ABSTRACT

In this study, free vibration analysis of cracked plates was performed by using peridynamics (PD). A peridynamic Mindlin plate formulation was used and the numerical implementation was done using commercial finite element software, ANSYS. First, the formulation was verified by considering intact and cracked plates and peridynamic solutions were compared against numerical, theoretical and experimental results available in the literature. Once the formulation was verified, the effect of plate thickness, crack size and crack orientation on the natural frequencies were investigated for a centrally cracked plate. It was found that natural frequency values increase as plate thickness increases. On the other hand, an increase in crack length decreases the natural frequency values. Moreover, crack orientation also increases natural frequencies for larger cracks. Finally, linear variation of thickness inside the plate causes a tilt of the mode shapes towards the thin side of the plate.

摘要

在这项研究中，通过使用peridynamics（PD）进行了裂纹板的自由振动分析。使用了蠕动的Mindlin板配方，并使用商业有限元软件ANSYS进行了数值实现。首先，通过考虑完整的板和破裂的板来验证配方，并将周动力解决方案与文献中提供的数值，理论和实验结果进行比较。验证配方后，就可以研究中心开裂的板的板厚，裂纹尺寸和裂纹取向对固有频率的影响。已经发现，固有频率值随着板厚度的增加而增加。另一方面，裂纹长度的增加使固有频率值降低。此外，裂纹取向还会增加较大裂纹的固有频率。最终，板内部厚度的线性变化导致模式形状朝板的薄侧倾斜。