含裂纹梁非线性静动力特性及简化动力学建模

摘要

T he influence of cracks on the dynamic behavior of the beam is studied to provide a theoretical basis for crack monitoring .Firstly ,the cracked zone is analyzed by establishing a 2D contact nonlinear finite element model ,and its different compressive and tensile stiffness in static characteristics is clari‐fied .Secondly ,through the analysis of the mechanism model ,it points out that different compressive and tensile stiffness will cause coupling vibration in axial and bending directions .Then ,the coupling vibration phenomena is observed w hen using nonlinear dynamic analysis methods to study its dynamic characteris‐tics .Moreover ,it has an important feature that there is twice frequency component of bending vibration in axial vibration spectrogram .Finally ,a new simplified dynamic model is established ,and its rationality is verified compared with refined finite element analysis .This model converts the contact nonlinear prob‐lem to the material nonlinear problem to avoid complex solving process .%主要研究裂纹对梁结构动力特性的影响规律，进而为含裂纹梁结构状态监测提供理论依据。首先，对裂纹影响区域进行分析，建立含裂纹梁二维接触非线性有限元模型，阐明含裂纹梁具有拉压不同刚度的静力特性；其次，通过对机理模型的分析，指出拉压不同刚度会引起轴向与弯曲的耦合振动；然后，通过非线性动力学分析方法研究其动力特性，观察到含裂纹梁在冲击荷载下会产生轴向与弯曲的耦合振动现象，并指出这种轴向与弯曲耦合振动的一个重要特征是轴向振动频谱图中含有弯曲振动基频的两倍频成分；最后，通过引入非线性弹簧建立一种新颖的含裂纹梁简化动力学模型，通过与精细有限元分析对比，验证了模型的合理性。该简化动力学模型将接触非线性问题转换为材料非线性问题，避免了费时的接触非线性动力学求解过程。