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Free vibration analysis of a flat stiffened plate with side crack through the Ritz method

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Abstract

The free vibration of a flat plate with a side crack of Mode I fracture, reinforced by one stiffener parallel to the edges of the plate, is studied in this paper. Based on the classical theories of plate and beam, the plate and its stiffener are modeled separately and jointed by implementing the condition for compatibility of displacement. To describe the singularity in stress at the tip of the crack and the discontinuity in displacement across the crack, a set of functions are introduced and incorporated into the admissible functions of the displacement. The effects of location, length and orientation of side cracks on the vibration frequencies and mode shapes of the stiffened plate are demonstrated through the Ritz method with the special admissible functions. The natural frequencies of the intact and cracked stiffened plates with different stiffener locations are analyzed with two typical boundary conditions, i.e., SSSS and FSFS. The accuracy of the present solutions is verified through a convergence test. The solutions are compared with the finite element results as well.

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Acknowledgements

This research is funded by the Natural Science Foundation of China (Grant U1808214), the Fundamental Research Funds for the Central Universities of China (Grant DUT18ZD22), and the Collaborative Innovation Center of Major Machine Manufacturing in Liaoning. We would like to thank the anonymous reviewers for their helpful advises on the first draft of this paper.

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Authors and Affiliations

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

    Jian Xue & Yuefang Wang

  2. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian, 116024, China

    Jian Xue & Yuefang Wang

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  1. Jian Xue
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Correspondence to Jian Xue.

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Xue, J., Wang, Y. Free vibration analysis of a flat stiffened plate with side crack through the Ritz method. Arch Appl Mech 89, 2089–2102 (2019). https://doi.org/10.1007/s00419-019-01565-6

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