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High-order free vibration analysis of elastic plates with multiple cutouts

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Abstract

This paper aims to conduct the free vibration analysis of single-layer and laminated composite plates with multiple cutouts based on the scaled boundary finite element method (SBFEM) incorporated with the precise integration method (PIM) and the technique of the degree of freedom transform. It is applicable to a variety of shaped plates containing cordiform, circular and other complicated cutouts. The key equations are formulated built on the two-dimensional model, and the discretization is carried out in terms of only three translational displacement components as the basic unknowns. The high-order spectral elements are applied in the proposed technique to accurately simulate the arc boundaries of cutouts. Characterized by the important semi-analytical feature of the SBFEM, responses of the transverse free vibration are accurately explored. The derivation of governing equations strictly follows the 3D theory of elasticity without introducing any assumptions. The general solution of the SBFEM key equation is in the form of the matrix exponent, which is calculated by the PIM. As a type of highly precise approach, the PIM is introduced to create the global stiffness matrix from the analytical exponential matrix, which can make sure the eigensolutions with enough accuracy. Aided by the methodology of the kinetic energy formula, the global mass matrix of the perforated plate structure is constructed. According to the thin plates, the degree of freedom transform is employed to lower the dimensions of eigenvalue equation and thus improve the computational efficiency. Numerical examples of flexible square and circular plates with various cutouts reveal that excellent agreement is achieved between the natural frequencies predicted by the developed method and those from other methods and exact solutions. Furthermore, the effect of boundary conditions, skew angles, thickness-to-length ratios and sizes of cutouts on distributions of vibration frequencies is discussed.

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  • 13 January 2021

    Journal abbreviated title on top of the page has been corrected to “Arch Appl Mech”

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Acknowledgements

This research is supported by Grants 2018M641168, 2018M641169 from China Postdoctoral Science Foundation, Grants 51908022 from the National Natural Science Foundation of China, Grants 19YJC630148 from the Humanity and Social Science Youth foundation of Ministry of Education of China, for which the authors are gratefully acknowledged.

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  1. School of Civil and Transportation Engineering, Beijing University of Civil Engineering and Architecture, Beijing, 102616, China

    Xu Sun, Pengchong Zhang, Hong Qiao & Kun Lin

  2. Beijing Advanced Innovation Center for Future Urban Design, Beijing University of Civil Engineering and Architecture, Beijing, 100044, China

    Pengchong Zhang

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Sun, X., Zhang, P., Qiao, H. et al. High-order free vibration analysis of elastic plates with multiple cutouts. Arch Appl Mech 91, 1837–1858 (2021). https://doi.org/10.1007/s00419-020-01857-2

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