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.

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 Mathematical models of the evolution of classical and solitary cylindrical waves

2020 ◽  
Vol 2020 (1) ◽  
pp. 19-31
Author(s):  
V. M. Yurchuk ◽  
Y. V. Simchuk
Keyword(s):  
Harmonic Wave ◽  
Maximum Amplitude ◽  
Hankel Function ◽  
Macdonald Function ◽  
Initial Profile ◽  
Approximate Methods ◽  
Single Wave ◽  
Cylindrical Waves ◽  
The Difference ◽  
Nonlinear Elastic

The evolution of nonlinear elastic cylindrical displacement waves for initial profiles in the form of a Hankel and Macdonald functions is analyzed theoretically and numerically. The difference between the two waves is that the MacDonald function has no hump, decreases monotonically and has a concave downward profile, and the Hankel function is a harmonic attenuating wave. The main novelty is that the evolution of cylindrical waves is studied for two different approaches to the solution of a nonlinear equation. Some significant differences of these waves are shown. First, the features of the Hankel wave, a harmonic wave (symmetrical profile), are briefly described. Then, theoretically and numerically, a single wave with an initial profile in the form of a MacDonald function is analyzed in more detail. Distortion of the initial profile due to the nonlinear interaction of the wave itself and the increase in the maximum amplitude during wave propagation is common to these profiles. Significant features of the McDonald wave are shown - an uncharacteristic initial profile (a profile without a classical hump) evolves in an uncharacteristic way - the profile becomes much steeper and remains convex downwards. Keywords: classical and solitary cylindrical waves; five-constant Murnaghan potential; approximate methods; Hankel and Macdonald initial wave profiles; evolution.

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