This is an experimental and theoretical study on systems with frictional damping and frictional excitation. Part of the project focuses on characterizing and modeling friction during oscillations. To this end, we have modeled hysteretic friction-velocity behavior in a mass spring system, and "developed" a decrement method for identifying friction parameters in a system with viscous and dry friction. (I say "developed" because we found later that Watari of Japan did something similar back in the 1960s.) The wavelet transform and geometric analyses have been helpful in the friction modeling. Another aspect of the project has focused on friction induced vibration, in effort to gain understanding of squeak and squeal problems. We are applying proper orthogonal decomposition in the study of friction induced vibration of distributed systems. We also are seeking experimental evidence of squeak mechanisms in automotive suspension parts in effort to find a squeak criterion for designers.

**Support:** National Science Foundation, CMS-9624347,
8/96-7/00;
Ford Motor Company, 9/95-5/96.

**Publications**

- J.-W. Liang and B. F. Feeny, 2011, "Balancing energy to
estimate damping in a forced oscillator with compliant contact,"
Journal of Sound and Vibration 330 (9) 2049-2061. (similar paper presented at a
conference)

- B. F. Feeny, 2009, "Estimating damping parameters in
multi-degree-of-freedom vibration systems by balancing energy,"
Journal
of Vibration and Acoustics, 131 (4) 041005. (preprint)

- J. L. Quinby and B. F. Feeny, 2009, "Low-frequency behavior in
a
frictionally excited beam," Journal of Sound and Vibration 325,
884-893. (preprint, with Movie 1, Movie 2, and Movie
3.)

- B. F. Feeny and F. C. Moon, 2007, "Empirical friction modeling
in
forced oscillators using chaos," Nonlinear Dynamics 47 (1-3)
129-141. Preprint.

- J.-W. Liang and B. F. Feeny, 2006, "Balancing energy to
estimate
damping parameters in forced oscillators," Journal of Sound and
Vibration 295 (3-5) 988-998. (Preprint).

- J.-W. Liang and B. F. Feeny, 2005, "Wavelet analysis of
stick-slip signals in oscillators with dry friction", Journal of
Vibration and Acoustics 127 (2) 139-143. (Preprint).

- J.-W. Liang and B. F. Feeny, 2004, "Identifying Coulomb and
viscous friction in forced dual-damped oscillators," Journal of
Vibration and Acoustics 126(1) 118-125. (preprint).

- J. L. Quinby and B. F. Feeny, 2004, "Low-frequency phenomena in a frictionally excited beam," IDETC 04, Anaheim, November. (Preprint)
- J. W. Liang and B. F. Feeny, 2002, "Identifying Coulomb and
viscous friction in forced oscillators by using a harmonic
energy
balance," IMECE '02, New Orleans, November. (preprint)

- C. M. Jung and B. F. Feeny, 2002, "Friction-induced vibration in periodic linearly elastic media," Journal of Sound and Vibration 252 (5) 945-954. (preprint)
- C. M. Jung and B. F. Feeny, 2002, "On the discretization of an elastic rod with distributed sliding friction," Journal of Sound and Vibration 252 (3) 409-428. (preprint)
- B. F. Feeny and F. C. Moon, 2000, "Quenching stick-slip chaos with dither," Journal of Sound and Vibration 237(1) 173-180 (preprint, figures).
- R. Kappagantu and B. F. Feeny, 2000, "Part 1: Dynamical characterization of a frictionally excited beam," Nonlinear Dynamics 22(4) 317-333. (Preprint).
- R. Kappagantu and B. F. Feeny, 2000, "Part 2: Proper orthogonal modeling of a frictionally excited beam," Nonlinear Dynamics 23(1) 1-11. (Preprint).
- B. F. Feeny and J.-W. Liang, 2000, "Stick-slip and the
phase-space reconstruction," in Applied Nonlinear Dynamcis and
Chaos of Mechanical Systems with Discontinuities, M.
Wiercigroch
and B. de Kraker (eds.), pp. 261-291, World Scientific,
Singapore. (preprint)

- R. Kappagantu and B. F. Feeny, 1999, "An 'optimal' modal reduction of a system with fritional excitation," Journal of Sound and Vibration 224(5) 863-877. Article jsvi.1999.2165 on "IdeaL".
- J. W. Liang and B. F. Feeny, 1998, "Dynamical friction behavior in a forced oscillator with a compliant contact," Journal of Applied Mechanics 65 (1) 250-257. (preprint)
- J. W. Liang and B. F. Feeny, 1998, "A comparison between direct and indirect friction measurements in a forced oscillator," Journal of Applied Mechanics 65 (3) 783-786. (preprint)
- B. F. Feeny, A. Guran, N. Hinrichs, and K. Popp, 1998, "A historical review of dry friction and stick-slip phenomena," Applied Mechanics Reviews 51 (5) 321-341.
- J. W. Liang and B. F. Feeny, 1998, "Identification of Coulomb and viscous friction from free-vibration decrements," Nonlinear Dynamics 16 (4) 337-347.
- B. F. Feeny and J. W. Liang, 1997, "Phase-space reconstructions and stick-slip," Nonlinear Dynamics 13 (1), 39-57. (preprint)
- S. W. Shaw and B. F. Feeny, 1997, "Nonlinear dynamics with impact and friction: new analysis methods," Dynamics and Chaos in Manufacturing Processes, F. C. Moon, ed., Wiley, 241-264.
- B. F. Feeny, 1996, "The nonlinear dynamics of oscillators with stick-slip friction," Dynamics with Friction: Modeling, Analysis and Experiments, A. Guran, F. Pfeiffer, and K. Popp, eds., World Scientific. (preprint)
- B. F. Feeny and J. W. Liang, 1996, "A decrement method for the simultaneous estimation of viscous and Coulomb friction," Journal of Sound and Vibration 195 (1) 149-154. (preprint)
- B. F. Feeny, 1996, "The nonlinear dynamics of oscillators with
stick-slip friction," in Dynamics with Friction, A. Guran, F.
Pfeiffer
and K. Popp (eds.), pp. 36-92, World Scientific, River Edge. (preprint)

- J.-W.Liang and B. F. Feeny, 1995, "Wavelet analysis of stick-slip in an oscillator with dry friction," Design Engineering Technical Conferences, Boston. (preprint)
- B. F. Feeny and F. C. Moon, 1994, "Chaos in a forced
dry-friction
oscillator:
experiment and numerical modeling," Journal of Sound
andVibration 170,
303-323. (preprint)

- B. F. Feeny and F.C. Moon, 1993, "Bifurcation sequences of a
Coulomb
friction
oscillator," Nonlinear Dynamics 4, 25-37. (preprint)

- B. Feeny, 1992, "A nonsmooth Coulomb friction oscillator," Physica D 59, 25-38. (preprint)
- B. F. Feeny and F.C. Moon, 1989, "Autocorrelation on symbol
dynamics
for
a chaotic dry-friction oscillator," Physics Letters A, 141, nos.
8,9,
Nov.
20, 397-400. (preprint)

- J. L. Quinby, 2003, Nonlinear Dynamics of a Frictionally Excited Beam, MS Thesis, Michigan State University, East Lansing.
- C. M. Jung, 1999, Friction-Induced Vibration in Linear Elastic Media with Distributed Contacts, PhD thesis, Michigan State University.
- R. Kappagantu, 1997, An Optimal Modal Reduction for Frictionally Excited Systems, PhD thesis, Michigan State University.
- J.-W. Liang, 1996, Characterizing the Low-Order Friction Dynamics in a Forced Oscillator, PhD thesis, Michigan State University.