On the Discretization of an Elastic Rod With Distributed Sliding Friction

Jung, Chulwoo; Feeny, Brian F.

doi:10.1006/jsvi.2001.3936

Cited by 5 publications

(4 citation statements)

References 17 publications

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“…The rigid-body solutions u P (t)"u #v t# t/2, which in reality would be physically limited by damping or restraints. We could ground the medium with a distributed spring, but have not done so for direct comparison with the problem of "xed boundary conditions [13]. (Grounding the system with springs will a!ect the details in the stability analysis, but we expect the general phenomena to be similar.…”

Section: Undamped Modelmentioning

confidence: 96%

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Friction-Induced Vibration in Periodic Linear Elastic Media

Jung¹,

Feeny

2002

Journal of Sound and Vibration

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Section: Undamped Modelmentioning

confidence: 96%

“…Applying equation (13) to equations (1) and (2), an equation of motion including internal damping is given by…”

Section: Addition Of Internal Dampingmentioning

confidence: 99%

Friction-Induced Vibration in Periodic Linear Elastic Media

Jung¹,

Feeny

2002

Journal of Sound and Vibration

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“…The above shows that the force-position relation in a kinetic friction state on a flat surface is determined by matrix K in (16). Since K in (16) is non-symmetric, it is not a stiffness matrix in a generally accepted sense of the term.…”

Section: Stiffness Matrix and Flat Surface Propertiesmentioning

confidence: 98%

Recognizing object surface properties using impedance perception

Kikuuwe¹,

Yoshikawa²

2005

Robotica

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By using the impedance perception algorithm, which we previously proposed, the stiffness matrix that constrains the motion-force relation of a robot's end-effector is calculated in real-time. In this paper, we describe methods of extracting information concerning certain local properties of object surfaces from the stiffness matrix when the end-effector is slid on the surfaces. We develop two algorithms to deal with two classes of surfaces: flat and convex cylindrical surfaces. Since the proposed methods are designed separately from control strategies, they can be used for both autonomous and remote controlled robots. The results of preliminary experiments are presented.

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“…To cope with non-selfadjoint problems it is still possible to expand the solution in terms of eigenfunctions but, in this case, the projection of the residual has to rely upon the adjoint eigenfunctions; the convergence of the technique is assured by the general expansion theorem for non-selfadjoint systems, called the dualexpansion theorem (Jung and Feeny, 2002).…”

Section: Introductionmentioning

confidence: 99%

A discrete approach for a generalized Beck’s column in parametric resonance

Vasta

Romeo

Paolone

2009

International Journal of Solids and Structures

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a b s t r a c tA Galerkin projection based on non-standard bases is conceived to derive an equivalent discrete model of a continuous system under non-conservative forces. The problem of deriving a discrete model capable of describing critical and post-critical scenarios for non-selfadjoint systems is discussed and an heuristic rule for a proper choice of trial functions is given. The procedure is utilized to analyze the effect of non-conservative autonomous and non-autonomous (pulsating) forces acting on a linearly damped Beck's column involving geometrical nonlinearities. The linear and nonlinear behaviours arising from the analysis of the proposed discrete model are in good agreement with those observed through the unavoidably more involved direct continuous approach. Critical scenarios for the autonomous and non-autonomous cases are investigated and the multiple scales method is applied in order to obtain the bifurcation equations in the neighborhood of a Hopf bifurcation point in primary parametric resonance. A comparison between critical and post-critical continuous and discrete model is performed adopting two control parameters, namely the amplitudes of the static and dynamic components of the forces, playing the role of detuning and bifurcation parameters, respectively.

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On the Discretization of an Elastic Rod With Distributed Sliding Friction

Cited by 5 publications

References 17 publications

Friction-Induced Vibration in Periodic Linear Elastic Media

Friction-Induced Vibration in Periodic Linear Elastic Media

Recognizing object surface properties using impedance perception

A discrete approach for a generalized Beck’s column in parametric resonance

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