In this paper, the buckling and free vibration of a Mindlin plate with a side crack are presented considering a uniaxial in-plane compressive or tensile load. The side crack is through the thickness of the plate. In the Ritz method, a series of corner functions are incorporated into the admissible functions which consist of the modified characteristic functions. With this treatment, one can describe the singularity in stress near the tip of the crack as well as the discontinuities in both displacement and bending rotations across the crack. The buckling loads and natural frequencies are solved through eigenvalue problems considering the existence of the crack. The effects of location, length and orientation of the crack on the buckling and free vibration of the loaded plate are demonstrated. The coupling effect of the crack and the in-plane load on the vibrational characteristics of the plate is analyzed with varying parameters. It is shown that the influences of the tensile and compressive preloads are enhanced by the crack, and the tensile preload can cause the low-order frequency to increase with the growing crack.

中文翻译：

---

轴向平面内载荷下侧裂Mindlin板的屈曲和自由振动

在本文中，考虑了单轴面内压缩或拉伸载荷，提出了带有侧裂纹的Mindlin板的屈曲和自由振动。侧面裂纹贯穿板的厚度。在Ritz方法中，一系列角函数被合并到允许的函数中，这些函数由修改后的特征函数组成。通过这种处理，可以描述裂纹尖端附近的应力奇异性，以及贯穿裂纹的位移和弯曲旋转的不连续性。考虑到裂纹的存在，通过特征值问题可以解决屈曲载荷和固有频率。演示了裂纹的位置，长度和方向对加载板的屈曲和自由振动的影响。用不同的参数分析了裂纹和平面载荷对板振动特性的耦合作用。结果表明，裂纹会增加拉伸和压缩预紧力的影响，而拉伸预紧力会导致低阶频率随裂纹扩展而增加。