A reduced basis approach for the parametric low frequency response of submerged viscoelastic structures

• Parametric ROM is derived for viscoelastic structure–acoustic interaction problems.
• A monolithic formulation is used for the space-parameter decomposition of the fields.
• Variability of the system parameters is explicitly taken into account within the ROM.
• A greedy algorithm is developed to build iteratively the monolithic trial basis.
• The ROMs can be evaluated in real-time, to obtain fields at new parameters values.
• The ROMs are evaluated on a large-scale industrial problem.

Reduced Order Models (ROMs) are proposed to compute the frequency response of submerged viscoelastic structures with variation of parameters. A parameterized matrix system is first derived from the finite element discretization of a structural-acoustic formulation, to constitute both the full model of reference and the starting point of the ROMs building. The low dimensional trial subspace is obtained offline with an iterative greedy algorithm inspired by the Reduced Basis method. Galerkin and Minimum Residual projections are then considered to determine the test subspace and construct the parametric online-efficient ROMs. Their accuracy and robustness are evaluated on two test cases: a submerged composite viscoelastic plate and a submerged propeller with viscoelastic patches. They are moreover compared to established methods conceived to tackle in vacuo viscoelastic problems, and extended here for submerged structures. Convergence properties as functions of the decomposition order are computed and discussed on parameter spaces of dimensions one and four. The resulting CPU time gain compared to full model evaluations opens the way to efficient design strategies, taking into account the parameters variabilities.