Frequency Response Characteristics of Parametric Vibrational System
Wang Jianjun1, 2; Han Qinkai1,2; Li Qihan1
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1 School of Jet Propulsion, BeiHang University, Beijing 1001912 The State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400030
Utilizing Sylvester’s theorem and Fourier series expansion method, commonly used in the spectral decomposition for matrix, the frequency response functions (FRFs) for parametrically excited system are derived theoretically and the external resonant condition is obtained . Then, a spur-gear-pair parametric vibration system is selected as an example to simulate its frequency response characteristics. The effects of parametric stability, time-varying parameters (parametric frequency and contact ratio) and damping are considered in the simulation. It is shown from both the theoretical and simulation results that the frequency response of the parametric system has the following properties: 1 there are multi-FRFs corresponding to the multi-frequency response for the system; 2 there are multi-outer excitation resonant regions in the system. Besides the resonance caused by the excited frequency equals to the natural frequency, the system will also be external resonant if excitation frequency meets the combination of natural frequency and parametric frequency; 3 When the system is external resonant, the dominant frequency component in the response is the natural frequency; 4 Damping makes the peak values of FRFs drop evidently, while it has almost no impact on the FRFs in non-resonant regions.
Wang Jianjun;;Han Qinkai;Li Qihan.
Frequency Response Characteristics of Parametric Vibrational System[J]. Journal of Vibration and Shock, 2010, 29(3): 103-108