STUDY OF PARAMETRIC VIBRATION OF GYROSCOPIC CONTINUA BASED ON NONLINEAR NORMAL MODES AND A NUMERICAL ITERATIVE APPROACH |
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Authors: | QI Hui LIANG Feng |
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Institution: | 1.School of Technology, Shenyang Open University, Shenyang 110003,China; 2.College of Mechanical Engineering and Applied Electronics, Beijing University of Technology,Beijing 100124, China; 3.School of Energy and Power Engineering, Shenyang University of Chemical Technology, Shenyang 110142, China |
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Abstract: | 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. |
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Keywords: | gyroscopic continua|pipes conveying fluid|parametric vibration|nonlinear normal modes|iterative approach |
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