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

Volume 5
1990


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NOTE: The journal articles are listed alphabetically by first author.

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Arif, G. M. and Pettersson, O., Lund University

5(3):141-154; Jul. 1990.

APPLICATION OF FINITE ELEMENT METHOD TO THE STABILITY OF AN
ECCENTRICALLY LOADED COLUMN BY SLAVE LOADS INCLUDING DAMPING

ABSTRACT - The finite element method is used to analyze the stability
of a cantilever column resting on elastic foundation and subjected to
an eccentric slave load at its free end.  The analysis has been
conducted according to Bernoulli-Euler and Timoshenko beam theories.
Effects of the mass offset, coupling effects and damping has been
taken into account.


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Biswas, M., Pandey A. K., and Samman, M. M., Duke University

5(1):33-42; Jan. 1990.

DIAGNOSTIC EXPERIMENTAL SPECTRAL/MODAL ANALYSIS OF A HIGHWAY BRIDGE

ABSTRACT - Experimental modal analysis is considered a viable method
of non-intrusive inspection for detecting incipient failure in
bridges.  For evaluation of such techniques, a probable failure mode
of a large fatigue crack was simulated by unfastening a set of high-
strength bolts of a splice connection of a steel girder of a typical
highway bridge and experimental modal testing was performed for the
intact case as well as the cracked case.  Details of experiments and
typical test results are presented.  Test and analysis data includes
time domain records, frequency spectra, frequency response functions,
modal parameters and modal assurance criteria.  As a result of
simulated crack development, detectable sensitivity of response data
are observed.  An Appendix includes information about equipment and
instruments used.
 
 
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Brandon, J., University of Wales College of Cardiff
 
5(4):205-212; Oct. 1990.
 
CHARACTERISTIC BEHAVIOR OF RANDOM AND SYSTEMATIC ERRORS IN INVERSE
PLANE FREQUENCY IDENTIFICATION ALGORITHMS
 
ABSTRACT - This paper describes three types of error, each of which
has a different, and distinctive, effect on the results of inverse
plane circle fitting algorithms.  By examining the characteristics of
the error patterns, strategies for eliminating their effects are
devised.  This paper demonstrates how these errors may be identified
by consideration of data plots and indicates how their identification
may be incorporated in software.
 
 
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Cobb, R. E., Contract Engineer and Mitchell, L. D., Virginia
Polytechnic Institute and State University
 
5(3):185-194; Jul. 1990.
 
ESTIMATES OF VARIANCE AND CONFIDENCE BANDS FOR THE THREE-CHANNEL
FREQUENCY RESPONSE FUNCTION ESTIMATOR
 
ABSTRACT - Closed-form and numerical methods of calculating three-
channel FRF magnitude variance are discussed.  The closed-form
solution is shown to be numerically ill-conditioned, while the
numerical method is shown to give good estimates of FRF magnitude
variance in both simulations and experimental results.  Variance
estimates allow ?confidence bands? to be placed on the experimentally
measured FRF magnitude.  This quantifies the amount of variation that
can be expected in the FRF measurement at any given spectral line and
should be useful in assigning weighting factors for curve-fitting
algorithms. This magnitude bias is shown and discussed.
 
 
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Craig R. R., Jr., University of Texas, Kurdila, A. J., Texas A & M
University, and Kim, H. M., McDonnell Douglas Astronautics Co.
 
5(3):169-183; Jul. 1990
 
STATE-SPACE FORMULATION OF MULTI-SHAKER MODAL ANALYSIS
 
ABSTRACT - As modal testing techniques have improved in recent years,
the demands placed on the accuracy of modal test results has
increased.  This paper describes a multi-input, multi-output modal
parameter estimation algorithm suitable for the identification of
reduced-order models of structures.  The method described is a
frequency-domain method based on excitation and response spectra.  The
principal features of the algorithm are: (1) its applicability to
general linear, time-invariant systems, (2) the direct use of multiple
input and multiple response data, (3) the identification of reduced-
order models with minimum user interaction through the use of two
automatic model-reduction techniques and the (4) identification of a
consistent set of modal parameters through the use of numerically
stable least-squares techniques.
 
 
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Doyle, J. F., and Farris, T. N., Purdue University
 
5(2):99-107; Apr. 1990
 
A SPECTRALLY  FORMULATED FINITE ELEMENT FOR FLEXURAL WAVE PROPAGATION
IN BEAMS
 
ABSTRACT - A spectral formulation of the dynamics of beams suitable
for a finite element implementation is presented.  The analysis gives
the exact frequency dependent stiffness matrix for the beam.  The
frequency domain response is converted to the time domain response
using the Fast Fourier Transform algorithm.  The formulation is
verified by comparison with conventional finite element results.
 
