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The present paper deals with the interior solid-fluid interaction problem inharmonic regime with randomly perturbed boundaries. Analysis of the shapederivative and shape Hessian of vector- and tensor-valued functions isprovided. Moments of the random solutions are approximated by those of theshape derivative and shape Hessian, and the approximations are of third orderaccuracy in terms of the size of the boundary perturbation. Our theoreticalresults are supported by an analytical example on a square domain.

A Shape calculus approach for time harmonic solid-fluid interaction problem in stochastic domains