船舶航行受风浪等多因素影响，如垂荡、横荡、纵摇、横摇、纵摇、艏摇等运动，因此，研究垂荡激励下旋转机械耦合浮筏气囊系统的随机动力学特性具有十分重要的意义。本文考虑了垂荡对船舶运动的影响，根据机械振动和随机非线性动力学理论，构建了适用于垂荡运动的旋转机械系统动力学模型；应用第二类Chebyshev正交多项式逼近法和蒙特卡洛方法深入研究系统的动力学响应。研究结果如下：

(1) 以船用旋转机械系统为研究对象，构建了垂荡激励下船用旋转机械系统的动力学模型，分析了船舶在垂荡运动时转子转速以及频率比对系统的动力学影响。仿真结果显示：转子的旋转速度越高，系统的振动位移和速度也会相应增大；随着转子转速的增大，系统的运动状态阶段为：准周期-混沌-准周期；高频率比下系统振幅降低，频率比的增加会导致旋转机械系统转向相对平稳的准周期振动。

(2) 运用第二类Chebyshev正交多项式展开逼近法和蒙特卡洛法对船用旋转机械系统进行数值求解。结果显示：当三次非线性系数作为随机参数时，其随机扰动对系统的动力学行为影响很小，但是随着外部激励幅度的不断增加，两者之间的响应差异也将变得更大；在随机参数和随机白噪声激励的共同作用下，随着转子速度或频率比的增加，两个系统之间的差异也会增加。

(3) 以船用旋转机械耦合气囊隔振系统为对象，首先采用非线性弹簧和线性阻尼器来模化气囊，构建了系统在垂荡作用下的动力学模型，运用数值方法探讨了转子转速以及频率比对系统动力学特性的影响。结果表明：在低转速时，系统垂荡运动产生的力对系统振动特性的影响比较大，随着转速的增大，不平衡激振力对系统动力学特性的影响也随之增大。

(4)在垂荡作用的基础上引入噪声激励，采用蒙特卡洛法以及四阶龙格库塔法对船用旋转机械耦合浮筏气囊系统进行数值求解分析。分析结果显示：当转子转速较低时，确定性系统和随机系统的振幅差异较小，转速增加时，两系统的振幅差异也越来越大；此外转子转速越大，旋转机械和浮筏的质量比对随机系统的振幅影响也越明显。

Ships are affected by various factors (mainly wind and waves) when sailing at sea. Therefore, it is of great significance to study the random vibration characteristics analysis of marine rotating machinery coupled floating raft airbag system under heave excitation. The heave motion is an important form of implicated motion, and this thesis considers the impact of heave on ship motion. Based on probability theory, stochastic processes, and the theory of nonlinear dynamics under basic heave effects, a dynamic model of rotating mechanical systems is established. Various nonlinear dynamic theories are used to study the dynamic characteristics of rotor systems. The main content and conclusions are as follows:

(1) A dynamic model of a marine rotating machinery system under heave excitation was constructed, taking the ship's rotating machinery system as the research object. Analyzed the dynamic effects of rotor speed and frequency ratio on the system during ship heave motion. The simulation results show that the higher the rotational speed of the rotor, the corresponding increase in the vibration displacement and speed of the system; As the rotor speed increases, the motion state stages of the system are: quasi period chaos quasi period; Under high frequency ratios, the amplitude of the system decreases, while an increase in frequency ratios leads to relatively stable quasi periodic vibrations of the rotor.

(2) This thesis applies the second type Chebyshev orthogonal polynomial expansion approximation method and Monte Carlo method to numerically solve marine rotating machinery systems. The results show that when the cubic nonlinear coefficient is used as a random parameter, its random disturbance has little effect on the dynamic behavior of the system. However, as the external excitation amplitude increases, the response difference between the two will also become larger; Under the combined effect of random parameters and random white noise excitation, as the rotor speed or frequency ratio increases, the difference between the two systems will also increase.

(3) The dynamic model of the rotor-bearing system coupled with a floating raft isolation structure was established. Firstly, nonlinear springs and dampers are used to model airbags. A dynamic model of a coupled airbag isolation system for marine rotating machinery under heave excitation is established, and dynamic differential equations are derived. The influence of rotor speed and frequency ratio on the vibration characteristics of the system is analyzed using numerical methods. The results show that at low speeds, the force generated by the system's oscillation motion has a significant impact on the system's vibration characteristics. As the speed increases, the impact of unbalanced excitation force on the system's dynamic characteristics also increases.

(4) On the basis of the effect of heave motion, noise excitation is added, and Monte Carlo method and fourth-order Runge Kutta method are introduced for numerical solution. The analysis results show that when the rotor speed is low, the amplitude difference between the deterministic system and the stochastic system is small. As the speed increases, the amplitude difference between the two systems also becomes larger; In addition, the higher the rotor speed, the more significant the impact of the mass ratio of rotating machinery and floating raft on the amplitude of the random system.