Question

.1 A visco-elastic material is described by means of a Maxwell model. The model consists of a linear dashpot, with damping coefficient c in series with a linear spring, with spring constant c (see figure below. The numerical values for the material properties are: INc Cn 0.8 104[Ncs] 8 104 (a) (b) Derive the differential equation for this model. Give the response for a unit step in the strain. Make a drawing of the response (c) The material is subjected to an harmonic strain excitation with ampli tude ε0 and an angular frequency o. Give the complex modulus E*(a) and the phase shift φ(a) for this material.

Answer 1

According to equation C = 8 times 10^4 NC C_n = 0.8 times 10^- 4 NCS IN this model liner & spring are in series E = E_1 + E_2 gamma = gamma_1 + gamma_2 of stain with respect to time eq^n dE/dt = dE_1/dt + dE/dt putting values of dE_1/dt & dE_2/dt \r\n dE/dt = 1/E d gamma/dt + gamma/n ---2) Maxwell model gamma + n/E gamma = nE oR n/E gamma + gamma = nE for unit step stain dE/dt rightarrow 0 0 = 1/E d gamma /dt + gamma /n Solving differential eq^n we get gamma = ce
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