Part 1: Dynamical Characterization of a Frictionally Excited Beam

The dynamics of an experimental frictionally excited beam areinvestigated. The friction is characterized and shown to involve contactcompliance. Beam displacements are approximated from strain gagesignals. The system dynamics are rich, including a variety of periodic,quasi-periodic and chaotic responses. Proper orthogonal decomposition isapplied to chaotic data to obtain information about the spatialcoherence of the beam dynamics. Responses for different parameter valuesresult in a different set of proper orthogonal modes. The number ofproper orthogonal modes that account for 99.99% of the signalpower is compared to the corresponding number of linear normal modes,and it is verified that the proper orthogonal modes are more efficientin capturing the dynamics.

[1]  H. Abarbanel,et al.  Determining embedding dimension for phase-space reconstruction using a geometrical construction. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[2]  B. Friedland,et al.  Modeling and simulation of elastic and friction forces in lubricated bearings for precise motion control , 1994 .

[3]  G. P. King,et al.  Extracting qualitative dynamics from experimental data , 1986 .

[4]  Matthew A. Davies,et al.  SOLITONS, CHAOS AND MODAL INTERACTIONS IN PERIODIC STRUCTURES , 1997 .

[5]  B. Feeny,et al.  On the physical interpretation of proper orthogonal modes in vibrations , 1998 .

[6]  J. Cusumano,et al.  Period-infinity periodic motions, chaos, and spatial coherence in a 10 degree of freedom impact oscillator , 1993 .

[7]  P. Holmes,et al.  The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows , 1993 .

[8]  Alexander F. Vakakis,et al.  Interaction Between Slow and Fast Oscillations in an Infinite Degree-of-Freedom Linear System Coupled to a Nonlinear Subsystem: Theory and Experiment , 1999 .

[9]  David J. Ewins,et al.  MODELLING TWO-DIMENSIONAL FRICTION CONTACT AND ITS APPLICATION USING HARMONIC BALANCE METHOD , 1996 .

[10]  B. Ravindra,et al.  COMMENTS ON “ON THE PHYSICAL INTERPRETATION OF PROPER ORTHOGONAL MODES IN VIBRATIONS” , 1999 .

[11]  Carlos Canudas de Wit,et al.  A new model for control of systems with friction , 1995, IEEE Trans. Autom. Control..

[12]  Jhy-Horng Wang.  DESIGN OF A FRICTION DAMPER TO CONTROL VIBRATION OF TURBINE BLADES , 1996 .

[13]  A. Wolf,et al.  Determining Lyapunov exponents from a time series , 1985 .

[14]  Aldo A. Ferri,et al.  Vibration Analysis of Dry Friction Damped Turbine Blades Using Singular Perturbation Theory , 1998 .

[15]  P. Dahl.  A Solid Friction Model , 1968 .

[16]  Aldo A. Ferri,et al.  Friction Damping and Isolation Systems , 1995 .

[17]  J. Griffin.  Friction Damping of Resonant Stresses in Gas Turbine Engine Airfoils , 1980 .

[18]  J. S. Courtney‐Pratt,et al.  The effect of a tangential force on the contact of metallic bodies , 1957, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[19]  J. T. Oden,et al.  Models and computational methods for dynamic friction phenomena , 1984 .

[20]  Andrew M. Fraser,et al.  Information and entropy in strange attractors , 1989, IEEE Trans. Inf. Theory.

[21]  B. Feeny,et al.  Dynamical Friction Behavior in a Forced Oscillator With a Compliant Contact , 1998 .