539.3 Modeling of dynamic and spectral viscoelastic characteristics of materials based on numerical inversion of the Laplace transform

Valishin A. A. (Bauman Moscow State Technical University), Tinyaev M. A. (Bauman Moscow State Technical University)

VISCOELASTICITY, RELAXATION, CREEP, DYNAMIC CHARACTERISTICS, SPECTRAL CHARACTERISTICS, LAPLACE TRANSFORM, METHOD OF QUADRATURE FORMULAS


doi: 10.18698/2309-3684-2022-1-4262


When designing products made of composite materials intended for use in difficult conditions of inhomogeneous deformations and temperature, it is important to take into account viscoelastic, including spectral and dynamic, properties of the binder and fillers. The article considers dynamic characteristics (complex modulus, complex malleability,their real and imaginary parts, loss angle tangent) and spectral characteristics of relaxation and creep and their dependence on each other. The characteristics mentioned above were found for all known types of creep kernel and relaxation kernel. To find the spectral characteristics, one of the numerical methods of inverting the Laplace transform was used — the method of quadrature formulas with equal coefficients. Algorithms and computer programs for the implementation of this method have been compiled. The obtained graphs are quite accurate (the maximum error of calculations in the average does not exceed 5%), despite the fact that the error is very noticeable in the initial time segments.


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