Winkler基础上连续裂纹梁的动力特性

Dynamic Characteristics of Continuous Cracked Beam on Winkler Foundation

基于梁中开裂纹的无质量线性扭转弹簧模型,建立了Winkler基础上连续裂纹Euler-Bernoulli梁的动力响应控制微分方程,给出了其动力特征的一种简便求解方法,得到了Winkler基础上具有任意裂纹数目连续EulerBernoulli梁自振频率特征方程以及自振模态的统一显式解析表达式.在此基础上,数值分析了Winkler基础上两等跨简支连续裂纹梁的动力特性,揭示了长高比、裂纹深度、位置和数目等参数对连续裂纹梁动力特性的影响,结果表明:连续裂纹梁自振频率和模态依赖于基础反力系数、裂纹位置和深度,但当裂纹处的弯矩为零时,裂纹对梁自振频率和模态无影响;基础反力系数越大,梁自振频率越高,但随着裂纹深度和裂纹数目增加,自振频率愈发降低,这些结果可为结构安全评估提供指导.

Based on the massless linear torsional spring model of open crack in beam, the dynamic governing differential equation of continuous cracked Euler-Bernoulli beam on Winkler foundation was established, and a simple method for solving its dynamic characteristics was presented. The characteristic equation of natural frequency and the unified explicit analytical expression of vibration mode of continuous Euler-Bernoulli beam with arbitrary number of cracks on Winkler foundation were obtained. Based on this, the dynamic characteristics of simply supported two equi-span continuous crack beams on Winkler foundation were studied numerically, and the influences of beam’s length-height ratio, crack depth, crack location and crack number on the dynamic characteristics of continuous cracked beams were revealed. It is revealed that the natural frequencies and the modes of the continuous cracked beam depend on the foundation reaction coefficient, the crack location and depth. When the bending moment is zero at the crack location, the crack has no effect on the natural frequency and mode. Furthermore, the natural frequency increases as the foundation reaction coefficient increases, and decreases as the depth and number of cracks increase. These results can provide guidance for the evaluation of structural safety.