00032___fbaeace055379df1e9ec49f9c6bd67af

00032___fbaeace055379df1e9ec49f9c6bd67af - reaction by the...

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Sec. 1.2 LINEAR SOLIDS WITH MEMORY: MODELS OF . . . 11 (10) Kelvin solid: Here we have used the symbol s(t) to indicate the unit-impulse function, or Dimc-delta function, which is defined as a function with a singularity at the origin: qt) = 0 for t < 0, and t > 0, (‘ f(t)b(t)dt = f(0) , E>O, J--E where f(t) is an arbitrary function continuous at t = 0. These functions, c(t) and k(t), are illustrated in Figs. 1.2:2 and 1.2:3, respectively, for which we add the following comments. Fig. 1.2:2. Creep function of (a) Maxwell, (b) Voigt, (c) Kelvin solid. A negative phase is superposed at the time of unloading. For the Maxwell solid, a sudden application of a load induces an imme- diate deflection by the elastic spring, which is followed by “creep” of the dashpot. On the other hand, a sudden deformation produces an immediate
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Unformatted text preview: reaction by the spring, which is followed by stress relaxation according to an exponential law Eq. (8). The factor ~ / p , with dimengions of time, may be called a relaxation time: it characterizes the rate of decay of the force. For the Voigt solid, a sudden application of force will produce no im- mediate deflection because the dashpot, arranged in parallel with the spring, will not move instantaneously. Instead, as shown by Eq. (5) and Fig. 1.2:2(b), a deformation will be gradually built up, while the spring takes a greater and greater share of the load. The dashpot displacement relaxes exponentially. Here the ratio q/p is again a relaxation time: it characterizes the rate of decay of the deflection....
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