0
TECHNICAL PAPERS

Nonlinear Transient Localization and Beat Phenomena Due to Backlash in a Coupled Flexible System

[+] Author and Article Information
Xianghong Ma, Alexander F. Vakakis

Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801

J. Vib. Acoust 123(1), 36-44 (Aug 01, 2000) (9 pages) doi:10.1115/1.1320813 History: Received October 01, 1999; Revised August 01, 2000
Copyright © 2001 by ASME
Your Session has timed out. Please sign back in to continue.

References

Li,  W., 1991, “Vector Transform and Image Coding,” IEEE Trans. Circuits Syst. Video Technol., 1, pp. 297–307.
Ding,  W., 1994, “Optimal Vector Transform for Vector Quantization,” IEEE Signal Process. Lett., 1, pp. 110–113.
Sirovich,  L., and Kirby,  M., 1989, “An Eigenfunction Approach to Large Scale Transitional Structures in Jet Flow,” Phys. Fluids A, A2, pp. 127–136.
Sirovich,  L., 1982, “Turbulence and the Dynamics of Coherent Structures. Part I: Coherent Structures,” Quarterly Appl. Math., 45, pp. 561–571.
Sirovich,  L., Knight,  B. W., and Rodrigues,  J. D., 1990, “Optimal Low-Dimensional Dynamic Approximation,” Quarterly Appl. Math., XLVIII, pp. 535–548.
Rodriguez,  J. D., and Sirovich,  L., 1990, “Low Dimensional Dynamics for the Complex-Landau Equation,” Physica D, 43, pp. 77–86.
Bengeudouar, A., 1995, Proper Orthogonal Decomposition in Dynamical Modeling: A Qualitative Dynamic Approach, Ph.D. thesis, Boston University, Boston, MA.
Tarman,  H., 1996, “A Karhunen-Loeve Analysis of Turbulent Thermal Convection,” Int. J. Numer. Methods Fluids, 22, pp. 67–79.
Cusumano,  J. P., Sharkady,  M. T., and Kimble,  B. W., 1994, “Dynamics of a Flexible Beam Impact Oscillator,” Philos. Trans. R. Soc. London, Ser. B, 347, pp. 421–438.
Georgiou, I. T., “Dynamics of Large Scale Coupled Structure/Mechanical System: A Singular Perturbation/Proper Orthogonal Decomposition Approach,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. (in press).
Georgiou, I. T., Schwartz, I., Emaci, E., and Vakakis, A. F., “Interaction Between Slow and Fast Oscillations in an Infinite Degree-of-Freedom Linear System Coupled to a Nonlinear Subsystem: Theory and Experiment,” ASME J. Appl. Mech. (in press).
Azeez, M. F. A., 1998, Theoretical and Experimental Studies of the Nonlinear Dynamics of a Class of Vibroimpact Systems, Ph.D. thesis, University of Illinois at Urbana-Champaign, Illinois.
Azeez, M. F. A., and Vakakis, A. F., “Proper Orthogonal Decomposition (POD) of a class of Vibro-impact Oscillations,” J. Sound Vib. (in press).
Holmes, P., Lumley, J. L., and Berkooz, G., 1996, Turbulence, Coherent Structures, Dynamical Systems and Symmetry, Cambridge, New York.
Ma, X., Vakakis, A. F., and Bergman, L. A., “Proper Orthogonal (Karhunen-Loeve) Modes of a Flexible Truss: Transient Response Reconstruction and Experimental Verification,” AIAA J. (submitted).
Kappagantu,  R. V., and Feeny,  B. F., 2000, “An Optimal Modal Reduction of a System with Frictional Excitation,” J. Sound Vib., 224, No. 5, pp. 863–877.
Feeny,  B. F., and Kappagantu,  R. V., 1998, “On the Physical Interpretation of Proper Orthogonal Modes in Vibrations,” J. Sound Vib., 211, No. 4, pp. 607–616.

Figures

Grahic Jump Location
Configuration of the coupled rod system
Grahic Jump Location
(a) The displacements at the middle points, (b) The energy distribution, (c) FFT of the displacements at the middle points of rod 1 ([[dashed_line]]), rod 2 (–) when a=0.0m,b=0.0m,S=9.0 * 104N/m
Grahic Jump Location
(a) The displacements at the middle points, (b) The energy distribution, (c) FFT of the displacements at the middle points of rod 1 ([[dashed_line]]), rod 2 (–) when a=0.002m,b=0.03m,S=9.0 * 104N/m
Grahic Jump Location
(a) The displacements at the middle points, (b) The energy distribution, (c) FFT of the displacements at the middle points of rod 1 ([[dashed_line]]), rod 2 (–) when a=0.0m,b=0.0m,S=2.6 * 104N/m
Grahic Jump Location
(a) The displacements at the middle points, (b) The energy distribution, (c) FFT of the displacements at the middle points of rod 1 ([[dashed_line]]), rod 2 (–) when a=0.002m,b=0.03m,S=2.6 * 104N/m
Grahic Jump Location
(a) The displacements at the middle points, (b) The energy distribution, (c) FFT of the displacements at the middle points of rod 1 ([[dashed_line]]), rod 2 (–) when a=0.0m,b=0.0m,S=3.5 * 104N/m
Grahic Jump Location
(a) The displacements at the middle points, (b) The energy distribution, (c) FFT of the displacements at the middle points of rod 1 ([[dashed_line]]), rod 2 (–) when a=0.002m,b=0.03m,S=3.5 * 104N/m
Grahic Jump Location
(a) The first K-L mode shape of rod 1 (–), rod 2 ([[dashed_line]]), when a=0.0m,b=0.005m,S=104N/m, (b) The first K-L mode shape of rod 1 (–), rod 2 ([[dashed_line]]), when a=0.0m,b=0.037m,S=104N/m
Grahic Jump Location
(a) Numerical simulation of the time response at the middle points of rod 1 ([[dashed_line]]), rod 2 (–) when a=0.0m,b=0.001m,S=104N/m, (b) Reconstruction of the responses using 2 K-L modes
Grahic Jump Location
(a) Numerical simulation of the time response at the middle points of rod 1 ([[dashed_line]]), rod 2 (–) when a=0.0m,b=0.037m,S=104N/m, (b) Reconstruction of the responses using 2 K-L modes
Grahic Jump Location
(a) The energy transfer between the first “.-” and second “-” K-L modes with varying stiffness S, when a=0.002m,b=0.03m, (b) The energy transfer between the first “.-” and second “o-” K-L modes with varying b, when a=0.002m,S=2.6 * 104N/m
Grahic Jump Location
Components of the system for constructing the 2-DOF model
Grahic Jump Location
The Poincare map of the system with S=2.6 * 104N/m,a=0.002m,b=0.03m
Grahic Jump Location
The time evolution of a1(t) ([[dashed_line]]) and a2(t) (–): (A) periodic orbit, (B) subharmonic orbit
Grahic Jump Location
The Poincare map of the system with S=3.5 * 104N/m,a=0.002m,b=0.03m
Grahic Jump Location
The time evolution of a1(t) ([[dashed_line]]) and a2(t) (–): (A) periodic orbit, (B) subharmonic orbit 1, (C) subharmonic orbit 2
Grahic Jump Location
The Poincare map of the system with S=9.0 * 104N/m,a=0.002m,b=0.03m
Grahic Jump Location
The time evolution of a1(t) ([[dashed_line]]) and a2(t) (–): (A) periodic orbit, (B) subharmonic orbit

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In