翼型弹性元件动力学与稳定性问题的数学建模

Q3 Physics and Astronomy

Cybernetics and Physics Pub Date : 2021-11-30 DOI:10.35470/2226-4116-2021-10-3-201-212

P. A. Velmisov, A. Ankilov

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引用次数: 0

摘要

提出了描述机翼结构弹性元件动力学和偏微分方程组初边值问题的数学模型。在不可压缩介质模型中，研究了气体或液体流动时机翼弹性元件的动力学和稳定性。为了研究弹性元件和气液介质的动力学，使用了固体可变形体的线性和非线性力学模型以及液体和气体力学的线性模型。在构造了偏微分方程泛函的基础上，以解析形式得到了方程稳定性的充分条件。这些条件对机械系统的参数施加了限制。所得到的稳定性条件是解决气动弹性系统参数控制问题所必需的。在Galerkin方法的基础上，对弹性单元的动力学进行了数值研究，得到的分析结果证实了该方法的可靠性。

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Mathematical modeling in problems about dynamics and stability of elastic elements of wing profiles

The mathematical models describing the dynamics of elastic elements of wing structures and representing the initial-boundary value problems for systems of partial differential equations are proposed. The dynamics and stability of elastic elements of wings, flown around by a gas or liquid stream in a model of an incompressible medium, are investigated. To study the dynamics of elastic elements and a gas-liquid medium, both linear and nonlinear models of the mechanics of a solid deformable body and linear models of the mechanics of liquid and gas are used. On the basis of the constructed functionals for partial differential equations, the sufficient stability conditions are obtained in analytical form. The conditions impose restrictions on the parameters of mechanical systems. The obtained stability conditions are necessary for solving the problems of controlling the parameters of the aeroelastic system. On the basis of the Galerkin method, a numerical study of the dynamics of elastic elements was carried out, the reliability of which is confirmed by the obtained analytical results.

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来源期刊

Cybernetics and Physics Chemical Engineering-Fluid Flow and Transfer Processes

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

10 weeks

期刊介绍： The scope of the journal includes: -Nonlinear dynamics and control -Complexity and self-organization -Control of oscillations -Control of chaos and bifurcations -Control in thermodynamics -Control of flows and turbulence -Information Physics -Cyber-physical systems -Modeling and identification of physical systems -Quantum information and control -Analysis and control of complex networks -Synchronization of systems and networks -Control of mechanical and micromechanical systems -Dynamics and control of plasma, beams, lasers, nanostructures -Applications of cybernetic methods in chemistry, biology, other natural sciences The papers in cybernetics with physical flavor as well as the papers in physics with cybernetic flavor are welcome. Cybernetics is assumed to include, in addition to control, such areas as estimation, filtering, optimization, identification, information theory, pattern recognition and other related areas.