학술논문
Generalized model of nonlinear elastic foundation and longitudinal waves in cylindrical shells.
Document Type
Journal
Author
Zemlyanukhin, A. I. (RS-STU-AM) AMS Author Profile; Bochkarev, A. V. (RS-STU-AM) AMS Author Profile; Ratushny, A. V. (RS-STU-ISA) AMS Author Profile; Chernenko, A. V. (RS-STU-ISA) AMS Author Profile
Source
Subject
74 Mechanics of deformable solids -- 74B Elastic materials
74B20Nonlinear elasticity
74Mechanics of deformable solids -- 74J Waves
74J30Nonlinear waves
74B20
74
74J30
Language
English
Russian
Russian
Abstract
Summary: ``A non-integrable quasi-hyperbolic sixth-order equation is derived that simulates the axisymmetric propagation of longitudinal waves along the generatrix of a cylindrical Kirchhoff - Love shell interacting with a nonlinear elastic medium. A six-parameter generalized model of a nonlinear elastic medium, which is reduced in particular cases to the models of Winkler, Pasternak, and Hetenyi, is introduced into consideration. The equation was derived by the asymptotic multiscale expansions method under the assumption that the dimensionless parameters of nonlinearity, dispersion, and thinness have the same order of smallness. The use of the introduced model made it possible to reveal additional high-frequency and low-frequency dispersions characterizing the response of the external environment to bending and shear. It is shown that non-classical shell theories should be used to reveal nonlinear effects that compensate for dispersion. It was found that the Pasternak model admits a `dispersionless' state when the dispersion due to the inertia of normal displacement is compensated by the dispersion generated by the reaction of the nonlinear elastic foundation to shear.''