Multiple Shaker Random Vibration Control--An Update Page: 1 of 12
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Multiple Shaker Random Vibration Control-An Update
David 0. Smallwood
Sandia National Laboratories
Albuquerque, NM 87185-0553
David Smallwood received his BSME degree from
New Mexico State University in 1962 and his
MSME degree from New York University in 1964.
He has worked for Sandia National Laboratories
since 1967 and is currently a Distinguished
Member of the Technical Staff in the Environments
Engineering Group of the Mechanical and Thermal
Environments Department at Sandia. He is a fellow
of the IEST.
The theory of the control of multiple shakers
driving a single test item is reviewed. Several
improvements that have been introduced since the
original papers on the subject will be discussed.
The improvements include: 1) specification of the
control spectra; 2) the control of non-square
systems (the number of shakers does not have to be
equal to the number of control points); 3) the
connection between sine testing, waveform control,
and random control; 4) improvements in feedback
control; 5) overlap-add versus time domain
randomization; and 6) reproduction of non-
Multiple shaker control, multiple axis vibration
testing, vibration, testing, random, sine, waveform
control, transient vibration.
The elements in the upper case matrices and vectors
are all functions of frequency. The elements in the
lower case matrices and vectors are all functions of
time. In actual application the functions of
frequency are defined at a discrete set of
frequencies using the fast Fourier transform, FFT.
--Sandia is a multiprogram laboratory operated by
Sandia Corporation, a Lockheed Martin Company,
for the United States Department of Energy under
AR 0 3 199
It has been over ten years since I have published a
paper on the control of multiple shakers driving a
single test item (Smallwood,1978, 1982a,1982b and
Smallwood, Woodall, and Buksa, 1986). These
systems are becoming more important as
applications increase and the control systems
become more robust. Improvements in hardware
and algorithms have made the improved systems
possible. Systems are now being used in the
aerospace, defense, automotive, and seismic
Since 1978 at least four commercial companies
have marketed control systems for this purpose (for
example, Hamma, en al, 1996, Chen and Wilson,
1998). The commercial companies marketing these
systems rarely discuss the technical aspects of their
systems in detail for competitive reasons. However,
some of the improvements have been investigated
independently by the author and can be discussed.
Testing of systems using multiple shaker control
can be divided into several categories. First is the
control of multiple independent test items on
separate shakers using a single control system. This
paper will not discuss this category. Testing of a
single test item driven with multiple shakers will be
discussed. This includes multiple axis control at a
single control point and the control of multiple
points in one or more axes. The test environment
can then be divided into three broad categories: sine
inputs, waveform control, and random. Some
environments are a combination of these.
Combined environments will not be discussed.
Waveform control involves testing where the
desired waveforms are deterministic and
predetermined. The waveforms might have a
random character, but a particular realization is
reproduced. The control system attempts to
reproduce the reference waveforms at the control
points on the test item. Transient or shock testing
falls into this category. The road simulations
commonly performed in the automobile industry
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Smallwood, D.O. Multiple Shaker Random Vibration Control--An Update, article, February 18, 1999; Albuquerque, New Mexico. (digital.library.unt.edu/ark:/67531/metadc676130/m1/1/: accessed December 14, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.