Vibrations of three-dimensional pipe systems with acoustic coupling

A general algorithm is developed to calculate the beam-type dynamic response of three dimensional multiplane finite length pipe systems, consisting of elbow and straight ducts with continuous interfaces. Emphasis is on secondary acoustic wave effects giving rise to coupling mechanisms; and the simulation accounts for one-dimensional elastoacoustic coupling from a plane acoustic wave and secondary loads resulting from wave asymmetries. The transfer matrix approach is adopted in modeling the elastodynamics of each duct, with allowance for distribution loads. Secondary loads from plane wave distortion are considered with a solution of the Helmholtz equation in an equivalent rigid waveguide, and effects of path imperfection are introduced as a perturbation from the hypothetical perfectly straight pipe. Computations indicate that the one-dimensional acoustic assumption is valid for frequencies below one-half the first cut-off frequency, and the three-dimensional acoustic effects produce an increase in response levels near and above cut-off.