A Finite Element Formulation of the Eigenvalue Problem of Sound Propagation in Uniform Ducts with Shear Flow

摘要

The equations describing the propagation of sound waves in lined ducts with shear flow are given from first principles. The flow variables along the duct are assumed constant and an eigenvalue formulation to the problem is obtained. The eigenvalues are the axial wave numbers while the eigenfunctions are the transverse acoustic modes. The problem is discretized into finite elements using a weighted residual approach and the resulting cubic eigenvalue problem is solved by transforming it into a linear form.