含裂纹平板振动特性裂纹扩展的分析.pdfVIP

第九部分 结构动力学 含裂纹平板的振动特性及裂纹扩展分析* 1 2 刘文光 , 陈国平 （1.南昌航空大学航空制造工程学院，南昌，330063 ； 2.南京航空航天大学航空宇航学院，南京，210016 ） 摘要：针对含裂纹平板的振动疲劳问题，建立了含裂纹板的振动分析模型，并探讨了含裂纹板的振动特 性及裂纹扩展行为。首先，用附加外部载荷等效代替裂纹，基于力学平衡原理推导了含裂纹平板的运动 方程式，并通过应力关系式形成裂纹项；而后，利用 Galerkin 法把振动微分方程简化成一单自由度振动 系统，并分析了含裂纹平板的固有频率、动应力响应以及非线性频响；最后，运用Paris 方程模拟裂纹扩 展，研究了含裂纹平板的振动疲劳裂纹扩展行为。分析表明，阻尼大小和激励力对含裂纹板的振动及裂 纹扩展特性影响显著。含裂纹平板振动模型为分析含裂纹平板的振动及裂纹扩展特性提供了有力的工具。 关键词：振动疲劳；裂纹扩展；含裂纹板 中图分类号：V216.3 ；V224 Analysis on Vibration and Crack Growth of the Cracked Plate 1 2 Liu Wenguang ,Chen Guoping 1.School of Aeronautical Manufacturing Engineering, Nanchang Hangkong University, Nanchang, 330063 2.College of Aerospace Engineering, Nanjing University of Aeronautics Astronautics, Nanjing, 210016 Abstract: According to the vibration fatigue problem, the vibration analytical model was derived; vibration and crack growth were analyzed at the same time. Firstly, the crack was replaced by an additional external force and the vibration equation of the cracked plate was derived through mechanics balance principle, and the crack terms were obtained by using stress relational expression. Then, the cracked plate was simplified to one single freedom system through Galerkin method and the natural frequency and dynamic stress and nonlinear response were discussed. Crack growth was analyzed by Paris equation and the law of crack growth for the cracked plate was analyzed in the end. Results indicate that the impacts of damping and exciting force on vibration and crack growth of the cracked plate is obvious. The vibration analytical model of the cracked plate is a good tool for vibration analysis and crack propagation. Key words: Vibration Fatigue; Crack Growth; Cracked Plate 在机械振动中，含裂纹平板的振动及其疲劳裂纹扩展研究一直受到广泛的重视。在过 去有很多的研究者对于含裂纹平板的振动分析提出了诸多解析方法，以解决此类问题的振 动行为。早期研究者们提出了诸多求解固有频率的方法[1~5]，例如把含裂纹平板的自然振动 频率方程式问题转换成齐次方程式的特征值问题；通过试验得到平板含裂纹时的固有频率； 利用傅立叶变化的方法来求得板的固有频率以及利用Rayleigh-Ritz 方法来求得此类系统的 固