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(Solved): a) Derive the differential equation for the Zener model of the standard linear solid. b) For the ca ...
a) Derive the differential equation for the Zener model of the standard linear solid. b) For the case of creep with a unit stress input, determine the creep function, . Let E0 = 15 , and , and c) Solve for the strain response using the hereditary integral formulation. Plot the stress - strain response for a sinusoidal input, where omega . d) Plot the storage modulus and loss modulus as a function of frequency from 10 to
Expert Answer
a) The differential equation for the Zener model of the standard linear solid can be derived as follows:Let ?(t) be the strain and ?(t) be the stress. The constitutive equations for the model components are:1. Elastic spring: ?_spring(t) 2. Viscous dashpot: ?_dashpot(t) 3. Zener spring: ?_zener_spring(t) 4. Zener dashpot: ?_zener_dashpot(t) The total stress ?(t) is the sum of the stresses in the individual components: