A weak formulation for exterior acoustic-structure interaction problem of a spherical shell in infinite domain

In this paper, a variational approach is developed to solve the exterior acoustic-structure interaction problem. The Reissner-Naghdi's thin shell theory and Helmholtz equation are adopted to formulate the energy functionals for structural and acoustic domains, respectively. With introduced Lagrangian multipliers, a domain partitioning technique for both structural and acoustic domains is developed. Meanwhile, a least-square weighted residual method is adopted on the common interfaces of adjacent segments to guarantee the numerical stability of the present method. Taking the Sommerfeld radiation condition into account, the local absorbing boundary condition is introduced at the boundary of the acoustic domain. The robust performance of the present method at the interfaces and boundaries allows the use of any closed orthogonal polynomials to expand the structural displacements and acoustic pressure. Free and forced vibration responses of a submerged spherical shell are compared with available exact solutions or FEM results to validate the present method. Additionally, the advantages and stability of the local absorbing boundary condition are carefully examined. The effects of the radius of the acoustic domain and the structural damping are also analyzed to present the power of proposed method to address the acoustic-structure interaction problem. (C) 2020 Elsevier Inc. All rights reserved.