Abstract
A nonlinear differential equation is derived which describes the propagation of axisymmetric stationary longitudinal-bending waves in infinite cylindrical shell of Timoshenko type, interacting with the external nonlinear elastic medium. A modified perturbation method based on the use of diagonal Pade approximants was applied to build exact solitary-wave solutions of the derived equation in the form of traveling front and the traveling pulse. Numerical solutions of the equation, obtained by means of finite difference method, are in good agreement with the corresponding exact analytical ones.
Highlights
The shell theory is a well-developed section of deformable solids mechanics and has numerous technical applications
The interest in nonclassical variants of shell theory has grown recently due to the need of analysing nanoobjects elastic properties, carbon nanotubes (CNTs), in particular [1,2,3,4]
Longitudinal waves in rectilinear rods and plates interact with bending waves only in nonlinear approximation
Summary
The shell theory is a well-developed section of deformable solids mechanics and has numerous technical applications. For the axisymmetric case this allows us to integrate the first equation of the system and reduce the problem to solving a single equation for the normal displacement. This approach is traditional for onedimensional deformable systems and is often referred to as the Kirchhoff hypothesis [7]. The article aims at deriving and analysing the equation modeling the propagation of axisymmetric longitudinalbending waves in infinite cylindrical shell, interacting with a external nonlinear elastic medium [11, 12]. In this paper we will restrict our search to solitary-wave (soliton-like) solutions
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