Modal Analysis: The International Journal of Analytical and Experimental Modal Analysis

Volume 6, Number 1
January 1991


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January issue. --


The International Journal of Analytical and Experimental Modal Analysis
6(1) 1991 Jan.


ELIMINATION OF RIGID BODY MODES FROM ASYMMETRIC DYNAMICAL SYSTEMS
by S. Natsiavas and H. D. Nelson, Arizona State University

This  investigation  presents  a  methodology  for  analyzing  the  dynamic
response  of semi-definite  mechanical systems  with linear  but asymmetric
equations of motion.  This is done by deriving a modified set of equations,
characterized  by a nonsingular stiffness  matrix, after proper elimination
of  the rigid body modes  from the original equations  of motion.  Standard
modal analysis procedures are employed and both undamped and damped systems
are  analyzed.  The applicability and accuracy of the method is illustrated
by a number of numerical examples.
 
 
COMPLEX MODAL ANALYSIS OF NON-PROPORTIONALLY DAMPED CONTINUOUS RODS
by G. Prater, Jr., University of Louisville and R. Singh, The Ohio
State University
 
This  paper presents  techniques that can  be used to  formulate, solve and
interpret  the  complex  eigenproblems  associated  with  nonproportionally
damped,   longitudinally  vibrating  continuous   rods.    The  formulation
procedures  yield  none of  the errors  associated with  discretized system
approaches,  and  the  algorithm  used to  solve  the  nonlinear eigenvalue
equation  is efficient  and accurate.  Interpretation of  the system normal
modes  is facilitated  by special  complex domain  normalization techniques
that  allow immediate assessment of the  degree of nonproportionality.  The
concepts  involved have been implemented in a computer program, and this is
used  to  analyze example  cases involving  lumped and  distributed viscous
damping elements and various classical boundary conditions.  The modal data
are  compared  with values  from a  closed-form  analytical solution  and a
lumped  parameter model.  Graphical results show how the eigenfunctions and
eigenvalues  change with increasing degrees  of nonproportional damping and
which  parts of the system  are most affected when  the damper location and
magnitude are changed.
 
 
PROBABILISTIC DISTRIBUTION OF MULTIPLE CRACKS IN STRUCTURES DUE TO
RANDOM MODAL OSCILLATIONS
Y.-M. Lu, the Aerospace Corporation and F.D. Ju, University of
New Mexico
 
This  paper considers the development  of the probabilistic methodology for
the  prediction  of  multiple-crack  distribution in  a  structure  of beam
elements  associated with individual modal oscillations.  The probabilistic
measure  of  crack  distribution can  then  be used  for  the probabilistic
diagnosis  of crack damage (depth) and  its location (spacing) under random
loading  and to  resolve some of  the intrinsic uncertainties  in the modal
theories  of  fracture diagnosis.    The structural  system  considers some
randomness  of  material strength.    The arresting  fracture  toughness is
characterized  as  a  random  variable  with  the  appropriate  probability
distribution.   The application of LEFM (Linear Elastic Fracture Mechanics)
in  connection with the stress relief effect due to the presence of a crack
suggests  a means of  predicting depth and  spacing of tension  cracks at a
given random modal oscillation.  The resulting redistributed random bending
stresses (moments) will be a measure to compute the subsequent crack state.
With  postulation  that secondary  cracking is  dominantly affected  by its
immediately  preceding crack, the process of the successive cracking can be
treated  as  a Markov  process.   The analyses  are performed,  under these
probabilistic assumptions, for the first few representative normal modes of
interest.   The probability distribution  of the overall structural system,
therefore,  is obtained dependent on a weighted distribution of modes for a
particular excitation spectrum.
 
 
EMPLOYING PATTERN RECOGNITION FOR DETECTING CRACKS IN A BRIDGE MODEL
M. M. Samman, M. Biswas and A. K. Pandey, Duke University
 
A  scaled model  of a  typical highway  bridge is  used to  investigate the
change  in the  frequency-response-function signals  due to  development of
cracks  in its  girders.   The Freeman's  code for  boundary recognition, a
method  used in the fields of  pattern recognition and image processing, is
modified  and  employed to  accentuate  the differences  in  the frequency-
response  function between the intact-bridge  signal and the cracked-bridge
signal.   The method is a good candidate for detecting cracks in full scale
bridges and other structures because it is found to be capable of detecting
relatively  minor cracks.   The  method is  also helpful  in estimating the
location  of the  crack.   Since this method  requires only  one signal per
girder, the time and effort required for inspection are kept at a minimum.
 
 
CALCULATED AND MEASURED DYNAMICS OF ELASTOMER SUPPORT MOUNTS
L. Gaul, University of the Federal Armed Forces Hamburg
 
Optimization  of  active  and  passive  isolation  of  machine  foundations
requires  knowledge about  the propagation  of structureborne  sound in its
substructures.    The  substructure  behavior  of  elastomer  isolators for
resiliently  mounted engines defines mixed  boundary value problems for the
field  equations.   It is  shown that  the CAD  compatible boundary element
method  (BEM) provides a powerful tool to predict the substructure dynamics
in the design state by taking complicated three-dimensional (3-D) geometry,
viscoelastic material properties and temperature influence into account.
 
 
DETERMINATION OF MODAL PARAMETERS OF TALL BUILDINGS WITH AMBIENT
VIBRATION MEASUREMENTS
Z. W. Bao, Tsinghua University and J. M. Ko, Hong Kong Polytechnic
 
Dynamic  characteristics of tall buildings are essential for the assessment
of  earthquake loads and the corresponding dynamic responses.  In addition,
they  are useful for safety evaluation  of existing structures.  This paper
gives  the natural frequencies,  the mode shapes and  the damping ratios of
five  buildings  in Hong  Kong.  These characteristics  were  determined by
spectral  analysis of the  ambient vibration signal.   The data analysis is
discussed  including the method of determining  mode shapes, how to improve
the accuracy of damping ratios, and the identification and decomposition of
torsional vibration.

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