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  • 1.
    Dankowicz, Harry
    et al.
    Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign.
    Svahn, Fredrik
    KTH, Skolan för teknikvetenskap (SCI), Farkost och flyg, Fordonsdynamik.
    On the stabilizability of near-grazing dynamics in impact oscillators2007Inngår i: International Journal of Robust and Nonlinear Control, ISSN 1049-8923, E-ISSN 1099-1239, Vol. 17, nr 15, s. 1405-1429Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A constructive proof is presented for the existence of event-driven control strategies that guarantee the local persistence of system attractors with at most low-velocity contact in vibro-impacting oscillators. In particular, sufficient conditions are formulated on the linearization of the control strategies along a grazing periodic trajectory, i.e. an oscillating motion that achieves zero-relative-velocity contact with a mechanical obstacle, to ensure the asymptotic stability of the grazing trajectory and, consequently, sustained dynamics in the vicinity of the grazing trajectory even under small changes in system parameters. The implications of the methodology are illustrated with linear and nonlinear, single- and multiple-degree-of-freedom examples of vibro-impact oscillators.

  • 2.
    Svahn, Fredrik
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Farkost och flyg, Fordonsdynamik.
    Dankowicz, Harry
    Controlled onset of low-velocity collisions in a vibro-impacting system with friction2009Inngår i: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, E-ISSN 1471-2946, Vol. 465, s. 3647-3665Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper investigates the onset of low-velocity, near-grazing collisions in an example vibro-impacting system with dry friction with particular emphasis on feedback control strategies that regulate the grazing-induced bifurcation behaviour. The example system is characterized by a twofold degeneracy of grazing contact along an extremal stick solution that is shown to result in a locally one-dimensional and piecewise-linear description of the near-grazing dynamics. Explicit control strategies are derived that ensure a persistent, low-impact-velocity, steady-state response across the critical parameter value corresponding to grazing contact even in instances where the dynamics in the absence ofcontrol exhibit a sudden transition to a high-impact-velocity response.

  • 3.
    Svahn, Fredrik
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Farkost och flyg, Fordonsdynamik.
    Dankowicz, Harry
    Energy Transfer in Vibratory Systems with Friction Exhibiting Low-velocity Collisions2008Inngår i: Journal of Vibration and Control, ISSN 1077-5463, E-ISSN 1741-2986, nr 1-2, s. 255-284Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper investigates the dynamic response of an initially stationary part of a mechanism in the presence of a restoring force and dry friction to low-velocity collisions with a relatively more massive oscillating element. Of particular interest is the persistence of a local attractor in the motion of the less massive part as the path of the oscillating element grows to encompass the entire set of possible equilibrium positions in the absence of contact. It is argued that loss of a local attractor and the associated large-amplitude oscillations of the less massive part affords a means for energy transfer through the mechanism and a means for energy damping. The paper contains a rigorous derivation of conditions that appear sufficient for the persistence of a local attractor in the case where the massive oscillating element is replaced by an oscillating rigid unilateral constraint corresponding to an infinite mass ratio. Numerical simulations are subsequently used to investigate the response in the case where the mass ratio is assumed finite.

  • 4.
    Svahn, Fredrik
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Farkost och flyg, Fordonsdynamik.
    Jerrelind, Jenny
    KTH, Skolan för teknikvetenskap (SCI), Farkost och flyg, Fordonsdynamik.
    Dankowicz, Harry
    University of Illinois at Urbana-Champaign, Department of Mechanical Science and Engineering, Illinois, USA.
    Suppression of bumpstop instabilities in a quarter-car model2009Inngår i: Non-smooth Problems in Vehicle Systems Dynamics: Proceedings of the Euromech Colloquium, Berlin Heidelberg: Springer-Verlag , 2009Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Vehicle manufacturers are constantly pushed to reduce the aerodynamic drag of vehicles, for example by constructing lower vehicles with less road clearance. This, however, reduces the available margin for oscillations within the suspension. If the oscillation amplitude exceeds a critical value, the suspension will impact a bumpstop. Under periodic excitation, the onset of low-velocity impacts is associated with a strong instability in favor of high-velocity impacts. Such impacts reduce comfort and could be damaging to the vehicle. Efforts should therefore be made to limit impact velocities with the bumpstop, for example by suppressing the instability associated with low-velocity impacts. This paper proposes a low-cost feedback-control strategy, based on making small adjustments to the position of the bumpstop, that serve to suppress the transition to high-velocity impacts with the bumpstop in the case of periodic excitation. The control law is derived from the theory of discontinuity maps. The results demonstrate that the feedback strategy works even when wheel-hop is present.

  • 5.
    Wilcox, Bryan
    et al.
    University of Illinois at Urbana-Champaign, Department of Mechanical Science and Engineering, Illinois, USA.
    Svahn, Fredrik
    KTH, Skolan för teknikvetenskap (SCI), Farkost och flyg, Fordonsdynamik.
    Dankowicz, Harry
    University of Illinois at Urbana-Champaign, Department of Mechanical Science and Engineering, Illinois, USA.
    Jerrelind, Jenny
    KTH, Skolan för teknikvetenskap (SCI), Farkost och flyg, Fordonsdynamik.
    Transient growth rates of near-grazing impact velocities: Theory and experiments2009Inngår i: Journal of Sound and Vibration, ISSN 0022-460X, E-ISSN 1095-8568, Vol. 325, nr 4-5, s. 950-958Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper, nonsmooth fold bifurcations associated with the onset of low-relative- velocity (near-grazing) impacts in an oscillatory mechanical system are proposed as a potential operating principle for high-speed limit switches. Specifically, analytical, numerical, and experimental methods are employed to investigate the near-grazing transient behavior in a representative system. It is shown that the rate of growth of successive impact velocities increases beyond all bounds as the threshold parameter value is approached. A limit switch based on the proposed nonsmooth fold scenario would thus be expected to outperform one that relies on a smooth bifurcation, such as the cyclic-fold bifurcation, in terms of switching speed and sensitivity.

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