含裂纹平板的振动及裂纹扩展分析

针对含裂纹平板的振动与疲劳问题，研究含裂纹平板耦合动力学建模方法。首先在变形相似性原则下通过力学平衡原理推导出含裂纹项的平板振动方程，进而基于应力关系式形成裂纹项的表达式。在此基础上，利用Galerkin法将含裂纹板简化成单自由度振动系统，根据Berger经验方法产生方程的非线性项构建含裂纹板的非线性振动模型。最后通过算例探讨含裂纹板的动力学特性，协同Paris方程研究含裂纹平板动力学与裂纹扩展的耦合行为。研究结论表明，阻尼大小和激励力的变化对含裂纹板的振动特性及裂纹扩展规律具有显著影响。所提出的含裂纹平板耦合动力学建模方法，考虑了振动与裂纹扩展的耦合效应，为飞行器板结构抗振动疲劳设计提供理论依据。

Analysis of Vibration and Crack Growth of a Cracked Plate

Aiming at the vibration and fatigue problems, a vibration analytical modeling method for analyzing cracked plate was derived. Based on the principle of deformation similarity, the crack was replaced by an external force, and the force equilibrium condition was used to obtain the governing equation of vibration of the cracked plate. In addition, expression of the crack terms was obtained based on stress relation. On this basis, the cracked plate was simplified to a single freedom system by means of Galerkin method. Then, the nonlinear vibration equation of the cracked plate was established via Berger＇ s empirical method. As an example, the vibration characteristics and the crack growth behavior of a cantilever cracked plate was studied. Results indicated that the impact of damping and exciting force on vibration and crack growth of the cracked plate is obvious. This vibration analytical model of the cracked plate is a good tool for analysis of vibration and crack propagation.