Transient Hydroelastic Vibration of Piping With Local Nonlinearities

A mode superposition algorithm is presented to solve fluid and structural dynamics problems in piping systems with a local cross-sectional material nonlinearity, such as cavitation of fluid or circumferential cracking of the pipe material. Two families of eigenmodes are used to decompose the total response into so-called compatibility-controlling and resistance-controlling responses which satisfy the governing partial differential equations. The responses are simultaneously solved in time by means of convolution integral techniques. Either response is always predicting for the other an additional excitation—load or displacement—at the nonlinear cross section in such a manner that the resulting boundary conditions fully simulate the inelastic material behavior. The algorithm is applied to a test problem of waterhammer-induced coupled acoustic and mechanical piping vibrations with cavitating fluid. The coupling is shown to reduce the dynamical loading of the pipe and to eliminate unrealistic beating of closely spaced acoustic and mechanical eigenmodes appearing in uncoupled analysis.