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Use of correlation techniques in vibration studies of plate systems

The dynamic-response characteristics of plate systems can be identified by a statistical procedure which offers advantages of noise immunity, small amplitude disturbances and avoidance of excitation near resonant conditions

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Abstract

This paper describes the application of pseudo-random test signals and cross-correlation analysis to the determination of the dynamic-response characteristics of plate systems. The statistical nature of the technique allows such information to be obtained even in the presence of considerable background noise. The method is demonstrated by a pilot study performed on a rectangular isotropic plate and by additional tests on plates with longitudinal rib stiffeners. In all cases the results compare favorably with those given by an alternative (but more tedious) experimental procedure and, to a lesser extent, with theoretical solutions.

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Abbreviations

b :

transverse width (mm)

d :

depth of rib stiffener (mm)

E :

Young's modulus (MPa)

f :

frequency (Hz)

H(f) :

system function

h(t) :

impulse-response function

h 1,h 2 :

plate and rib thicknesses, respectively (mm)

l :

longitudinal span (mm)

m, n :

number of nodal lines in X and Y directions, respectively

n(t) :

noise signal

R(τ):

correlation function

S(f) :

spectral-density function

T :

period (s)

ΔT :

clock period (ms)

T c :

computational averaging time (s)

t :

time (s)

x(t) :

input (test) signal

x, y :

plate coordinates (mm)

|Y|:

amplitude of oscillation

y(t) :

output (displacement) signal

δ(t):

unit-impulse function

ν:

Poisson's ratio

ρ:

mass density (kg/m3)

τ:

delay time (s)

Δτ:

delay-time increment (ms)

ψ:

RMS value

References

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  2. Davies, W. D. T., “System Identification for Self-Adaptive Control,”Wiley-Interscience, London (1970).

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  4. Charlton, W. andRoberts, A. W., “A Method of Natural Response Determination using Pseudo-Random Test Signals,”The South African Mechanical Engineer,24 (3),54–61 (March 1974).

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  5. Roberts, A. W. andCharlton, W. H., “Determination of Natural Responses of Mechanical Systems Using Correlation Techniques,”Experimental Mechanics,15 (1),17–22 (Jan. 1975).

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  6. Warburton, G. B., “The Vibration of Rectangular Plates,”Proc. Instn. Mech. Engrs.,168 (12),371–384 (1954).

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  7. Lowrey, M. J., “Matrix Progression Stiffness Method for Cellular Bridge Structures,” Proc. 3rd Australasian Conf. Mechs. of Structures and Materials, Auckland (1971).

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Authors and Affiliations

  1. Department of Civil Engineering, University of Wollongong, 2500, NSW, Australia

    M. J. Lowrey (Lecturer)

Authors
  1. M. J. Lowrey
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Lowrey, M.J. Use of correlation techniques in vibration studies of plate systems. Experimental Mechanics 15, 476–481 (1975). https://doi.org/10.1007/BF02318363

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  • DOI: https://doi.org/10.1007/BF02318363

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