Application of SID to non-linear engine mounts design

Forces are generally defined in physics as functions of position (Newton: gravity) or velocity (Laplace: magnetic force on a moving electric charge). Damping forces are little known even today and represent one of the most intriguing subjects of physics. Maxwell elements and fractional derivatives are used to modelize time domain hysteretic damping. The resulting models are comparatively complicated and have a limited domain of validity especially when strong non-linearity is involved. The mathematical model we use is based on the introduction of a new state variable and is particularly suitable in the non-linear vibration case. S.I.D. (Strain Integral Damping: see ref. [2]) is a very suitable mean to modelize hysteretic damping in the time domain and for engine mounts in particular [3]. In the present paper some very important technical advice is given to possible SID users. The theory is better explained and enriched in comparison with previous papers. The effectiveness of SID is shown by some examples one of them concerning a strongly non-linear model. Two "Scilab'' scripts are provided to better explain.