Estimation of natural frequencies of torsional vibrations of a composite nonlinearly viscoelastic shaft

Tarasyuk I.A., Kravchuk A.S.
 pdf (4055K)  / List of references

The article presents a method for linearization the effective function of material instantaneous deformation in order to generalize the torsional vibration equation to the case of nonlinearly deformable rheologically active shafts. It is considered layered and structurally heterogeneous, on average isotropic shafts made of nonlinearly viscoelastic components. The technique consists in determining the approximate shear modulus by minimizing the root-mean-square deviation in approximation of the effective diagram of instantaneous deformation.

The method allows to estimate analytically values of natural frequencies of layered and structurally heterogeneous nonlinearly viscoelastic shaft. This makes it possible to significantly reduce resources in vibration analysis, as well as to track changes in values of natural frequencies with changing geometric, physico-mechanical and structural parameters of shafts, which is especially important at the initial stages of modeling and design. In addition, the paper shows that only a pronounced nonlinearity of the effective state equation has an effect on the natural frequencies, and in some cases the nonlinearity in determining the natural frequencies can be neglected.

As equations of state of the composite material components, the article considers the equations of nonlinear heredity with instantaneous deformation functions in the form of the Prandtl’s bilinear diagrams. To homogenize the state equations of layered shafts, it is applied the Voigt’s hypothesis on the homogeneity of deformations and the Reuss’ hypothesis on the homogeneity of stresses in the volume of a composite body. Using these assumptions, effective secant and tangential shear moduli, proportionality limits, as well as creep and relaxation kernels of longitudinal, axial and transversely layered shafts are obtained. In addition, it is obtained the indicated effective characteristics of a structurally heterogeneous, on average isotropic shaft using the homogenization method previously proposed by the authors, based on the determination of the material deformation parameters by the rule of a mixture for the Voigt’s and the Reuss’ state equations.

Keywords: composite material, homogenization, torsional vibrations, nonlinear viscoelasticity
Citation in English: Tarasyuk I.A., Kravchuk A.S. Estimation of natural frequencies of torsional vibrations of a composite nonlinearly viscoelastic shaft // Computer Research and Modeling, 2018, vol. 10, no. 4, pp. 421-430
Citation in English: Tarasyuk I.A., Kravchuk A.S. Estimation of natural frequencies of torsional vibrations of a composite nonlinearly viscoelastic shaft // Computer Research and Modeling, 2018, vol. 10, no. 4, pp. 421-430
DOI: 10.20537/2076-7633-2018-10-4-421-430
URL: http://crm-en.ics.org.ru/journal/article/2708/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.
Views (last year): 27.

Indexed in Scopus

Full-text version of the journal is also available on the web site of the scientific electronic library eLIBRARY.RU

The journal is included in the Russian Science Citation Index

The journal is included in the RSCI

International Interdisciplinary Conference "Mathematics. Computing. Education"

Copyright © 2009–2024 Institute of Computer Science