基于有限元位移模式的含裂纹梁结构动力学模型

针对裂纹的存在将降低梁的刚度的实际情形,首先根据断裂力学理论,引入裂纹梁因裂纹扩展而释放的应变能表达式，然后根据金属材料的特点，运用有限元位移法建立裂纹梁单元的动力学模型，再在梁单元模型的基础上应用有限元位移法建立裂纹梁结构的动力学方程。研究表明：基于有限元位移模式所建立的动力学方程较好地体现了裂纹梁动态性能与其结构参数和裂纹参数之间的内在关系，反映了裂纹的位置及长度对含裂纹梁结构动态性能的影响，为建立含裂纹梁结构动力学模型提供了一种新的有效方法。最后通过实例对理论分析结果进行了验证。

Dynamics Equation of Cracked Beam Based on Finite Element Displacement Mode

Considering the influences of a cracks on the stiffness of cracked beam, the formula of strain energy of a cracked beam was introduced based on the theory of fracture mechanics, which showed that the strain energy of cracked beam will be released due to crack propagation. According to the characteristics of beam material, the dynamics model of cracked beam element was established by the finite element displacement method. Based on the dynamics model of cracked beam element, a dynamics equation of the beam structure with cracks was obtained. The results show that the dynamics equation discovers the actual relation among the macro dynamic characteristics of beam structure with cracks and the structural parameters and cracked parameters; and that the position and length of crack have effects on the dynamic properties of beam structure with cracks. Finally, an example was presented to verify the theoretical results.