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Non-uniform rational B-spline based free vibration analysis of axially functionally graded tapered Timoshenko curved beams

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Abstract

The free vibration of axially functionally graded (FG) tapered Timoshenko curved beams is studied with the numerical approach. By using the non-uniform rational B-spline (NURBS) basis functions, the exact geometry and the generalized displacement field are formulated. Variable geometric parameters and material properties, including the curvature, cross-sectional area, area moment of inertia, mass density, and Young’s modulus, are expanded as functions of the coordinate in a parametric domain. Based on Hamilton’s principle, the weak formulation is derived by applying a refined constitutive relation which considers the thickness effect. Natural frequencies and mode shapes are obtained from the eigenvalue equation. Circular, elliptic, and parabolic curved beams are considered in numerical examples. The obtained results are in good agreement with those in the existing studies and those calculated by the finite element software ANSYS. Moreover, the effects of the material gradient, taper ratio, slenderness ratio, and height-span ratio on vibration behaviors are discussed.

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Author information

Authors and Affiliations

  1. School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China

    Zhiwei Zhou & Meixia Chen

  2. College of Engineering, Huazhong Agricultural University, Wuhan, 430070, China

    Kun Xie

Authors
  1. Zhiwei Zhou
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  2. Meixia Chen
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  3. Kun Xie
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Corresponding author

Correspondence to Meixia Chen.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 51779098 and 51909098) and the Natural Science Foundation of Hubei Province of China (No. 2019CFB132)

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Zhou, Z., Chen, M. & Xie, K. Non-uniform rational B-spline based free vibration analysis of axially functionally graded tapered Timoshenko curved beams. Appl. Math. Mech.-Engl. Ed. 41, 567–586 (2020). https://doi.org/10.1007/s10483-020-2594-7

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  • DOI: https://doi.org/10.1007/s10483-020-2594-7

Keywords

Chinese Library Classification

2010 Mathematics Subject Classification

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