The frequency response characteristic of a general time-invariant system has been extensively analyzed in literature. However, it has not gained sufficient attentions in the parametrically excited system. In fact, due to the parametric excitation, the frequency response of time-periodic system differs distinctly from that of the time-invariant system. Utilizing Sylvester’s theorem and Fourier series expansion method, commonly used in the spectral decomposition for matrix, the frequency response functions (FRFs) of a single-degree-of-freedom (SDOF) parametrically excited system are derived briefly in the paper. The external resonant condition for the system is obtained by analyzing the specific expressions of FRFs. Then, a spur-gear-pair with periodically time-varying mesh stiffness is selected as an example to simulate the frequency response characteristics of parametric system. The effects of parametric stability, periodic mesh stiffness parameters (mesh frequency and contact ratio), and damping are considered in the simulation. It is shown from both theoretical and simulation results that the frequency response of parametric system has the following properties: there are multiple FRFs even for a SDOF periodic system as the forced response contains many frequency components and each FRF is corresponding to a certain response spectrum; the system has multiple external resonances. Besides the resonance caused by the external driving frequency equals to the natural frequency, the system will also be external resonant if external frequency meets the combination of natural frequency and parametric frequency. When the system is in external resonant state, the dominant frequency component in the response is the natural frequency; damping makes the peak values of FRFs drop evidently while it has almost no impact on the FRFs in nonresonant regions.
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August 2010
Research Papers
Frequency Response Characteristics of Parametrically Excited System
Jianjun Wang,
Jianjun Wang
School of Jet Propulsion,
e-mail: wangjianjun@buaa.edu.cn
Bei Hang University
, Beijing 100191, China
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Qihan Li
Qihan Li
School of Jet Propulsion,
Bei Hang University
, Beijing 100191, China
Search for other works by this author on:
Qinkai Han
Jianjun Wang
School of Jet Propulsion,
Bei Hang University
, Beijing 100191, Chinae-mail: wangjianjun@buaa.edu.cn
Qihan Li
School of Jet Propulsion,
Bei Hang University
, Beijing 100191, ChinaJ. Vib. Acoust. Aug 2010, 132(4): 041004 (11 pages)
Published Online: May 20, 2010
Article history
Received:
December 5, 2008
Revised:
July 31, 2009
Online:
May 20, 2010
Published:
May 20, 2010
Citation
Han, Q., Wang, J., and Li, Q. (May 20, 2010). "Frequency Response Characteristics of Parametrically Excited System." ASME. J. Vib. Acoust. August 2010; 132(4): 041004. https://doi.org/10.1115/1.4000772
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