Forced vibration responses of nonlinear systems contain harmonics of the excitation frequency. These harmonics are either directly forced or are subharmonic, superharmonic, or combination resonances. Nonlinear responses of this type have been modeled historically using continuous time, discrete time, and continuous frequency models. A new approach to dynamic systems analysis is introduced here that uses difference equations in the discrete frequency domain to describe the evolution of forced, single degree of freedom, steady state vibration responses in frequency instead of time. A variety of possible applications in nonlinear experimental structural vibrations are also discussed.
Issue Section:
Technical Papers
1.
Nayfeh, A. H., and Mook, D. T., 1979, Nonlinear Oscillations, Wiley, New York.
2.
Beranek, L. L., 1993, Acoustics, Acoustical Society of America, Woodbury, New York.
3.
Schetzen, M., 1989, The Volterra and Wiener Theories of Nonlinear Systems, Krieger Publishing, Malabar.
4.
Leontaritis
, I. J.
, and Billings
, S. A.
, 1985
, “Input-Output Parametric Models for Nonlinear Systems Part I: Deterministic Nonlinear Systems
,” Int. J. Control
, 41
, pp. 303
–328
.5.
Chen
, S.
, and Billings
, S. A.
, 1989
, “Representations of Nonlinear Systems: The NARMAX Model
,” Int. J. Control
, 49
, pp. 1012
–1032
.6.
Storer
, D. M.
, and Tomlinson
, G. R.
, 1993
, “Recent Developments in the Measurement and Interpretation of Higher Order Transfer Functions from Non-Linear Structures
,” Mech. Syst. Signal Process.
, 7
, pp. 173
–189
.7.
Storer, D. M., and Tomlinson, G. R., 1991, “An Explanation of the Cause of the Distortion in the Transfer Function of a Duffing Oscillator Subject to Sine Excitation,” Proceedings of the International Modal Analysis Conference, Vol. 2, pp. 1197–1205.
8.
Collis
, W. B.
, White
, P. R.
, and Hammond
, J. K.
, 1998
, “Higher-Order Spectra: The Bispectrum and Trispectrum
,” Mech. Syst. Signal Process.
, 12
, pp. 375
–394
.9.
Bendat, J. S., 1998, “Nonlinear Systems Techniques and Applications,” Wiley Sons, New York.
10.
Mohammad
, K. S.
, Worden
, K.
, and Tomlinson
, G. R.
, 1992
, “Direct Parameter Estimation for Linear and Non-Linear Structures
,” Sound Vib.
, 152
, pp. 471
–499
.11.
Ljung, L., 1987, System Identification Theory for the User., PTR Prentice Hall, Englewood Cliffs, New Jersey.
12.
Bendat, J. S., and Piersol, A. G., 1980, “Engineering Applications of Correlation and Spectral Analysis,” Wiley, New York.
13.
Strogatz, S. H., 1994, Nonlinear Dynamics and Chaos, Addison-Wesley, Reading, Massachusetts.
14.
Adams
, D. E.
, and Allemang
, R. J.
, 1999
, “Characterization of Nonlinear Vibrating Systems Using Internal Feedback and Frequency Response Modulation
,” ASME J. Vibr. Acoust.
, 121
, pp. 495
–500
.15.
Adams
, D. E.
, and Allemang
, R. J.
, 1999
, “A Frequency Domain Method for Estimating the Parameters of a Nonlinear Structural Dynamic Model through Feedback
,” Mech. Syst. Signal Process.
, 14
, pp. 637
–656
.16.
Vold, H., Crowley, J., and Rocklin, G., 1985, “A Comparison of H1,H2,Hv Frequency Response Functions,” Proceedings of the International Modal Analysis Conference, Vol. 1, pp. 272–278.
17.
Adams, D. E., and Allemang, R. J., 2000, “Residual Frequency Autocorrelation As An Indicator of Nonlinearity,” accepted for publication in Int. J. Non-Linear Mech., in press.
18.
Ayyub, B. M. and McCuen, R. H., 1996, Numerical Methods for Engineers, Prentice-Hall, Upper Saddle River, New Jersey.
Copyright © 2001
by ASME
You do not currently have access to this content.
