Abstract 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.

中文翻译：

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无限域球壳外声-结构相互作用问题的弱公式

摘要 在本文中，开发了一种变分方法来解决外部声-结构相互作用问题。分别采用 Reissner-Naghdi 薄壳理论和亥姆霍兹方程来制定结构域和声学域的能量泛函。通过引入拉格朗日乘子，开发了一种用于结构域和声学域的域划分技术。同时，在相邻段的公共界面上采用最小二乘加权残差法，保证了本方法的数值稳定性。考虑到 Sommerfeld 辐射条件，在声域边界引入局部吸收边界条件。本方法在界面和边界处的稳健性能允许使用任何闭合正交多项式来扩展结构位移和声压。将水下球壳的自由和受迫振动响应与可用的精确解或 FEM 结果进行比较，以验证本方法。此外，还仔细检查了局部吸收边界条件的优点和稳定性。还分析了声域半径和结构阻尼的影响，以展示所提出方法解决声-结构相互作用问题的能力。将水下球壳的自由和受迫振动响应与可用的精确解或 FEM 结果进行比较，以验证本方法。此外，还仔细检查了局部吸收边界条件的优点和稳定性。还分析了声域半径和结构阻尼的影响，以展示所提出方法解决声-结构相互作用问题的能力。将水下球壳的自由和受迫振动响应与可用的精确解或 FEM 结果进行比较，以验证本方法。此外，还仔细检查了局部吸收边界条件的优点和稳定性。还分析了声域半径和结构阻尼的影响，以展示所提出方法解决声-结构相互作用问题的能力。