A modeling method for transverse vibration of cracked plate containing multiple internal curved through cracks is presented and experimental studies are performed to validate its effectiveness. The cracked plate is assumed to be divided into several rectangular and curved trapezoidal domains in the global coordinates system. For each sub-domain, the transverse displacement is expanded as Chebyshev orthogonal polynomials series in local coordinates system. As for the shared edges between neighboring two sub-domains, the local collocation method is adopted and a number of Chebyshev zero points are selected to ensure the displacement continuity condition. To verify the convergence and correctness of the presented model and solutions, the natural frequencies, mode shapes and dynamic responses for several cases are compared with reference results and experimental results, with good agreement observed. In addition, the influence of several significant parameters of cracks are investigated, including the number, location and geometrical shape of the cracks. It is shown that the crack inside the plate presents less influence than that at the boundary on the mode change of the plate. The investigations in the study implies that the present model method is effective and convenient for plate with multiple curved through cracks.

中文翻译：

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多弯曲贯通裂纹板的横向振动


提出了一种含有多个内部弯曲贯通裂纹的裂纹板横向振动建模方法，并进行了实验研究以验证其有效性。假设裂纹板在全局坐标系中被划分为多个矩形域和曲线梯形域。对于每个子域，横向位移在局部坐标系中展开为切比雪夫正交多项式级数。对于相邻两个子域之间的共享边，采用局部搭配方法，选择多个切比雪夫零点来保证位移连续性条件。为了验证所提出的模型和解的收敛性和正确性，将几种情况下的固有频率、振型和动态响应与参考结果和实验结果进行了比较，观察到了良好的一致性。此外，还研究了裂纹的几个重要参数的影响，包括裂纹的数量、位置和几何形状。结果表明，板内裂纹对板模态变化的影响小于边界裂纹。研究结果表明，该模型方法对于具有多条弯曲贯通裂纹的板来说是有效且方便的。