Non-linear vibrations of a harmonically excited autoparametric system

Dynamics of Autoparametric Vibration Absorbers Using Multiple Pendulums

“…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…”

Global dynamics of an autoparametric spring–mass–pendulum system

“…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.…”

“…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.…”

“…Examples of nonlinear modal coupling due to 1:2 internal resonance include pitch and roll motion in ships and surface waves in fluid containing cavities. Others [3][4][5][6][7] have studied these systems with a view to using the pendulum as a vibration absorber or neutralizer. To enhance the effectiveness of the absorber, a computer-controlled mass sliding over a collar on an oscillating rod was used in [8] as a tunable vibration absorber, and active vibration control laws have been also developed on the basis of this concept (e.g., see [9]).…”

The Response of a Dynamic Vibration Absorber System With a Parametrically Excited Pendulum

“…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.…”