刘利琴^*

（  天津大学水利工程仿真与安全国家重点实验室，天津，300072；  ）

摘要： 非线性振动是船舶与海洋工程结构物的一种重要振动形式，本课程针对船舶与海洋工程专业的硕士研究生开设。以船舶与海洋工程领域中的实际问题为背景，数值求解非线性运动方程，借助时间历程、相位图、傅里叶变化谱图、最大Lyapunov指数、分岔图及响应的庞加莱截面等数值工具，以图像展示的方式解释各种抽象的非线性现象，如超谐分岔、亚谐分岔、混沌运动等，促进学生进一步掌握非线性振动理论在船舶与海洋工程领域的应用。???
关键词： 非线性振动；船舶与海洋工程；数值模拟；图像教学?????

LIU Liqin^*

（  State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University , Tianjin 300072；  ）

Abstract： Nonlinear vibration is one of the most important motion forms of the ship and ocean structures. This course is for the master degree candidates of the major of ship and ocean engineering, and it is based on the real problems of the field of ship and ocean engineering. The time histories, phase portraits, fft figures, max Lyapunov exponents, bifurcation figures and Poincare maps are calculated. The nonlinear phenomena that hard to understand are interpreted by the image showing, such as super harmonic bifurcation, sub harmonic bifurcation and chaos. This will help the students to grasp the application of nonlinear vibration theory in the field of ship and ocean engineering.
Keywords： nonlinear vibration, ship and ocean engineering, numerical simulation,image teaching

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