Basic transfer and time-response functions of the three parameter fluid and solid viscoelastic model

Student: Kampas Georgios
Supervisors: Prof Nicos Makris

ABSTRACT

In this thesis, the basic transfer functions and time response functions of the three parameter fluid and solid models (Jeffreys' and Poynting-Thomson's model) are revisited. The two models find application in several areas of engineering and geophysics, including in the modeling of the behavior of earth strata. The relation between the analyticity of the transfer functions and the causality of the corresponding time response functions is established by identifying all singularities at ω=0 after applying the partial fraction expansion method. The strong singularity at ω=0 in the imaginary part of the transfer functions in association with the causality requirement imposes the addition of a Dirac delta function in their real part. This operation makes possible the application of time domain techniques that do not suffer from violating the premise of causality.

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