基于离散弹簧模型的裂纹梁随机振动分析

Random Vibrations of a Cracked Beam Based on a Discrete Spring Model

  • 摘要: 将裂纹等效为无质量扭转弹簧,利用广义函数描述裂纹梁的等效抗弯刚度,建立了具有任意开裂纹数目梁挠度振型和弯矩振幅的显式解析通解,并讨论了随机激励下裂纹梁挠度和弯矩功率谱密度及相应方差的计算方法.数值结果表明:本文建立的计算方法与Monte-Carlo模拟结果吻合较好.同时,裂纹深度越大,裂纹梁的挠度和弯矩功率谱密度的峰值越大,其峰值对应频率越小,而裂纹梁的跨中挠度和弯矩的方差也越大.

     

    Abstract: Considering the crack as a massless rotational spring, the equivalent stiffness of the beam with an arbitrary number of cracks is described by the generalized function. The explicit analytical expressions of the mode functions of the transverse displacement and bending moment for the cracked beam are presented. The methods to calculate the power spectral density and variance of deflection and moment for the cracked beam subjected to a random excitation are studied. The numerical results show that the results calculated in this paper are in good agreement with those of Monte-Carlo simulation. Meantime, with the crack depth increasing, the curve peaks of deflection power spectral density and bending moment power spectral density of the cracked beam increase, the corresponding frequencies reduce, and the variances of mid-span deflection and bending moment increase as well.

     

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