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Modified Asymptotic Method of Studying the Mathematical Model of Nonlinear Oscillations Under the Impact of a Moving Environment

  • Petro PukachEmail author
  • Volodymyr Il’kiv
  • Zinovii Nytrebych
  • Myroslava Vovk
  • Pavlo Pukach
Conference paper
First Online:
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1080)

Abstract

Wave theory of movement is used to study the mathematical model of a physical system which describes oscillations of a one-dimensional elastic body under the impact of a moving continuous flow of a homogeneous environment. This model accounts for nonlinear elastic properties of the body at transverse oscillations, as well as environment density and movement velocity. Oscillation amplitude and frequency variation laws in nonresonant modes and under the impact of harmonic perturbation are obtained. Variation laws of the aforesaid parameters are defined by geometrical characteristics of the elastic body, physical and mechanical properties of the material, the velocity of the moving environment, the angular velocity of elastic body rotation, and external factors.

Keywords

Mathematical model Physical system Dynamical process Nonlinear oscillations Wave theory 
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Authors and Affiliations

  1. 1.Department of Computational Mathematics and ProgrammingLviv Polytechnic National UniversityLvivUkraine
  2. 2.Department of MathematicsLviv Polytechnic National UniversityLvivUkraine
  3. 3.Department of Artificial Intelligence SystemsLviv Polytechnic National UniversityLvivUkraine

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