Shear waves in a nonlinear viscoelastic cylindrical shell
https://doi.org/10.26583/vestnik.2025.5.1
EDN: BPCIKB
Abstract
The propagation of a beam of shear waves along the generatrix of a nonlinear viscoelastic cylindrical shell of the Sanders–Koiter model is simulated by asymptotic integration methods. It is assumed that the shell is made of a material characterized by a cubic dependence between stress and strain intensities, the dimensionless parameters of wall thinness and physical nonlinearity are quantities of the same order of smallness, and the ratio of viscoelastic constants is a dimensionless parameter of a higher order of smallness. A variation of the multiscale expansion method is used, which makes it possible to determine the wave propagation velocity from the linear approximation equations and, in the first essentially nonlinear approximation, to obtain a resolving nonlinear quasi-hyperbolic equation for the leading term of the expansion of the shear component of the displacement. The derived equation is a cubic nonlinear modification of the dispersionless Kadomtsev–Petviashvili–Burgers equation, being a special case of the modified Khokhlov–Zabolotskaya–Kuznetsov equation. The solution of the derived equation is sought in the form of one harmonic with a slowly changing complex amplitude, since in deformable media with cubic nonlinearity the effect of wave self-action significantly prevails over the effect of higher harmonic generation. As a result, the Ginzburg-Landau equation is obtained for the complex amplitude, for which an exact physically consistent solution is constructed.
Keywords
nonlinear viscoelastic cylindrical shell,
shear waves,
asymptotic integration,
Ginzburg–Landau equation
Supporting agencies: The study was supported by grant No. 24-29-00071 from the Russian Science Foundation, https://rscf.ru/ project/24-29-00071/ .
About the Authors
A. I. Zemlyanukhin
Yuri Gagarin State Technical University of Saratov
Russian Federation
Russian Federation
A. V. Bochkarev
Yuri Gagarin State Technical University of Saratov
Russian Federation
Russian Federation
N. A. Artamonov
Yuri Gagarin State Technical University of Saratov
Russian Federation
Russian Federation
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Zemlyanukhin A.I., Bochkarev A.V., Artamonov N.A. Shear waves in a nonlinear viscoelastic cylindrical shell. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2025;14(5):379-392. (In Russ.) https://doi.org/10.26583/vestnik.2025.5.1. EDN: BPCIKB
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