通过非扰动方法检查船舶一般滚动阻尼的稳定性
Galal M Moatimid1, Mona A A Mohamed2, M K Abohamer3
1Department of Mathematics, Faculty of Education, Ain Shams University, Cairo, 11566, Egypt.
Scientific reports
|February 23, 2026
概括
这项研究通过使用先进方法分析非线性稳定性,提高了海上船舶的安全性. 该研究通过详细的建模和分析,确保在现实条件下可靠的船舶性能.
科学领域:
- 海军建筑和海洋工程.
- 非线性动力学和控制系统
- 分析海上安全与稳定
背景情况:
- 确保在现实的海上条件下确保船舶的稳定性对于安全至关重要.
- 现有的模型往往简化了非线性动态,限制了适用性.
- 滚动减压效应需要先进的分析来准确预测稳定性.
研究的目的:
- 在具有滚动阻尼的容器中探索非线性稳定性.
- 开发一个包含操作条件,非线性和水力动力学的通用模型.
- 为了研究非扰动方法 (NPA) 分析和,保守的合系统.
主要方法:
- 开发一个通用的非线性船舶动态模型 (1DOF).
- 应用非扰动方法 (NPA) 将非线性ODEs转换为线性ODEs,而无需泰勒扩展.
- 使用Galerkin技术推导出一个先进的线性ODE.
- 采用多次时间尺度方法 (MTSM) 进行近似解决方案和稳定性分析.
- 使用相位图,庞卡雷地图和分叉图进行分叉分析.
主要成果:
- 验证了非扰乱方法 (NPA) 与数值解决方案 (NS) 相比.
- 在衍生的先进线性ODE解决方案和数值解决方案之间取得了强大的一致性.
- 确定了物理性质对稳定区内的共振区域的影响.
- 评估系统稳定性配置,强调使用MTSM的稳定和不稳定特性.
- 证明了分叉参数对分叉曲线的影响.
结论:
- 非扰动方法 (NPA) 提供了一种验证的方法来分析海上船舶的非线性稳定性.
- 一般化的模型和先进的分析技术提高了对船舶动态和安全的理解.
- 分叉分析揭示了不同参数下的复杂系统行为和稳定性特征.
相关概念视频
Stability
429
The time response of a linear time-invariant (LTI) system can be divided into transient and steady-state responses. The transient response represents the system's initial reaction to a change in input and diminishes to zero over time. In contrast, the steady-state response is the behavior that persists after the transient effects have faded.
The stability of an LTI system is determined by the roots of its characteristic equation, known as poles. A system is stable if it produces a bounded...
The stability of an LTI system is determined by the roots of its characteristic equation, known as poles. A system is stable if it produces a bounded...
429
Types of Damping
7.9K
If the amount of damping in a system is gradually increased, the period and frequency start to become affected because damping opposes, and hence slows, the back and forth motion (the net force is smaller in both directions). If there is a very large amount of damping, the system does not even oscillate; instead, it slowly moves toward equilibrium. In brief, an overdamped system moves slowly towards equilibrium, whereas an underdamped system moves quickly to equilibrium but will oscillate about...
7.9K
Damped Oscillations
7.4K
In the real world, oscillations seldom follow true simple harmonic motion. A system that continues its motion indefinitely without losing its amplitude is termed undamped. However, friction of some sort usually dampens the motion, so it fades away or needs more force to continue. For example, a guitar string stops oscillating a few seconds after being plucked. Similarly, one must continually push a swing to keep a child swinging on a playground.
Although friction and other non-conservative...
Although friction and other non-conservative...
7.4K
Buoyancy and Stability for Submerged and Floating Bodies
2.7K
In fluid mechanics, buoyancy and stability are key concepts for understanding the behavior of submerged and floating bodies. When a stationary body is fully or partially submerged in a fluid, the fluid exerts a force on the body known as the buoyant force. This force acts vertically upward through a point called the center of buoyancy, which is the center of the displaced fluid volume. According to Archimedes' principle, the magnitude of the buoyant force is equal to the weight of the fluid...
2.7K
Stability of structures
544
In mechanical engineering, the stability of systems under various forces is critical for designing durable and efficient structures. One fundamental way to explore these concepts is by analyzing systems like two rods connected at a pivot point, O, with a torsional spring of spring constant k at the pivot point. This system is similar in appearance to a scissor jack used to change tires on a car. In this case, the arms of the linkage (equivalent to the rods in this system) are entirely vertical,...
544
Pole and System Stability
1.1K
The transfer function is a fundamental concept representing the ratio of two polynomials. The numerator and denominator encapsulate the system's dynamics. The zeros and poles of this transfer function are critical in determining the system's behavior and stability.
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's...
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's...
1.1K


