Coupling Model of Vibration Fatigue and Nonlinear Analysis for the Cracked Plate
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摘要: 为方便预报含裂纹板的振动疲劳寿命,建立了一种含裂纹板的振动疲劳耦合分析模型。首先,利用附加外载荷替代结构裂纹,基于力学平衡原理推导含裂纹项的板振动方程;而后,利用Rice和Levy得到的应力关系式形成方程的裂纹项,通过Galerkin法把双边悬臂裂纹板简化为单自由度系统,并基于中面应变表达式形成振动方程的二、三次非线性项;最后,通过多尺度法求解含裂纹板非线性振动方程。分析表明,应用该模型可较好地研究含裂纹板的振动疲劳耦合效应。Abstract: A coupling analytical model of vibration fatigue for the cracked plate was derived for the prediction of vibra-tion fatigue life. Firstly, the crack was replaced by an additional external force and the vibration equation of the cracked plate was derived based on Newton's second law. Then, the crack terms were obtained by using stress relational expres-sion introduced by Rice and Levy, and the vibration equation of the bilateral cantilevered cracked plate was simplified into a single-degree-of-freedom system using Galerkin method and nonlinearity terms of the equation were obtained by the formulation of middle plane strain. Vibration equation was solved by the method of multiple scales. Results indicate that the proposed coupling analytical model can be used in the coupling analysis for the cracked plate.
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Key words:
- vibration fatigue /
- nonlinearity /
- cracked plate /
- coupling model
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