基于横摇角速度变化的变形细长体运动稳定性仿真

Q3 Mathematics SPIIRAS Proceedings Pub Date : 2019-06-04 DOI:10.15622/SP.2019.18.3.645-676
I. Romanova
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引用次数: 1

摘要

考虑运动物体的类别,即由于某种原因使船体发生不可逆变形的旋转物体。所研究问题的即时性既与研究此类物体动力学的需要有关,也与已经进行的研究的不足有关,这些研究主要集中在研究气动弹性或质量不对称的影响,而不影响具有不可逆变形的物体的动力学。给出了考虑对象的运动稳定性问题,包括变形体的纵向和横向运动相互作用的过程。特别注意弯曲体绕轧辊旋转的运动和临界轧辊速度存在的识别。值得注意的是,对于被动运动的情况,这种相互作用有三种可能的原因:空气动力学,运动学,惯性。已经发展了一种理论方法,考虑到变形体的具体几何特征。该方法使实际研究中确定变形体的允许变形水平及其与运动参数的关系成为可能。根据Routh - Hurwitz准则对描述人体运动的系统解的稳定性准则进行稳定性分析。确定了对运动稳定性有不同程度影响的身体参数。在更一般的情况下,给定角速度的滚转稳定边界曲线将具有比简单双曲线更复杂的形式。给出了确定参数方程的非线性直接解的可能性。这将有可能获得临界脚跟速度和稳定范围对这些参数的依赖关系。基于所开发的技术对直体和弯曲体进行的数学建模表明,体曲率对相对于稳定极限的攻角的俯仰导数矩线的位移和滑移角的滑动矩有显著影响。确定了横摇角速度的范围,其中观察到弯曲体的稳定性损失。从直体和曲面体的稳定条件出发,分析了角速度的变化和滑移角中偏航力矩系数导数的相对变化对决定因子值的影响。它显示了身体的曲率如何导致鞍点的移动。分析了马赫数变化对特征方程决定系数的影响。
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Simulation of Motion Stability of Deformed Elongated Bodies Based on Variations of Angular Velocities in Roll
The class of moving objects, which are bodies of revolution, which for some reason have undergone irreversible deformations of the hull, is considered. The immediacy of the problem being studied has to do both with the need to study the dynamics of such objects and the insufficiency of the studies already conducted, which are mainly focused on the study of the effects of aeroelasticity or mass asymmetry and do not affect the dynamics of bodies with irreversible deformations. The problem of the motion stability of the considered objects, including the process of interaction of the longitudinal and lateral movements of the deformed body, is formulated. Particular attention is paid to the movement of the curved body with rotation about the roll and the identification of the presence of critical roll velocities. It is noted that for the case of passive movement there are three possible reasons for this interaction: aerodynamic, kinematic, inertial. A theoretical approach has been developed that takes into account the specific features of the geometry of deformed bodies. The approach made it possible in practical studies to determine the allowable deformation levels and its relationship with the motion parameters of deformed bodies. The stability analysis was carried out based on the stability criteria of the system solutions describing the body movement according to the Routh – Hurwitz criterion. The body parameters , which have a varying degree of influence on the stability of movement, are determined. In a more general case, the curve of the stability boundary for a given angular velocity in roll will have a more complex form than a simple hyperbola. The possibility of obtaining a direct solution to a nonlinear to the determining parameters equation is also shown. It will make it possible to obtain the dependences of the critical heel velocities and stability ranges on these parameters. Mathematical modeling based on the developed techniques, carried out for direct and curved bodies, showed that the body curvature has a significant effect on the displacement of the lines of derivative pitch moments in the angle of attack and the moment of sliding in the angle of slip relative to the limits of stability. The range of angular velocities for the roll is determined, in which a loss of stability is observed for the curved body. The effect of variations in the angular velocity and the relative change in the derivative of the yaw moment coefficient in the slip angle on the value of the determining factor from the stability conditions for the direct and curved bodies is analyzed. It is shown how the curvature of the body leads to a shift of the saddle point. The effect of a change in the Mach number on the determining coefficient of characteristic equations is analyzed.
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来源期刊
SPIIRAS Proceedings
SPIIRAS Proceedings Mathematics-Applied Mathematics
CiteScore
1.90
自引率
0.00%
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0
审稿时长
14 weeks
期刊介绍: The SPIIRAS Proceedings journal publishes scientific, scientific-educational, scientific-popular papers relating to computer science, automation, applied mathematics, interdisciplinary research, as well as information technology, the theoretical foundations of computer science (such as mathematical and related to other scientific disciplines), information security and information protection, decision making and artificial intelligence, mathematical modeling, informatization.
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