 
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Doyle, J. F., and Farris, T. N., Purdue University
 
5(4):223-237; Oct. 1990.
 
A SPECTRALLY FORMULATED ELEMENT FOR WAVE PROPAGATION IN 3-D FRAME
STRUCTURES
 
ABSTRACT - A spectral formulation of the dynamics of frame structures
suitable for a computer matrix method implementation is presented.
The analysis is based on a spectral frame element that is assembled to
give the exact frequency dependent stiffness matrix for the complete
structure.  The frequency domain response is converted to the time
domain response using the fast Fourier transform algorithm.  The
formulation is verified by comparison with conventional finite element
techniques.  It is found that the spectral method can be less costly
from a computational standpoint than the conventional finite element
method.  This is especially true for events involving high frequencies
such as impact.  The most significant strength of the spectral method,
however, lies in its ability to go directly to the heart of dynamics
problems; namely, the system frequency response function.  Some of the
implications of this are discussed.
 
 
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Ismail, F., University of Waterloo, and Fyfe, K. R., University of
Alberta
 
5(1):25-32; Jan. 1990.
 
MODELING CYLINDER ACOUSTICS OF FLEXURAL AND SHELL MODES
 
ABSTRACT - A boundary element model is presented in this work to study
the acoustic radiation of a finite cylinder in flexural and shell
modes of vibration.  For flexural modes, numerical results compare
well with experimental measurements reported in the literature.  These
results have the same trend as the infinite length cylinder solution.
Computed results for shell modes are also compared with test
measurements performed on a configured cylinder.  Modal analysis
testing was employed to obtain the shell mode velocity profiles which
were input to the acoustic model.  Details of the experimental setup
and procedure are given.  Results from the acoustic model compared
well with measurements for the low order shell modes.
 
 
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Jones, J. D., Purdue University, and Fuller, J. D., Virginia
Polytechnic Institute and State University
 
5(3):123-140; Jul. 1990.
 
ACTIVE CONTROL OF STRUCTURALLY-COUPLED SOUND FIELDS IN ELASTIC
CYLINDERS BY VIBRATIONAL FORCE INPUTS
 
ABSTRACT - Active control of structurally-coupled sound fields in
elastic cylinders is analytically and experimentally studied.  The
primary (noise) field in the cylinder model is generated by the
coupled dynamic response of the shell under loading by a single
exterior acoustic source.  Control of the interior sound field is
achieved by applying vibrational force inputs directly to the shell
wall.  Action of the point controllers serve to increase the input
impedance of select structural modes of the shell which are well-
coupled to the interior acoustic cavity, thus substantially reducing
sound transmission into the cavity.  Spatially-averaged noise
reductions in excess of 30 dB are demonstrated for acoustic resonant
conditions within the cavity.  Twin controller configurations are
presented which demonstrate the ability to independently control
orthogonal modes of the interior acoustic space. Benefits and
drawbacks of this new methodology for noise control are discussed and
clearly demonstrated.
 
 
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Kim, M. J., and Gupta, A., Northern Illinois University
 
5(3):195-203; Jul. 1990.
 
FINITE ELEMENT ANALYSIS OF FREE VIBRATIONS OF LAMINATED COMPOSITE
PLATES
 
ABSTRACT - The effects of lamination and extension-bending coupling,
shear and twist-curvature couplings on the lowest frequencies and
corresponding mode shapes for free vibration of laminated anisotropic
composite plates are presented by using a finite element method based
on the first order shear deformation theory.  The finite element
method uses quadratic interpolation functions with 5 degrees of
freedom (3 displacements and 2 slopes) to model the composite plates
and material properties typical of a highly directional composite
material (high modulus graphite/epoxy).  The numerical results for the
case of all edges simply supported show that the mode shapes are not
affected as much as the frequencies by the coupling effects of
laminated plates.
 
 
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Larsson, P. O., ABB Corporate Research
 
5(1):1-12; Jan. 1990.
 
DYNAMIC ANALYSIS OF ASSEMBLED STRUCTURES USING FREQUENCY- RESPONSE
FUNCTIONS: IMPROVED FORMULATION OF CONSTRAINTS
 
ABSTRACT - Methods for the analysis of assembled structures using a
set of frequency-response functions, or FRFs, were studied.  The FRFs
of the  components, or substructures, are either measured or
calculated.  The main objective was to show how the required
constraints, corresponding to the coupling of two substructures, can
be formulated in cases where only FRFs between translations, and not
between rotations, are available.  This is of interest since only FRFs
between translations can be measured effectively.  A new method of
formulating the constraints is presented which is useful when the
substructures are beam-like in the vicinity of the interface between
the coupled structures.  It is based on an interpolation of the
deformation of the substructures using polynomials.  It was found from
numerical simulations of ideal beams that the new method brings
considerable improvements in certain cases. Therefore, the accuracy of
the resulting FRFs and their sensitivity to small errors in the FRFs
of the substructures, as well as the choice of the points where the
FRFs are measured, were investigated.
 
