A formulation for elastodynamic scattering based on boundary algebraic equations

• Published in: The Journal of the Acoustical Society of America 2017-05, Vol.141 (5), p.4034-4034
• Main Authors: Poblet-Puig, Jordi, Shanin, Andrey V.
• Format: Article
• Language: English
• ISSN: 0001-4966; 1520-8524
• DOI: 10.1121/1.4989302

The solution of the elastodynamic problem arises in many scientific fields such as the wave propagation in the ground, non-destructive testing, the vibration design of buildings or vibroacoustics in general. We present here an integral formulation based on the boundary algebraic equations. It leads to a boundary numerical method and has the important advantage that no contour (2D) or surface (3D) integrals need to be computed. This is very helpful in order to use combined field integral equations (numerical damping of fictitious eigenfrequencies) without the problems caused by the evaluation of hypersingular integrals. The key aspects are: (i) the approach deals with discrete equations from the very beginning; (ii) discrete (instead of continuous) tensor Green’s functions are considered (the methodology to evaluate them is shown); (iii) the boundary must be described by means of a regular square grid. In order to overcome the drawback of this third condition the boundary integral is coupled, if needed, with a thin layer of finite elements. This improves the description of curved geometries and reduces numerical errors. The method is applied to the scattering of waves by objects and holes in an unbounded elastic medium and to the solution of interior elastic problems