中文摘要：

采用理论分析和数值模拟相结合的方式，用希尔无穷行列式法推导得到了纵摇响应的马休稳定性图谱，并用数值方法分析了平台纵摇马休不稳定运动的发生过程。结果表明：在平台参数确定的情况下，垂荡幅值的增大是导致纵摇响应发生马休失稳的主要原因，即除满足发生马休失稳的频率关系之外，只有当波浪激励作用引起的垂荡运动的幅值达到一定程度时，才会引起纵摇运动的失稳现象。

英文摘要：

This paper uses the infinite Hill determinant to derive the pitching response Mathieu stability map and applies the numerical method to analyze the platform pitching Mathieu unstable movements by the way of theoretical analysis and numerical simulation. The results show that in the case of platform parameters determined, the Mathieu instability of the pitching response is mainly due to the increase of heave amplitude. In addition to meeting the instability frequency relationship of the heave motion and wave , only when the heave motion amplitude inducing by the wave excitations reaches a certain level, will the instability of the pitching motion occur.