An interpolation method for coupling non-conforming patches in isogeometric analysis of vibro-acoustic systems

This paper presents an interpolation method for coupling non-conforming Non-Uniform Rational B-Splines (NURBS) patches in isogeometric analysis of vibro-acoustic systems. This coupling method is based on a master-slave formulation, in which a smooth interpolating function is first constructed to represent the sound pressure field of the master side and then is sampled to determine the discrete sound pressure of the slave side. The coupling constraints are studied by the interpolation matrix built in this process and imposed on the system by Lagrange multiplier method. For interfaces with weak non-conformity, the interpolating function is constructed by a direct linear combination of radial basis functions (RBF); for interfaces with strong non-conformity or curved shape, this basic interpolation method is enhanced by a moving least squares approximation to improve the coupling accuracy. The proposed method starts with non-conforming acoustic-acoustic interfaces and is extended to non-conforming structural-acoustic interfaces. In both cases, the RBF-based coupling constraints depend only on Euclidian distances between control points, allowing them to be generated in a problem-independent and dimension-insensitive way. The accuracy and convergence behavior of the proposed method are benchmarked by an eigenvalue analysis of a two-dimensional acoustic cavity. Its efficiency is further investigated through frequency response analyses of a three-dimensional car-like model, with both strong and weak structural-acoustic interactions.