A direct updating method for undamped vibroacoustic FE models

Abstract

Vibroacoustic systems involving an elastic structure enclosing an acoustic cavity are commonly found in aerospace, automobile, and other transportation equipment. This paper develops a direct method for simultaneously updating the mass and stiffness matrices of undamped vibroacoustic finite element (FE) models. The properties of updated coefficient matrices, including symmetry, characteristic equation and orthogonality, are imposed as constraints to form the matrix minimization problem. By utilizing the generalized singular value decomposition, the general solution of the constrained matrix equations is obtained. With it, the updated matrices are derived by using Kronecker product and matrix derivatives. Two numerical examples illustrate the effectiveness of the proposed method.