On the dynamic stability and efficiency of centrifugal pendulum vibration absorbers with rotating pendulums

On the stability of pairs of subharmonic centrifugal pendulum vibration absorbers allowing a rotational mobility

“…However, recent studies demonstrated that using rocking pendulums can considerably improve the efficiency of CPVAs [35][36][37][38][39]. These works encouraged researchers to investigate the impacts of rotation [14,15,[40][41][42][43][44], including the authors of the present paper [16,17,30], who extended former results on the subharmonic solution by considering pendulums that can rotate relatively to the rotor.…”

“…Figure 1 depicts the system investigated in this paper, which is the same as in [16,17,30]. A rotor of inertia J r rotates about its centre O. ϑ(t) = Ωt + θ(t) represents its total angular position, where t is the time, Ω is the mean rotational velocity and θ(t) is the fluctuating part of the rotation (with zero mean).…”

“…As in previous works [16,17,30], it is convenient to introduce dimensionless parameters and variables so as to write the equations of motion in a dimensionless form. To this aim, the following parameters and variables are introduced:…”

“…η and µ are inertia ratios, x(s i ) and z(s i ) are path functions and α(s i ) and γ(s i ) are rotation functions. As in previous works [16,17,30], it is convenient to write x(s i ) and α(s i ) as polynomials in the curvilinear abscissa s i such that…”

“…This causes the rotor to generate an antiresonance at the engine order, hence greatly reducing vibrations. However, due to the nonlinearities inherently present in CPVA systems, a number of dysfunctions -including jumps of the response [4], localisation of the pendulums' response [5][6][7][8][9][10][11][12][13][14][15][16][17], nonlinear antiresonance detuning [17,18], and the generation of higher rotor harmonics [17,[19][20][21][22][23][24] -can occur at moderate excitation levels.…”