspeaker suspensions-like structures”, Journal of Sound and Vibration. Vol. 416(0), pp. 213-223.

This paper shows that modeling loudspeaker suspensions are not that simple as it is usually presented. The fact that the materials from which the surround and the spider are made are viscoelastic materials makes their modeling very complicated. From the viscoelastic point of view, the stiffness exhibits a creep effect which results in a frequency dependent parameter $K_{ms}$. Moreover, the material is nonlinear, and so it depends also on the membrane excursion. Both effects are here joint together to form a frequency dependent nonlinear model of loudspeaker suspensions. This model is then converted to a Generalized Hammerstein Model (see the following figure).

The measurement setup is made of a shaker connected to a pushing rod that pushes the mechanical part of the speaker back and forth. The motor of the speaker separated from the mechanical part so that the latter is measured separately. The Force $F(t)$ is measured with an impedance head and the displacement of the membrane by a laser vibrometer (see the setup below).

Even if a very complex model is chosen (combination of used models taking into account viscoelasticity and nonlinear effects), it predicts different parameters for different excitation levels. E.g., the stiffness $K_{ms}$ varies not only with the instantaneous displacement but also with the input level (see figure below).

Mechanical properties of an electrodynamic loudspeaker are mainly determined by its suspensions (surround and spider) that behave nonlinearly and typically exhibit frequency dependent viscoelastic properties such as creep effect. The paper aims at characterizing the mechanical behaviour of electrodynamic loudspeaker suspensions at low frequencies using nonlinear identification techniques developed in recent years. A Generalized Hammerstein based model can take into account both frequency dependency and nonlinear properties. As shown in the paper, the model generalizes existing nonlinear or viscoelastic models commonly used for loudspeaker modelling. It is further experimentally shown that a possible input-dependent law may play a key role in suspension characterization.

@article{maillou2018modelling, author={Maillou, Balbine and Lotton, Pierrick and Novak, Antonin and Simon, Laurent}, title={Modelling nonlinear viscoelastic behaviours of loudspeaker suspensions-like structures}, journal={Journal of Sound and Vibration}, volume={416}, pages={213-223}, year={2018}, publisher={S. Hirzel Verlag} }