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A semi-analytical isogeometric analysis for wave dispersion in functionally graded plates immersed in fluids

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Abstract

The semi-analytical finite element (SAFE) method is widely used for studying properties of guided waves along composite waveguides. However, evaluating the modes associated to high wave numbers requires important mesh refinements and may significantly increase the computational cost. This paper presents a semi-analytical isogeometric analysis (SAIGA) to calculate the dispersion relation of functionally graded or multilayer plates coupling with fluids. High-order elements based on non-uniform B-splines (NURBS) basis functions are used. Several numerical examples are then studied for different problems in order to assess the efficiency of proposed method: (i) homogeneous plates; (ii) functionally graded plates; (iii) composite plates (with strong contrast of rigidity between layers); (iv) fluid-immersed plates. The results obtained are compared with the ones derived from analytical approaches and by the conventional SAFE method using Lagrange polynomials. For all cases, the dispersion curves evaluated by using enriched-NURBS basis functions achieve a significant better precision than using conventional Lagrangian functions (for the same number of degrees of freedom or the same order of shape functions), especially for the higher modes. The continuity of the stress shape modes at the interfaces is also shown to be much improved by using SAIGA.

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Authors and Affiliations

  1. Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, 61 avenue du Général de Gaulle, 94010, Créteil Cedex, France

    Fakhraddin Seyfaddini & Vu-Hieu Nguyen

  2. CIRTech Institute, Ho Chi Minh City University of Technology (HUTECH), 475 Dien Bien Phu, Binh Thanh, Ho Chi Minh City, Vietnam

    Hung Nguyen-Xuan

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  1. Fakhraddin Seyfaddini
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  2. Hung Nguyen-Xuan
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  3. Vu-Hieu Nguyen
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Correspondence to Vu-Hieu Nguyen.

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Seyfaddini, F., Nguyen-Xuan, H. & Nguyen, VH. A semi-analytical isogeometric analysis for wave dispersion in functionally graded plates immersed in fluids. Acta Mech 232, 15–32 (2021). https://doi.org/10.1007/s00707-020-02818-0

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  • DOI: https://doi.org/10.1007/s00707-020-02818-0

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