Two-degree-of-freedom systems with quadratic non-linearities subjected to parametric and self excitation |
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| Affiliation: | 1. International Islamic University Malaysia (IIUM), P.O. Box 10, 50728 Kuala Lumpur, Malaysia;2. University of Tripoli (UOT), P.O. Box 13154, Tripoli, Libya;1. Department of Mechanical Engineering, International Islamic University Malaysia, Kuala Lumpur-50728, Malaysia;2. Department of Aerospace Engineering, Indian Institute of Technology, Kanpur, Uttar Pradesh-208016, India;1. College of Economics & Management, Huazhong Agricultural University, Wuhan 430070 Hubei, PR China;2. Department of Economics & Development Studies, University of Swat, Khyber Pakhtunkhwa, Pakistan;3. College of Public Administration & Land Resource Management, Huazhong Agricultural University, Wuhan 430070, Hubei, PR China;1. Mechanical Engineering Department, Kulliyyah of Engineering, International Islamic University Malaysia (IIUM), Jalan Gombak, 53100 Kuala Lumpur, Malaysia;2. Department of Aeronautical Engineering, University of Tripoli, P.O. Box 13154, Tripoli-Libya;1. Department of Mechanical Engineering, International Islamic University Malaysia, 50728 Kuala Lumpur, Malaysia;2. Department of Aeronautical Engineering, University of Tripoli, P.O. Box 81507, Tripoli, Libya |
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| Abstract: | The method of multiple scales is used to study the response of two-degree-of-freedom systems with quadratic non-linearities under the simultaneous effects of a harmonic parametric excitation and self excitation. The principal parametric resonance of the first mode and a three-to-one internal resonance is considered, followed by the case of internal and parametric resonance of the second mode. In both cases the stability of the system is also studied. Amplitude and frequency response curves are presented for both cases. The character of stability and the mode in which the system loses its stability is also discussed. |
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