考虑裂纹效应的弹性板振动分析模型

针对含裂纹板的动力学问题，提出了一种耦合裂纹效应的弹性板动力学建模方法。该方法依据变形等效原则用虚拟外部载荷代替裂纹作用，并通过力学平衡原理建立了耦合裂纹项的弹性板运动方程，且基于Rice和Levy应力关系式推导出裂纹项表达式；在此基础上，结合Galerkin法和Berger经验，把含裂纹弹性板振动系统简化成一单自由度非线性振动模型进行动力学特性分析。通过算例探讨了裂纹尺度、阻尼以及激励力位置对弹性板振动特性的影响。结论表明，裂纹尺度和板尺寸对振动非线性作用明显，动应力幅值受阻尼与激励力位置的控制。

Vibration Analytical Model of an Elastic Plate with Cracked Effects

The modeling method of an elastic plate under vibration with cracked effects is proposed according to dynamic problems of cracked plates. The crack is replaced by an external force approximately on the basis of deformation equivalence. The motion equation of an elastic plate considering crack is derived via the principle of mechanical equilibrium, and the cracked terms is derived through the stress relations that are introduced by Rice and Levy. Therefore, Galerkin method and Berger’s experience are used to simplify the cracked plate into a nonlinear one single freedom nonlinear vibration system, and the dynamic character of a simply support plate is analyzed. Then, a case study is carried out for the impact of crack size, plate dimension, damping and loading point on the vibration nonlinear and response. Results indicate that vibration response is affected by the plate dimension and crack size obviously; the stress response amplitude is controlled by damping and loading point.