 
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Lee, C. W., and Hong, S. W., Korea Advanced Institute of Science and
Technology
 
5(2):51-65; Apr. 1990.
 
ASYNCHRONOUS HARMONIC RESPONSE ANALYSIS OF ROTOR/BEARING SYSTEMS
 
ABSTRACT - This paper develops a generalized modal analysis scheme for
forced vibration analysis of rotor bearing systems with rotational
speed dependent parameters subject to asynchronous harmonic
excitations.  The essence of the method is that the rotational speed
dependent eigenvalue problem of the original system is transformed
into the rotational speed independent eigenvalue problem by
introducing a lambda matrix, assuming that the bearing dynamic
coefficients are well represented by polynomial functions of
rotational speed over the operating speed range of interest.  This
method deals with closed form solution in response calculations and
the influence coefficients, the critical speeds and the corresponding
logarithmic decrements for an asynchronous harmonic excitation are
readily identified.
 
 
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Lu, S. L., National Taiwan Institute of Technology, and Ju, F. D.,
University of New Mexico
 
5(4):251-260; Oct. 1990.
 
THE RANDOM STRUCTURAL RESPONSE OF A SDF SYSTEM WITH STIFFNESS
DEGRADATION
 
ABSTRACT - This paper presents a stochastic model to describe the
response of hysteretic, degrading structures subjected to random
excitations.  The analysis calculates the response using a nonlinear
hysteretic structural model, which takes into account both work
hardening and stiffness degradation effects.  The constitutive
hysteretic loop is modeled by linear segments, with degrading elastic
stiffness.  Since the restoring force of a hysteretic system depends
on both the current displacement and the history, it is a loop-
dependent variable which is a random process in this study.  The mean
and variance of displacement and restoring force are computed with the
finite difference method with recursive scheme.  The present
investigation emphasizes the effects of the system degradation and the
randomness of stiffness for the random response analysis.
 
 
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Moustafa, K. A. F., King Fahd University of Petroleum and Minerals,
and Asfar, K. R., Jordan University of Science and Technology
 
5(4):213-221; Oct. 1990.
 
IDENTIFICATION OF JOURNAL BEARING MODAL PARAMETERS
 
ABSTRACT - Identification of the natural frequencies and modal
dampings of a flexible rotor-journal bearing system is considered in
this paper and a real-time modal sweeping scheme which identifies the
unknown parameters on-line is proposed.  The identification is carried
out by using a single excitation and a single response record.  This
simplifies considerably the measurement and instrumentation
requirements for experimental work.
 
 
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Ojalvo, I. U., Ting, T., and Pilon, D., University of Bridgeport
 
5(1):43-49; Jan. 1990.
 
PAREDYM--A PARAMETER REFINEMENT COMPUTER CODE FOR STRUCTURAL DYNAMIC
MODELS
 
ABSTRACT - A computationally efficient parameter refinement program,
named PAREDYM, for structural dynamic models with up to 100 variables
has been developed.  The method compares limited modal test data with
corresponding analytical results and employs a minimum least squares
algorithm, based upon modal parameter sensitivities, to iteratively
improve model stiffness and mass parameters.  Sensitivity computations
are augmented with scaling techniques to facilitate numerical solution
by minimizing matrix ill-conditioning. PAREDYM has been applied
successfully to a beam model with 83 mass and stiffness parameters,
starting with artificially manufactured parameter errors of the order
of 10\%.  Results to date have yielded rapid convergence to the known
exact answer within a few iterations.
 
 
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Smallwood, D. O., and Lauffer, J. P., Sandia National Laboratories
 
5(2):115-122; Apr. 1990.
 
QUALIFICATION OF FREQUENCY-RESPONSE FUNCTIONS USING THE RIGID-BODY
RESPONSE
 
ABSTRACT - The response of a structure at low frequencies with free
boundary conditions is dominated by the rigid-body modes.  The
displacement shapes obtained form the low frequency values of the
frequency-response functions can be compared with ideal rigid-body
motion to point out errors in the measurements.  Insight is enhanced
when the comparisons are made in the coordinate system of the
measurements.  Without this procedure intuition can rarely determine
the proper rigid-body response at each measurement location.  Typical
errors identified are scaling errors, errors in location or direction,
measurements with poor dynamic range and other instrumentation
problems.  The procedure is particularly useful when the test object
is multi-dimensional, has a complicated geometry, has measurements in
other than rectangular coordinates, and where more than one rigid-body
mode is excited.  It is suggested that data qualification using this
method would be a useful addition to most modal tests.  A least
squares approach, to determine the proper rigid-body response, is
reviewed and several experimental examples are given.
 
