Probabilistic approach for structural-acoustic finite element analysis

A probabilistic finite element method (PFEM) for the structure acoustic fluid interaction problem is presented. The formulation is developed by applying the second-order perturbation technique to the weak form of the governing equations with the scattering pressures and the structural displacements as random functions. The material properties, geometric imperfections and loadings are modeled as uncertainties by discretizing their respective random functions. The Kuhn-Tucker necessary conditions, by which the formulation can be extended to calculate reliability, are presented. A frequency domain procedure, which employs the 'derived Ritz vectors', is presented for solving the resulting probabilistic finite element equations.