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Unformatted text preview: 12 Chap. 1 INTRODUCTION a
l e l.2
E L 0 .
c
0) Q
‘0 Time I
Time Fig. 1 2 3 Relaxation function, of ( a) Maxwell, (b) Voigt, ( c) Kelvin solid.
.:. For t he Kelvin solid, a similar interpretation is applicable. The constant rEis the time of relaxation of load under the condition of constant
deflection [see Eq. ( lo)], whereas the constant ro is the time of relaxation
of deflection under the condition of constant load [see Eq. ( 4)]. As t + 00,
t he dashpot is completely relaxed, and the loaddeflection relation becomes
that of the springs, as is characterized by the constant E R in Eqs. ( 4) a nd
( 10). Therefore, E R is called the relaxed elastic modulus.
Loaddeflection relations such as ( 1)(3) were proposed t o extend the
classical theory of elasticity to include anelastic phenomena. Lord Kelvin
(Sir William Thomson, 18241907), on measuring the variation of the rate
of dissipation of energy with frequency of oscillation in various materials, showed the inadequacy of the Maxwell and Voigt equations. A more
successful generalization using mechanical models was first made by John
H. Poynting (18521914) a nd Joseph John Thomson ( “J.J.,”18561940) i n
their book Properties of M atter (London: C . Griffin and Co., 1902).
1.3. SINUSOIDAL OSCILLATIONS IN A VISCOELASTIC MATERIAL I t is interesting to examine the relationship between the load and the
deflection in a body when it is forced t o perform simple harmonic oscillations. A simple harmonic oscillation can be described by the real or
imaginary part of a complex variable. Thus, if Fo is a complex variable
FO= A eib = A(cos 4 + i sin d ), t hen a simple harmonic oscillatory force can
be written as
( 1) F ( t ) = FoeiWt A (cos4 + i sin4)(coswt + i sinwt)
=
= A cos(wt + 4) + i A sin(wt + 4) . ...
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This note was uploaded on 01/04/2012 for the course ENG 501 taught by Professor Thomson during the Fall '05 term at MIT.
 Fall '05
 Thomson

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