A numerical approach for the computation of dispersion relations for plate structures using the Scaled Boundary Finite Element Method

• Published in: Journal of sound and vibration Vol. 331; no. 11; pp. 2543 - 2557
• Main Authors: Gravenkamp, Hauke, Song, Chongmin, Prager, Jens
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 21-05-2012; Elsevier
• Subjects: Boundary element method; Computational techniques; Convergence; Dispersions; Exact sciences and technology; Finite element method; Finite-element and galerkin methods; Fundamental areas of phenomenology (including applications); Mathematical analysis; Mathematical methods in physics; Mathematical models; Physics; Plates (structural members); Solid mechanics; Structural and continuum mechanics; Vibration; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Finite element method; Dispersion (wave); Dispersion relations; Guided wave; Layered materials; Modelling; Eigenvalue problem; Non linear effect; scaled boundary finite element method; Plates; Numerical stability; Time-varying systems
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/j.jsv.2012.01.029

In this paper, a method is presented for the numerical computation of dispersion properties and mode shapes of guided waves in plate structures. The formulation is based on the Scaled Boundary Finite Element Method. The through-thickness direction of the plate is discretized in the finite element sense, while the direction of propagation is described analytically. This leads to a standard eigenvalue problem for the calculation of wave numbers. The proposed method is not limited to homogeneous plates. Multi-layered composites as well as structures with continuously varying material parameters in the direction of thickness can be modeled without essential changes in the formulation. Higher-order elements have been employed for the finite element discretization, leading to excellent convergence for complex structures. It is shown by numerical examples that this method provides highly accurate results with a small number of nodes while avoiding numerical problems and instabilities.
► We develop a numerical method for the calculation of dispersion relations of plates. ► The formulation is based on the scaled boundary-finite element method. ► A standard eigenvalue problem is derived for the calculation of wave numbers. ► Dispersion relations are calculated for composites and functionally graded materials. ► Higher-order elements highly improve accuracy and efficiency for complex structures.