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Iterative method of determining the relaxation-time spectrum from the components of the complex shear modulus

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Polymer Mechanics Aims and scope

Abstract

The determination of the relaxation-time spectrum from the results of measurements carried out under conditions of steady-state shear vibrations involves the solution of a Fredholm integral equation of the first kind, and constitutes an example of incorrectly formulated problems. Regularizing conditions are presented for the solution of the problem, together with one of a number of possible algorithms for constructing an iterative procedure in order to determine the relaxation-time spectrum from both components of the complex shear modulus at the same time. An example of the determination of such a spectrum is presented, together with an analysis of the relative errors.

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Authors
  1. É. É. Yakobson
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Additional information

Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, pp. 1069–1076, November–December, 1975.

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Yakobson, É.É. Iterative method of determining the relaxation-time spectrum from the components of the complex shear modulus. Polymer Mechanics 11, 912–918 (1975). https://doi.org/10.1007/BF00857613

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  • DOI: https://doi.org/10.1007/BF00857613

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