scholarly journals Axisymmetric Longitudinal-Bending Waves in a Cylindrical Shell Interacting with a Nonlinear Elastic Medium

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Alexander I. Zemlyanukhin ◽  
Andrey V. Bochkarev ◽  
Lev I. Mogilevich ◽  
Ekaterina G. Tindova
Keyword(s):  
Cylindrical Shell ◽  
Elastic Medium ◽  
Numerical Solutions ◽  
Bending Waves ◽  
Nonlinear Elastic Medium ◽  
Longitudinal Bending ◽  
Infinite Cylindrical Shell ◽  
Nonlinear Elastic ◽  
Traveling Pulse ◽  
Good Agreement

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.

Solitons in a nonlinear elastic medium

1991 ◽  
Vol 43 (4) ◽  
pp. 3493-3499 ◽  
Author(s):  
Yuri S. Kivshar
Keyword(s):  
Elastic Medium ◽  
Nonlinear Elastic Medium ◽  
Nonlinear Elastic

Thermal stress and magnetic effects on nonlinear vibration of nanobeams embedded in nonlinear elastic medium

2020 ◽  
Vol 43 (10) ◽  
pp. 1316-1332
Author(s):  
Sardar S. Abdullah ◽  
Shahrokh Hosseini-Hashemi ◽  
Nazhad A. Hussein ◽  
Reza Nazemnezhad
Keyword(s):  
Thermal Stress ◽  
Nonlinear Vibration ◽  
Elastic Medium ◽  
Magnetic Effects ◽  
Nonlinear Elastic Medium ◽  
Nonlinear Elastic

Transmission of oscillations through a layer of a nonlinear elastic medium

2010 ◽  
Vol 56 (6) ◽  
pp. 893-903
Author(s):  
A. G. Kulikovskiĭ ◽  
E. I. Sveshnikova
Keyword(s):  
Elastic Medium ◽  
Nonlinear Elastic Medium ◽  
Nonlinear Elastic

Buckling and Post-Buckling Analysis of Geometrically Imperfect FGM Pin-Ended Tubes Surrounded by Nonlinear Elastic Medium Under Compressive and Thermal Loads

2019 ◽  
Vol 19 (08) ◽  
pp. 1950089 ◽  
Author(s):  
Hadi Babaei ◽  
Yaser Kiani ◽  
M. Reza Eslami
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Elastic Medium ◽  
Axial Compression ◽  
Thermal Loads ◽  
Linear Temperature ◽  
Nonlinear Elastic Medium ◽  
Different Types ◽  
Post Buckling ◽  
Nonlinear Elastic

The present study aims to analyze the buckling and post-buckling behavior of the geometrically imperfect functionally graded pin-ended tube. Imperfect FGM tube is surrounded by nonlinear elastic medium and is subjected to the axial compression or various thermal loads. Pinned-pinned boundary conditions are movable or immovable for the FGM tube under axial compression or thermal loads, respectively. In thermal analysis, different types of thermal loads such as uniform temperature rise, linear temperature distribution, and heat conduction are analyzed and contrasted. Displacement field of the FGM tube satisfies the tangential traction-free boundary conditions on the inner and outer surfaces. Properties of the FGM tube are assumed to be temperature-dependent and are distributed through the radial direction of tube using a power law function. The governing equilibrium equations of the FGM tube are obtained by means of the virtual displacement principle. These are nonlinear coupled differential equations based on a higher order shear deformation tube theory and the von Kármán nonlinear assumption. The coupled nonlinear dimensionless differential equations are solved using the two-step perturbation method. These asymptotic solutions are as explicit functions of the axial compression or different types of thermal load. Numerical results are provided to explore the effects of the linear and nonlinear spring stiffness of elastic medium and imperfection parameter of the tube. The effects of the volume fraction index and two geometrical parameters of the FGM tube are also included.

scholarly journals Atypical evolution of solitary wave propagating in nonlinear elastic medium

2020 ◽  
pp. 28-37
Author(s):  
J.J. Rushchitsky ◽  
◽  
V.M. Yurchuk ◽  
Keyword(s):  
Numerical Modeling ◽  
Solitary Wave ◽  
Approximate Method ◽  
Elastic Medium ◽  
Cylindrical Wave ◽  
Macdonald Function ◽  
Initial Profile ◽  
Nonlinear Elastic Medium ◽  
Nonlinear Elastic ◽  
First Three Approximations

The atypical evolution of a solitary cylindrical wave that propagates in the nonlinear elastic medium and has the initial profile in the form of the Macdonald function is described and commented. In the analysis, the approximate method of restriction on the gradient of a deformation is used, and three first approximations are taken into account. Two examples of typical wave evolution — harmoniс and bell-shaped waves — are shown and commented, where the first three approximations are also taken into account. The numerical modeling showed that the atypical initial profile (profile without a hump) evolves atypically — the profile becomes essentially steeper, saving the concavity, and the wave bottom decreases almost two times.

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