Applications of domain partition in BEM for solving the vibration problem of a rod subjected to a spatially distributed harmonic loading

In this paper, the dual boundary element method is used in conjunction with the domain partition to solve the vibration problem for a rod subjected to a time harmonic loading. It is shown that when the constraint equations ar e all included in the solver and the real part singular or real part hypers ingular equation is used alone, the spurious resonance that may arise can b e eliminated by using the singular value decomposition method. Even when th e complex singular or hypersingular equation is used, if the structure is c omplicated or heterogeneous, domain partitioning and a subsequent parallel treatment become necessary, this gives rise to both spurious and "pseudo-sp urious" resonance. Three iteration schemes that are often used in parallel computation are shown to be inadequate here, and a new "mixed method" appro ach is proposed. Three benchmark examples are then used to show how the pro posed approaches can be applied to eliminate various kinds of spurious and pseudo-spurious resonance.