Sparse matrix techniques applied to modal analysis of multi-section duct liners

A simplified procedure is presented for analysis of ducts with discretely nonuniform properties. The analysis uses basis functions as the generalized coordinates. The duct eigenfunctions are approximated by finite series of these functions. The emphasis is on solution of the resulting large sparse set of linear equations. Characteristics of sparse matrix algorithms are outlined and some criteria for application are established. Analogies with structural methods are used to illustrate variations which can increase efficiency in generating values for design optimization routines. The effects of basis function selection, number of eigenfunctions and identification and ordering of equations on the sparsity and solution stability are included.