00033___ebfeef01262096bb578dc0f0490b0a1c

00033___ebfeef01262096bb578dc0f0490b0a1c - 12 Chap. 1...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 load-deflection 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. Load-deflection relations such as ( 1)-(3) were proposed t o extend the classical theory of elasticity to include anelastic phenomena. Lord Kelvin (Sir William Thomson, 1824-1907), 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 (1852-1914) a nd Joseph John Thomson ( “J.J.,”1856-1940) 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) . ...
View Full Document

This note was uploaded on 01/04/2012 for the course ENG 501 taught by Professor Thomson during the Fall '05 term at MIT.

Ask a homework question - tutors are online