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A simple model to illustrate some aspects of vibration excitation by delayed terms

Investigation indicates that excitation of vibration by the artificial introduction of delayed terms may have some advantages in vibration testing or fatigue testing

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Abstract

It is shown that the excitation of vibration by the artificial introduction of delayed terms may have certain advantages in vibration testing or fatigue testing. As illustration, in the simple mechanical system studied, the amplitude and frequency of vibration were relatively unaltered by large changes in damping. With varying delay time, large changes were produced in the frequency of vibration. Analytical predictions agree with experimental results and confirm the observation that an increase in the magnitude of the delayed term, beyond a certain limit, leads to unstable behavior.

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Abbreviations

C1, C2, C3 :

constants

F :

force applied to shake table (lb)

L :

unit of length (=0.431 in.)

M :

mass of table and attachments (lb sec2 in.−1)

P :

static load to deflect beam (lb)

a :

maximum value of dimensionless variablex

b, c :

constants

k 1 :

spring constant, lb in.−1

k 2 :

spring constant, lb in.−3

m :

mass of accelerometer and attachments (lb sec2 in.−1)

t :

time (sec)

x :

dimensionless displacement=z 1/L

z 1,z 2 :

displacements of massesm andM (in.)

α:

dimensionless parameter (=b/M)

δ:

central deflection of beam (in.)

ϕ:

phase angle (radians)

τ:

time delay (sec)

ω:

angular velocity (radians/sec)

References

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Authors and Affiliations

  1. University of California, Berkeley

    I. Finnie (Professor of Mechanical Engineering)

  2. Consolidated Electrodynamics Corp., Monrovia, Calif.

    B. Y. Lim (Development Engineer)

Authors
  1. I. Finnie
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  2. B. Y. Lim
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Finnie, I., Lim, B.Y. A simple model to illustrate some aspects of vibration excitation by delayed terms. Experimental Mechanics 4, 352–355 (1964). https://doi.org/10.1007/BF02322793

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  • DOI: https://doi.org/10.1007/BF02322793

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