 Peak frequencies in a standard linear solid

ID: peak-frequencies-in-a-standard-linear-solid

0 < G_{R} < G_{U}

, put

x = ω τ

G^{'} = G_{R} + (G_{U} - G_{R}) x^{2} / (1 + x^{2})

and its loss modulus is

G^{''} = (G_{U} - G_{R}) x / (1 + x^{2})

. The latter peaks at

x = 1

, whereas its loss tangent is

tan δ = \frac{( G _{U} - G _{R} ) x}{G _{R} + G _{U} x ^{2}} .

x = G_{R} / G_{U}

(G_{U} - G_{R}) / (2 G_{R} G_{U})

. A loss-modulus peak and a loss-tangent peak therefore need not occur at the same frequency. For weak relaxation,

G_{U} / G_{R}

is close to one and their frequencies are approximately equal.

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