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| Eigenvalue problems in forced harmonic responses analysis in structural dynamics |
| Received:May 25, 2016 Revised:June 12, 2016 |
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| DOI：10.7511/jslx201604020 |
| KeyWord:resonant anti-resonant minimum response frequencies sensitivity analysis |
| Author | Institution |
| 王波平 |
德克萨斯州立大学 阿灵顿分校 机械与航空工程系, 美国德克萨斯 76019 |
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| Abstract: |
| In structural dynamics,it is well known that resonance frequencies in forced harmonic response of an undamped structure are related to the eigenvalue for free vibration problem.These resonance frequencies are the peaks in the frequency response plots.In this paper,it is shown that the frequencies for the valleys (lowest points in vibration amplitude) in the frequency response plot can also be computed by solving eigenvalue problems associated with the forced harmonic response of the system.When the minimum response is zero,the corresponding frequencies are the well-known antiresonsnt frequencies.Otherwise,these are minimum response frequency between two resonances.Using the eigenvalue formulation,the sensitivities of the antiresonant or minimum response frequency can be readily computed using eigenvalue sensitivity results for general non-symmetrical matrices.Detailed formulations are presented in the paper. Several numerical examples are included to illustrate the general formulations. |