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Application of Canonical Polynomials for Describing the Stress-Strain State of Rotating Disks

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Abstract:

The widespread use of aging materials in engineering, along with the growing demands for reliability and cost-effective design, poses new challenges for researchers in improving mathematical tools, methods for describing experimental data, and developing both exact and approximate solution techniques for specific problems. This paper investigates the stress distribution in a viscoelastic rotating disk of variable thickness mounted on a rigid shaft. An approximate method is proposed for solving the governing differential equation with variable coefficients, based on the use of canonical polynomials and the τ-method of Lanczos. The resulting polynomials obtained using this approach approximate the desired solution approximately 2n times more accurately than hypergeometric functions. The generalization to the viscoelastic case is achieved by applying the Volterra principle. A numerical example is provided. The scientific novelty lies in the application of canonical polynomials and the τ-method instead of hypergeometric functions to solve the stress analysis problem of a rotating viscoelastic disk with variable thickness. The canonical polynomials – either in general form or numerically determined using the relationships derived in this study – can also be constructed for other similar problems.

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Periodical:

Advances in Science and Technology (Volume 172)

Pages:

276-285

DOI:

https://doi.org/10.4028/p-fM63QT

Citation:

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Online since:

January 2026

Authors:

Svitlana Tymchenko, Olena Sdvyzhkova*, Dmytro Babets, Inna Ilina, Assangiz Moldabayev, Olha Buhrym

Keywords:

Canonical Lanczos Polynomials, Differential Equations, Stress Analysis, Stress-Strain State, Volterra Principle, τ-Method

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© 2026 Trans Tech Publications Ltd. All Rights Reserved

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