Affiliations: Universidad Autonoma Metropolitana, Plantel
Azcapotzalco, Departamento de Energia, Av. San Pablo No. 180, Col. Reynosa
Tamaulipas, C.P. 02200 Mexico, D.F. Mexico | Centro de Investigacion y de Estudios Avanzados del I.
P. N., Departamento de Ingenieria Electrica, Seccion de Mecatronica, A.P.
14-740, C.P. 07360 Mexico, D.F. Mexico
Abstract: In this work we study the frequency and dynamic response of a damped
Duffing system attached to a parametrically excited pendulum vibration
absorber. The multiple scales method is applied to get the autoparametric
resonance conditions and the results are compared with a similar application of
a pendulum absorber for a linear primary system. The approximate frequency
analysis reveals that the nonlinear dynamics of the externally excited system
are suppressed by the pendulum absorber and, under this condition, the primary
Duffing system yields a time response almost equivalent to that obtained for a
linear primary system, although the absorber frequency response is drastically
modified and affected by the cubic stiffness, thus modifying the jumps defined
by the fixed points. In the absorber frequency response can be appreciated a
good absorption capability for certain ranges of nonlinear stiffness and the
internal coupling is maintained by the existing damping between the pendulum
and the primary system. Moreover, the stability of the coupled system is also
affected by some extra fixed points introduced by the cubic stiffness, which is
illustrated with several amplitude-force responses. Some numerical simulations
of the approximate frequency responses and dynamic behavior are performed to
show the steady-state and transient responses.
Keywords: Autoparametric systems, Duffing system, nonlinear frequency analysis, pendulum-type absorber
