(untitled) (Advances in Applied Mathematics and Mechanics, 2019)
Nonlinear normal modes and a numerical iterative approach are applied to study the parametric vibrations of pipes conveying pulsating fluid as an example of gyroscopic continua. The nonlinear non-autonomous governing equations are transformed into a set of pseudo-autonomous ones by employing the harmonic balance method. The nonlinear normal modes are constructed by the invariant manifold method on the state space and a numerical iterative approach is adopted to obtain numerical solutions, in which two types of initial conditions for the modal coefficients are employed. The results show that both initial conditions can lead to fast convergence. The frequency-amplitude responses with some modal motions in phase space are obtained by the present iterative method. Quadrature phase difference and traveling waves are found in the time-domain complex modal analysis.