A Weak Formulation for Isogeometric Analysis of Vibro-Acoustic Systems with Non-Conforming Interfaces

Abstract

This paper develops a weak formulation for steady-state dynamic analysis of vibro-acoustic systems in the isogeometric framework. The Non-Uniform Rational B-Splines (NURBS) polynomials are used as basis functions for both geometrical transformation and numerical approximation. Starting from a NURBS-based geometrical projection that transforms a general, complex domain to a regular, spectral domain, an energy-based numerical model is then built, in which NURBS are again used as wholly admissible functions to approximate the structural displacement and the acoustic sound pressure. This process eventually leads to a set of discretized equations, based on which the system’s dynamic properties can be obtained. Besides better accuracy and excellent geometrical adaptivity, the main merit of the proposed method lies in its element-free feature of system modeling, which provides a natural solution for structural-acoustic coupling with non-conforming interfaces. This non-conformity results from either non-matching control points along the boundary or distinct polynomial orders used by adjacent patches, which is inevitable for a vibro-acoustic system given its multi-physics nature. The reliability of the proposed method is validated by a benchmark example. Its accuracy and efficiency are further investigated through a more general, car-like vibro-acoustic system.