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Determination of natural responses of mechanical systems using correlation techniques

Paper describes an application in which the critical speeds and relative deflection amplitudes of a machine shaft-rotor system were found with the system either stationary or running at some arbitrary speed

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Abstract

The natural responses of linear systems may be found by observation of the system's response to a known stimulus. In such tests, the observations required ore the response as a function of time when the stimulus is deterministic in form. In practical situations, the application of this method is often hampered by the presence in the response of extraneous noise and the necessity of using large-amplitude excitations.

The difficulties of the method outlined may be avoided by using random stimuli and cross correlations to obtain a statistical estimate of the natural modes. This paper describes one application in which the critical speeds and relative deflection amplitudes of a machine shaft-rotor system were found with the system either stationary or running at some arbitrary speed.

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Abbreviations

h(t) :

impulse response or weighting function

N :

clock periods in a sequence lenght

n(t) :

input-noise signal

\(\bar n\) :

time average of n(t)

R(τ):

correlation function

S o :

power spectral density

ΔT :

clock period in seconds

t :

time in seconds

x(t) :

system input signal

\(\bar x\) :

time average ofx(t)

y(t) :

system output signal

τ:

delay time in seconds

References

  1. Desoer, C. A., “Modes in Linear Circuits,” I.R.E. Transactions on Circuit Theory (Sept. 1960).

  2. Roberts, A. W. andCharlton, W. H., “Application of Pseudo-Random Test Signals and Cross Correlation to the Identification of Bulk Handling Plant Dynamic Characteristics,”Trans. ASME, Jnl. Eng. Ind.,95 (B,1)31–36 (Feb.1973).

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  4. Briggs, P., Hammond, P., Hughes, M. andPlumb, G., “Correlation Analysis of Process Dynamics Using Pseudo-Random Binary Test Perturbations,”Proc. Inst. Mech. Engrs.,179,37 (1964–1965).

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  5. Hazelrigg, A., andNoton, A., “Application of Cross Correlating Equipment to Linear System Identification,”Proc. I.E.E.,112 (12) (Dec. 1965).

  6. Leary, B. G., “Linear System Identification,”Control Systems,1 (2) (May 1968)and 2(May 1969).

  7. Bendat, J. S. and Piersol, A. G., “Measurement and Analysis of Random Data,” John Wiley (1966).

  8. Charlton, W., “Linear System Identification Using Pseudo-Random Binary Signals,” Bulletin No. 16, Wollongong University College (March 1968).

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Authors and Affiliations

  1. The University of Newcastle, Australia

    A. W. Roberts (Professor of Industrial Engineering)

  2. Division of Engineering, Wollongong University College, 2500, Wollongong, N.S.W., Australia

    W. H. Charlton

Authors
  1. A. W. Roberts
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  2. W. H. Charlton
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Roberts, A.W., Charlton, W.H. Determination of natural responses of mechanical systems using correlation techniques. Experimental Mechanics 15, 17–22 (1975). https://doi.org/10.1007/BF02318520

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  • DOI: https://doi.org/10.1007/BF02318520

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