Journal
MECHANICS OF TIME-DEPENDENT MATERIALS
Volume 11, Issue 2, Pages 143-157Publisher
SPRINGER
DOI: 10.1007/s11043-007-9038-1
Keywords
creep compliance; relaxation modulus; regularization; optimization; linear viscoelasticity
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Two alternative approaches for estimating linear viscoelastic material functions from a single experiment under random excitation are derived and analyzed. First, Boltzmann's superposition integral is discretized into a system of linear equations. Due to the ill-posedness of the resulting matrix equation, Tikhonov's regularization is introduced. Second, the integral is transformed into a recursive formula, using a Prony series representation of viscoelastic material functions, in which gradient-based optimization is applied. Numerical results are provided to compare and verify the applicability of the presented numerical procedures.
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