scholarly journals The Analytical Form of the Dispersion Equation of Elastic Waves in Periodically Inhomogeneous Medium of Different Classes of Crystals

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Nurlybek A. Ispulov ◽  
Abdul Qadir ◽  
Marat K. Zhukenov ◽  
Talgat S. Dossanov ◽  
Tanat G. Kissikov
Keyword(s):  
Elastic Waves ◽  
Material Science ◽  
Analytical Form ◽  
Fundamental Solutions ◽  
Difficulty Level ◽  
Elastic Media ◽  
Thermoelastic Wave ◽  
First Order ◽  
First Order Differential Equations ◽  
Equations Of Motions

The investigation of thermoelastic wave propagation in elastic media is bound to have much influence in the fields of material science, geophysics, seismology, and so on. The heat conduction equations and bound equations of motions differ by the difficulty level and presence of many physical and mechanical parameters in them. Therefore thermoelasticity is being extensively studied and developed. In this paper by using analytical matrizant method set of equation of motions in elastic media are reduced to equivalent set of first-order differential equations. Moreover, for given set of equations, the structure of fundamental solutions for the general case has been derived and also dispersion relations are obtained.

scholarly journals The Propagation of Thermoelastic Waves in Anisotropic Media of Orthorhombic, Hexagonal, and Tetragonal Syngonies

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Nurlybek A. Ispulov ◽  
Abdul Qadir ◽  
Marat Zhukenov ◽  
Erkin Arinov
Keyword(s):  
Wave Propagation ◽  
Fundamental Solutions ◽  
Thermoelastic Medium ◽  
Thermoelastic Wave ◽  
Economic Implications ◽  
First Order ◽  
The Given ◽  
Thermoelastic Waves ◽  
Hexagonal Syngony ◽  
Equations Of Motions

The investigation of wave propagation in elastic medium with thermomechanical effects is bound to have important economic implications in the field of composite materials, seismology, geophysics, and so on. In this article, thermoelastic wave propagation in anisotropic mediums of orthorhombic and hexagonal syngony having heterogeneity along z-axis is studied. Such medium has second-order axis symmetry. By using analytical matriciant method, a set of equations of motions in thermoelastic medium are reduced to an equivalent set of the first-order differential equations. In the general case, for the given set of equations, structures of fundamental solutions are made and dispersion relations are obtained.

Asymptotics for third-order nonlinear differential equations: Non-oscillatory and oscillatory cases

2021 ◽  
pp. 1-19
Author(s):  
Calogero Vetro ◽  
Dariusz Wardowski
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Nonlinear Differential Equations ◽  
Oscillatory Behavior ◽  
Third Order ◽  
First Order ◽  
Third Order Differential Equation ◽  
Comparison Technique ◽  
First Order Differential Equations

We discuss a third-order differential equation, involving a general form of nonlinearity. We obtain results describing how suitable coefficient functions determine the asymptotic and (non-)oscillatory behavior of solutions. We use comparison technique with first-order differential equations together with the Kusano–Naito’s and Philos’ approaches.

Sign in / Sign up

Export Citation Format

Share Document