A semi-analytical isogeometric analysis for wave dispersion in functionally graded plates immersed in fluids
- PDF / 1,900,518 Bytes
- 18 Pages / 595.276 x 790.866 pts Page_size
- 99 Downloads / 261 Views
O R I G I NA L PA P E R
Fakhraddin Seyfaddini · Hung Nguyen-Xuan · Vu-Hieu Nguyen
A semi-analytical isogeometric analysis for wave dispersion in functionally graded plates immersed in fluids
Received: 7 February 2020 / Revised: 1 July 2020 / Accepted: 5 September 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
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. 1 Introduction Among the numerous techniques for non-destructive evaluation and structural health monitoring, the attractiveness of guided waves (GWs) stems from their capability of propagating for long distances while allowing the inspection of the entire cross section of the waveguide, from a single generation position, without substantial attenuation [43]. Specific applications using GWs include corrosion screening of oil and gas pipelines [32], damage detection [44], presence and nature of fluid loaded on structures [13], near-surface geophysics and earthquake engineering as well as ultrasound imaging of biological structures [40,41]. Through all of these applications, two categories of waveguides can be distinguished: closed waveguides (structures in vacuum) and open waveguides (immersed/embedded structures). Due to the presence of boundaries and variation of material properties, the guided waves show a strong dispersive behavior, i.e., the phase velocity and attenuation vary with frequency-content of wave package. The dispersion of guided waves depends not only on the material properties and the thickness of the structure but also on the surrounding unbounded fluid (in the case of open waveguides). This feature allows GW techniques to extract information on geometrical and or material properties of structures and its surrounding fluid f
Data Loading...
