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where the coefficients a m and b n with the derivatives in the model are chosen such that the model
captures the frequency dependent properties of the material accurately. For this, the storage and loss
moduli corresponding for this model are compared with the experimentally obtained moduli. The
coefficients are adjusted to obtain a good fit over the range of frequencies of interest. The complex
modulus for this model, which defines the storage and loss moduli, can be expressed as:
(1- a,
(3-6)
Figure 3.1 Mechanical representation of a linear model with 7 parameters
It can be shown that the system shown in Fig. 3.1 is equivalent to the model of Eqn. 3.5. The
coefficients in Eqn. 3.5 can now be expressed in terms of the spring and damper coefficients in Fig.
3.1. In this study, a third-order model has been used to obtain numerical results. For such a model,
there are seven coefficients, which can be written in terms of the spring coefficients ^...£4 and
damper coefficients c 2 , c 3 , and c 4 as follows:
)+ c ; (*,-'+tf+k- 1 )+c 4 (k- 1 +£+*,-«)]
;)+(^'+A 3 - 1 )(c I +c;)+(fc,- 1 +^')( C 3 +c 4 )l
(3.7)
"L
4A ;