摘要
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.
基金
This study was partially funded by the National Natural Science Foundation of China(Grant Nos.11672189,11672007)
the postdoctoral fund of Beijing Chaoyang District(Grant No.Q5001015201602)
the Program Funded by Liaoning Province Education Administration(Grant No.L2016010)
Prof.X.-D.Yang was founded by the Key Laboratory of Vibration and Control of Aero-Propulsion System Ministry of Education,Northeastern University(VCAME201601)
Prof.Melnik was funded by the Natural Sciences and Engineering Research Council(NSERC)of Canada,the Canada Research Chair(CRC)program,and the Bizkaia Talent Grant under the Basque Government through the BERC 2014-2017 program
as well as Spanish Ministry of Economy and Competitiveness MINECO:BCAM Severo Ochoa excellence accreditation SEV-2013-0323.
