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采用已推导的俯仰运动矩形贮箱受控刚-液-弹耦合系统在外力矩作用下的耦合动力学模型,在刚体上加入控制项,详细分析了系统固有频率的精确解与近似解.应用多尺度法对耦合系统1:1:1内共振进行解析分析,与数值解比较验证解析解的正确性.通过近似解析分析得到刚-液-弹之间的耦合作用机理:1)液深影响整个系统的软硬特性,当液体发生软硬特性转化时,处于液体原多值频率区域的刚体和弹性体幅频曲线分支峰值会减弱,且具有相同的特性转化趋势;处于液体新多值频率区域的刚体和弹性体幅频曲线分支峰值会增强,且具有相反的特性转化趋势.2)刚体和弹性体幅频曲线的峰值均在以受控刚体和弹性体为主的耦合系统固有频率处,以液体为主固有频率激励,刚体和弹性体振幅较小.
The coupled dynamics model of the controlled rigid-liquid-elastic coupled system of rectangular tanks under pitching motion was derived by adding the control term to the rigid body and the exact solutions and approximate solutions of the system natural frequencies were analyzed in detail. Scale method to analyze the internal resonance in 1: 1: 1 coupling system, and verify the correctness of the analytical solution by comparison with the numerical solution. The coupling mechanism between rigid-liquid-elastic is obtained through approximate analytical analysis: 1) The soft and hard characteristics of the system, when the liquid soft and hard properties of transformation, the liquid in the original multi-value frequency region rigid body and elastomer amplitude-frequency curve peak will be weakened, and have the same characteristics of the conversion trend; in liquid new multi-valued frequency region The peak of the amplitude-frequency curve of rigid body and elastomer will increase, and have the opposite trend of character transformation.2) The peaks of the amplitude-frequency curve of rigid body and elastomer are both at the natural frequency of the coupled system mainly controlled by rigid body and elastomer, In the liquid-based natural frequency excitation, rigid body and elastomer amplitude smaller.