The stability of the interface between two bodies compressed along interface cracks. 2. Exact solutions for the case of equal roots

2000 ◽  
Vol 36 (5) ◽  
pp. 615-622 ◽  
Author(s):  
A. N. Guz’ ◽  
I. A. Guz’
1973 ◽  
Vol 40 (1) ◽  
pp. 133-136 ◽  
Author(s):  
P. Z. Bulkeley

The stability of three known exact solutions to the nonlinear equations governing free transverse motions of spinning membrane disks is investigated for a particular choice of perturbations. A wave which travels circumferentially in the disk in the direction opposite to its rotation is shown to be infinitesimally unstable. A wave traveling in the direction of disk rotation and a nonlinear vibration are not shown to be unstable.


2013 ◽  
Vol 10 (03) ◽  
pp. 1250058 ◽  
Author(s):  
ALY MAHER ABOURABIA ◽  
KAWSAR MOHAMED HASSAN ◽  
EHAB SAID SELIMA

In this paper, we investigate the solitary wave solutions for the two-dimensional modified Korteweg–de Vries–Burgers (mKdV-B) equation in shallow water model. Despite that Painlevé test fails to prove the integrability of the mKdV-B equation by using the WTC-Kruskal algorithm, the Bäcklund transformation is obtained via the truncation expansion. The exact solutions of the mKdV-B equation are found using factorization techniques, Exp-function and energy integral approach of the corresponding ordinary differential equation. We found that the dispersion relation of the linearized mKdV-B equation lies on the complex plane yielding a damping character. By keeping the water height relatively small, we illustrate the resulting solutions in several figures showing the shock and solitary wave nature in the flow. The stability for the mKdV-B equation is analyzed by using the phase plane method.


2019 ◽  
Vol 33 (28) ◽  
pp. 1950338 ◽  
Author(s):  
Hadi Rezazadeh ◽  
Alper Korkmaz ◽  
Mostafa M. A. Khater ◽  
Mostafa Eslami ◽  
Dianchen Lu ◽  
...  

In this paper, the extended rational sinh-cosh method (ERSCM) and modified Khater method are applied to the biological population model to derive new exact solutions. Moreover, the stability property of some obtained solutions is discussed to show the ability of them for using in the model’s applications. Implementation of the direct algebraic methods, the equations derived by substitution of the predicted solution are solved. It is significant to point out that new traveling wave solutions are found. The present methods are easy to employ and sufficient to determine the solutions.


1972 ◽  
Vol 51 (1) ◽  
pp. 33-38 ◽  
Author(s):  
C. Sozou

Some exact solutions of the steady magnetohydrodynamic equations for a perfectly conducting inviscid self-gravitating incompressible fluid are discussed. It is shown that there exist solutions for which the free surface of the liquid is that of a planetary ellipsoid and rotates with constant angular velocity about its axis. The stability of the equilibrium configuration is not investigated.


Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 384
Author(s):  
Janusz Brzdȩk ◽  
Zbigniew Leśniak ◽  
Renata Malejki

We study the Ulam-type stability of a generalization of the Fréchet functional equation. Our aim is to present a method that gives an estimate of the difference between approximate and exact solutions of this equation. The obtained estimate depends on the values of the coefficients of the equation and the form of the control function. In the proofs of the main results, we use a fixed point theorem to get an exact solution of the equation close to a given approximate solution.


Author(s):  
Volodymyr Mykytenko ◽  
Volodymyr Senatorov ◽  
Oleksander Melnyk

Proposals on composition of the aiming and search system of land unmanned complex are offered. The work aims to improve one of the most important technical characteristics of land unmanned complex - survivability. Proposals are given for improving the layout of aiming and search system of land unmanned complex. Existing composition schemes have a low firing life because of the devices included in its structure have are installed into general body. Sniper impact in body makes ineffective all aiming and search system. Authors proposes to install the devices into two bodies along weapon sides. TV-sight should be installed into the first body and thermal-vision sight should be installed into the second body.  Then if sniper impact is affecting one body, then the devices of the second body are able to execute a battle task with some limitations thanks to efficient sight. The issues of controlling the stability of the aiming line of the aiming and search system at the stage of bench tests using a collimation-measuring unit are considered in detail. A technique for adjusting both television and thermal imaging sights is proposed. In addition to increasing the survivability of the entire unmanned complex, the proposed technical solution has a number of other advantages. First, the "cold" zeroing of the combat module is greatly simplified. Instead of a system of two penta mirrors, a BS-0 ° rhombus prism can be used for this. Secondly, the proposed layout potentially simplifies the further modernization of aiming and search system, which would require the inclusion of additional units. For example, to expand the functionality of the complex by analyzing the polarization of radiation from objects and backgrounds, an additional volume is provided to accommodate polarimetric attachments. Thirdly, an even greater increase in the survivability of the complex can be achieved by increasing the secrecy of the combat mission. Usage of the base distance between the entrance pupils of the sights makes it possible to passively measure the range to the target using the internal base rangefinder instead of the laser rangefinder.


2011 ◽  
Vol 9 (1) ◽  
pp. 23-33
Author(s):  
Snezana Mitic ◽  
Ratko Pavlovic

The influence of longitudinal constructive discontinuity on the stability of the plate in the domain of elastic stability is solved based on the classical thin plate theory. The constructive discontinuities divide the plate into fields of different thickness. The plate has two opposite edges simply supported while the other two edges can take any combination of free, simply supported and clamped conditions. The Levy method is used for the solution of the problem of stability, with the aim of developing an analytical approach when researching the stability of plates with longitudinal constructive discontinuities and also with the aim of obtaining exact solutions for plates with non-uniform thickness. The exact solutions for stability presented herein are very valuable as they may serve as benchmark results for researches in this area.


Author(s):  
Huw Griffiths

This chapter offers a conclusion to the book, through a movement away from the human body into the ways that animal bodies are also recruited for Shakespeare’s metaphorics of sovereignty. More than any other of Shakespeare’s history plays, Richard III is dominated by animal imagery. One way to understand this is as a form of moral commentary on the “bestial” state that England has been dragged into by the civil war and, particularly, by the evils of that war as concentrated in Richard himself, a concentration particularly in the image of his body as deformed. However, the slipperiness of metaphor does not allow for the stabilization of sovereignty in any one body, including the stability imagined in the metaphysical conceit of the “kings two bodies”. In this chapter, I offer a final countermand to Kantorowicz’s reading of Richard II wherein Richard’s abdication offers up the Christ-like sacrifice of the king as a concentrated image of divine sovereignty. In place of this, I read Richard III backwards from the moment of Richard’s own brief “abdication” at the end of the play: his willingness to exchange his kingdom for a horse, albeit in the face of death. Whilst not ascribing any revolutionary intent to the character of Richard, this moment affords an alternate insight into the translatable locations of sovereignty. Re-read through its figurations, sovereignty is conceived of as never inalienable; it is, rather, always dependent on the bodies of others including, here, the bodies of animals.


Sign in / Sign up

Export Citation Format

Share Document