Diffraction by an elongated body of revolution. A boundary integral equation based on the parabolic equation

Shanin, A. V.; Korolkov, A. I.

doi:10.1016/j.wavemoti.2018.10.006

Cited by 7 publications

(3 citation statements)

References 32 publications

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“…Furthermore, the authors in [21] studied convection-diffusion in fluid mechanics and modeled it through an integral equation. The problem of an elongated body that diffracts an incident wave was investigated and modeled as an integral equation in [22]. An integral equation was used to model the scattering of elastic waves problem in [23].…”

Section: Introductionmentioning

confidence: 99%

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Suitable Mass Density Function for an Artificial Satellite to Prevent Chaotic Motion after Collision with Space Debris

2022

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Artificial satellites are widely used in different areas such as communication, position systems, and agriculture. The number of satellites orbiting Earth is becoming huge, and many are set to be launched soon. This huge number of satellites in addition to space debris are sources of concern. Indeed, some incidents have occurred either between satellites or because of space debris. These incidents are a threat for the hit satellite and can be a source of irreversible damages. A hit satellite may diverge to a chaotic motion with all the entailed consequences. The inertia moment of a satellite is a main factor to determine if the hit satellite is heading toward a chaotic motion or not. The inertia moment is determined over the mass density function. In this paper, a circularly orbiting artificial satellite was modeled as a thin rotating rod. The objective was to determine a suitable mass density function for this satellite allowing the prevention as much as possible of the chaotic motion after being hit. This unknown density mass function satisfies a system of equations reflecting some physical constraints. Conventional procedures are not applicable to solve this system of equations. The presented resolution method is based on several mathematical transformations, allowing converting this system into a highly nonlinear one with several unknowns. Several mathematical techniques were applied, and an analytical solution was obtained. Finally, from the mechanical engineering point of view, the obtained mass density function corresponds to a Functionally Graded Material (FGM).

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Section: Introductionmentioning

confidence: 99%

“…Among these integral equations are the Volterra integral equations of the first and second kind [28]. In addition, the Fredholm integral equations of the first and second kind were exhibited in [22,24,[29][30][31][32][33][34]. For more details, the reader is referred to [35] for other kinds of integral equations.…”

Section: Introductionmentioning

confidence: 99%

Suitable Mass Density Function for an Artificial Satellite to Prevent Chaotic Motion after Collision with Space Debris

2022

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“…In this context, authors in [1] modeled a problem of fluid mechanic using the integral equations. The problem of diffraction by an elongated body was addressed and formulated as integral equation by [29]. In financial sector the problem of pricing puttable convertible bonds is investigated and modeled as an integral equation by [37].…”

Section: Introductionmentioning

confidence: 99%

Solution of a Non-Classical Integral Equation Modeling a Rotating Thin Rod Under Some Constraints and Technical Feasibility

Hidri

Gazdar

2020

IEEE Access

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In this paper, a mechanical system composed of a thin rotating rod under some constraints is considered. For this system, the total torque of the gravity forces is fixed and the unknown function to be determined is the mass density of the rod. This kind of problem is faced in several engineering applications as in aerospace. The resulting problem is formulated as a non classical integral equation, where the conventional methods of resolution do not apply. Therefore, a special treatment is required to solve the obtained integral equation. First, the obtained integral equation is transformed into a system of mixed integral and linear differential equations with two unknown functions. The latter transformation allows the inspiration of the general expression of the requested functions. Consequently, a highly non linear system with several unknowns is obtained. During the resolution of the latter system several mathematical technics are used. After applying all these technics an analytical solution of the studied integral equation is obtained. Finally, the technical feasibility from an engineering viewpoint of the production of a thin rod with the obtained mass density function is briefly discussed. In this context, the Functionally Graded Material is proposed as a material satisfying the obtained mass density function.

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Andronov

2023

Springer Series in Optical Sciences

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Diffraction by an elongated body of revolution. A boundary integral equation based on the parabolic equation

Cited by 7 publications

References 32 publications

Suitable Mass Density Function for an Artificial Satellite to Prevent Chaotic Motion after Collision with Space Debris

Suitable Mass Density Function for an Artificial Satellite to Prevent Chaotic Motion after Collision with Space Debris

Solution of a Non-Classical Integral Equation Modeling a Rotating Thin Rod Under Some Constraints and Technical Feasibility

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