1982
DOI: 10.1016/0022-460x(82)90201-2
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Non-linear vibrations of a harmonically excited autoparametric system

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Cited by 79 publications
(38 citation statements)
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“…Further note that L G r G "1 and L G G "1. The non-dimensional equations of motion for the system can now be obtained by using the non-dimensional parameters introduced by Hatwal et al [5] and Bajaj et al [13]. The resulting equations of motion are…”
Section: System Description and Equations Of Motionmentioning
confidence: 98%
“…Further note that L G r G "1 and L G G "1. The non-dimensional equations of motion for the system can now be obtained by using the non-dimensional parameters introduced by Hatwal et al [5] and Bajaj et al [13]. The resulting equations of motion are…”
Section: System Description and Equations Of Motionmentioning
confidence: 98%
“…In the nontrivial solution, both Y 3 and B are nonzero. In the frequency interval (region A) between the points denoted as "pitchfork bifurcations," it is known that the semi-trivial solution has larger amplitude of response compared to the response amplitude of the third mode in the nontrivial solution [3,4,11]. However, at larger mistunings (regions B) the amplitude of the semi-trivial solution is smaller than that in the nontrivial solution.…”
Section: Local Steady-state Periodic Solutionsmentioning
confidence: 99%
“…In case a Floquet multiplier is of modulus one, a bifurcation point is created. For details on the classification of bifurcation points based on such an approach, see [3] and [20]. It is noteworthy that this system has a strong dependence on its parameters R, ζ 2 , ζ 1 , β c , and ε.…”
Section: Local Steady-state Periodic Solutionsmentioning
confidence: 99%
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“…For higher excitation levels, the response was found to be chaotic. Also, Hatwal et al [6] studied the characteristics of the autoparametric vibration absorber system in which two types of restoring force on the pendulum were considered. Furthermore, Yabuno et al [7] investigated the stability of 1/3 order subharmonic resonance of the system.…”
Section: Introductionmentioning
confidence: 99%