Application of the Harmonic Balance Technique to Finite Element Models of Asymmetric Rotors Via Sparse Kronecker Products

Small vibrations of asymmetric rotors with non-axisymmetric shaft and non-isotropic bearings are represented by linear differential equations with periodic coefficients. For computation of a steady state response of the finite element model of these rotors, the present paper proposes a new form of the harmonic balance technique via sparse Kronecker products, which is especially suitable for direct representation in a compact form. This form of harmonic balance technique requires the finite element matrices to be assembled and stored in a compact form using a compact assembler routine. The sparse matrix generated in the harmonic balance technique can then be processed using standard sparse linear system solvers, direct or iterative. The present approach is particularly useful and efficient for large three-dimensional finite element models of rotors with complicated geometries.