00034___2a770c08e7b8a84a53032b665ea39e1e - lags behind the...

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Sec. 1.3 SINUSOIDAL OSCILLATIONS IN A VISCOELASTIC . . . 13 Similarly, if uo = Bei$, then a simple harmonic oscillatory displacement u(t) = uOeiWt is either the real part or the imaginary part of (2) u(t) = uOeiWt = B cos(wt + $1 + i~ sin(wt + $) . On substituting (1) and (2) into Eqs. (1)-(3) of Sec. 1.2, we can obtain the ratio uo/Fo, which is a complex number. The inverse, FO/UO, is called the complex modulus of a viscoelastic material, and is often designated by M: (3) M = FO/UO = lMleis where [MI is the magnitude and 6 is the phase angle by which the strain
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Unformatted text preview: lags behind the stress. The tangent of 6 is often used as a measure of the internal friction of a linear viscoelastic material: imaginary part of M tan6 = real part of M * (4) For the Kelvin model, we have (5) M = 1 + iwr, E R 1 IMI= (1+w2r~)1'2ER, 1 f w".," 1 + iwr, When [MI and tan6 in (5) and (6) are plotted against the logarithm of w , curves as shown in Fig. 1.3:l are obtained. Experiments with torsional I I I I - ,n I -. c .- c Internal friction - 0 Y .- - 2 0.01 0. I 10 100 0- Fig. 131. Frequency dependence of internal friction and elastic modulus....
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