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Buckling and free vibration of a side-cracked Mindlin plate under axial in-plane load

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Abstract

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.

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Acknowledgements

The authors gratefully acknowledge the National Natural Science Foundation of China through Grants U1808214 and 11172011 and the Fundamental Research Funds for the Central Universities of China (DUT18ZD221).

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Authors and Affiliations

  1. Department of Engineering Mechanics, Dalian University of Technology, Dalian, 116024, China

    Jian Xue & Yuefang Wang

  2. Beijing University of Technology, No. 100, Pingleyuan, Chaoyang District, Beijing, 100124, China

    Lihua Chen

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  1. Jian Xue
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  2. Yuefang Wang
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  3. Lihua Chen
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Correspondence to Jian Xue.

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Xue, J., Wang, Y. & Chen, L. Buckling and free vibration of a side-cracked Mindlin plate under axial in-plane load. Arch Appl Mech 90, 1811–1827 (2020). https://doi.org/10.1007/s00419-020-01698-z

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