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Area Control technology / Behaviour and characteristics of transfer elements

IEV ref351-45-19

en
damping ratio
for a linear time-invariant system described by the second order differential equation

d 2 x d t 2 +2ϑ ω 0 dx dt + ω 0 2 x=0 MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaamaalaaabaGaaeizamaaCaaaleqabaGaaGOmaaaakiaadIhaaeaacaqGKbGaamiDamaaCaaaleqabaGaaGOmaaaaaaGccqGHRaWkcaaIYaGaeyyXICTaeqy0dOKaeyyXICTaeqyYdC3aaSbaaSqaaiaaicdaaeqaaOGaeyyXIC9aaSaaaeaacaqGKbGaamiEaaqaaiaabsgacaWG0baaaiabgUcaRiabeM8a3naaDaaaleaacaaIWaaabaGaaGOmaaaakiabgwSixlaadIhacqGH9aqpcaaIWaaaaa@5522@

the value of the coefficient ϑ MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiabeg9akbaa@36F8@ ,

where

tis the time;
xis a state variable of the system;
ω0is the characteristic angular frequency of the system

Note 1 to entry: When ϑ<1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiabeg9akjabgYda8i aaigdaaaa@38B9@ , ω d = ω 0 1 ϑ 2 MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiabeM8a3naaBaaaleaacaqGKbaabeaakiabg2da9iabeM8a3naaBaaaleaacaaIWaaabeaakiabgwSixpaakaaabaGaaGymaiabgkHiTiabeg9aknaaCaaaleqabaGaaGOmaaaaaeqaaaaa@4290@ is the eigen angular frequency of the system.

Note 2 to entry: This entry was numbered 351-24-18 in IEC 60050-351:2006.


fr
taux d'amortissement, m
pour un système linéaire invariant dans le temps décrit par l'équation différentielle du deuxième ordre

d 2 x d t 2 +2ϑ ω 0 dx dt + ω 0 2 x=0 MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaamaalaaabaGaaeizamaaCaaaleqabaGaaGOmaaaakiaadIhaaeaacaqGKbGaamiDamaaCaaaleqabaGaaGOmaaaaaaGccqGHRaWkcaaIYaGaeyyXICTaeqy0dOKaeyyXICTaeqyYdC3aaSbaaSqaaiaaicdaaeqaaOGaeyyXIC9aaSaaaeaacaqGKbGaamiEaaqaaiaabsgacaWG0baaaiabgUcaRiabeM8a3naaDaaaleaacaaIWaaabaGaaGOmaaaakiabgwSixlaadIhacqGH9aqpcaaIWaaaaa@5522@

la valeur du coefficient ϑ MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiabeg9akbaa@36F8@ ,

test le temps;
xest une variable d’état du système;
ω0est la pulsation caractéristique du système

Note 1 à l’article: Quand ϑ<1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiabeg9akjabgYda8i aaigdaaaa@38B9@ , ω d = ω 0 1 ϑ 2 MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiabeM8a3naaBaaaleaacaqGKbaabeaakiabg2da9iabeM8a3naaBaaaleaacaaIWaaabeaakiabgwSixpaakaaabaGaaGymaiabgkHiTiabeg9aknaaCaaaleqabaGaaGOmaaaaaeqaaaaa@4290@ est la pulsation propre du système

Note 2 à l'article: Cet article était numéroté 351-24-18 dans la CEI 60050-351:2006.


ar
نسبة إخماد

de
Dämpfungsgrad, m

es
coeficiente de amortiguamiento, m

fi
suhteellinen vaimennus

it
tasso di smorzamento

ko
감쇠비
감쇄율

ja
減衰率

pl
współczynnik tłumienia względny

pt
factor de amortecimento

zh
阻尼比

Publication date: 2013-11
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