STUDY OF PARAMETRIC VIBRATION OF GYROSCOPIC CONTINUA BASED ON NONLINEAR NORMAL MODES AND A NUMERICAL ITERATIVE APPROACH

The nonlinear normal mode technique and a numerical iterative approach are applied to study the nonlinear 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 in the state space and a numerical iterative approach is adopted to obtain the modal coefficients, in which the modal solutions of the corresponding autonomous system are taken as the initial values. The results obtained see a fast convergence. The frequency-amplitude responses and the invariant manifolds are both obtained in the frequency-domain study, while the quadrature phase difference and the traveling waves are found in the time-domain complex modal analysis.