 
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Sriram, P., Craig, J. I., and Hanagud, S., Georgia Institute of
Technology
 
5(3):155-167; Jul. 1990.
 
A SCANNING LASER DOPPLER VIBROMETER FOR MODAL TESTING
 
ABSTRACT - Accelerometers are widely used to sense structural response
in modal testing.  The mass loading and local effects due to
accelerometers are not always negligible.  The laser Doppler
velocimeter/vibrometer (LDV) is a noncontact optical sensing tool for
accurately measuring point velocities.  The noncontact nature of the
instrument makes it particularly attractive for use on lightweight
structures where measurement interaction must be minimized. Real-time
scanning LDV?s have recently been introduced to measure fluid flow
velocity profiles rapidly.  In this paper, the development of a real-
time scanning LDV for structural applications is described.  The
instrument can be used to simultaneously measure the velocity response
at a series of locations on a vibrating structure.  Standard modal
analysis techniques can then be applied to extract the usual modal
data, e.g., natural frequencies, damping and mode shapes.  The special
case of beam vibration is considered in this paper though the
technique can be readily extended to generic planar measurements.  The
measurement technique has been validated through modal testing of a
simple beam structure.  Comparisons between theoretical and LDV
measured mode shapes and natural frequencies are presented.
 
 
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Stubbs, N., Texas A & M University, and Osegueda, R., University of
Texas at El Paso
 
5(2):81-97; Apr. 1990.
 
GLOBAL DAMAGE DETECTION IN SOLIDS - EXPERIMENTAL VERIFICATION
 
ABSTRACT - Experimental evidence, obtained from controlled laboratory
experiments, is provided to support a recent theory of nondestructive
damage detection.  In the experiment, known magnitudes of damage are
inflicted on cantilevered specimens and the dynamic responses of the
undamaged and damaged specimens are measured.  Using the experimental
frequency response of the specimens and a numerically-generated
sensitivity matrix, the theory is used to predict the location and
magnitude of damage inflicted in the specimens.  All damage locations
considered in this series of tests are correctly predicted by the
theory.  The correct order of magnitude is always predicted by the
theory and the error in the magnitude of the predicted damage
decreases with increasing damage magnitude.
 
 
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Stubbs, N., Texas A & M University, and Osegueda, R., University of
Texas at El Paso
 
5(2):67-79; Apr. 1990.
 
GLOBAL NON-DESTRUCTIVE DAMAGE EVALUATION IN SOLIDS
 
ABSTRACT - Variational analysis is applied to the homogeneous
equations of motion of an undamaged structure to yield expressions for
changes in modal stiffnesses in terms of modal masses, modal damping,
eigenfrequencies, eigenvectors, and their respective changes.
Expressions relating variations in stiffnesses of structural elements
to the variations in modal stiffness are generated from matrix
structural analysis.  The result is a system of algebraic equations
with a known load vector of fractional changes in modal stiffness and
unknowns of fractional changes in member stiffnesses.  Methods of
solution for the resulting system of equations are discussed along
with special cases in which the structure may be modeled to yield
unique predictions.  A  numerical example is presented to demonstrate
the potential of the formulation.
 
 
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Wang, J. H., and Liou, C. M., National Tsing Hua University
 
5(1):13-24; Jan. 1990.
 
EXPERIMENTAL SUBSTRUCTURE SYNTHESIS WITH SPECIAL CONSIDERATION OF
JOINTS EFFECTS
 
ABSTRACT - A method was proposed in this work to experimentally
synthesize the frequency-response functions (FRF) of a whole structure
using the FRF of each substructure and giving special consideration to
the effects of joints.  To identify the dynamic properties of joints,
a simple method based on statistical criteria is introduced to
overcome the problem caused by measurement noise.  The experimental
results show that the FRF of the whole structure can be accurately
reproduced by the FRF of substructures even with the effects of
joints.
 
 
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Weisensel, G. N., IBM Corporation, and Schlack, A. L.,Jr., University
of Wisconsin
 
5(4):239-250; Oct. 1990.
 
ANNULAR PLATE RESPONSE TO CIRCUMFERENTIALLY MOVING LOADS WITH SUDDEN
RADIAL POSITION CHANGES
 
ABSTRACT - The forced dynamic response of annular plates to
circumferentially moving concentrated transverse loads of harmonically
varying amplitude with sudden changes in radial position is
investigated.  Classical plate theory is used with damping included.
The boundary conditions are that the inner boundary of the plate is
clamped and the outer boundary is free.  The loading function
describes a concentrated transverse load of harmonically varying
amplitude moving around the plate in a concentric circular path at a
constant radial position which instantaneously moves to a concentric
circular path at a different radial position.  The general solution
for this loading function is derived in integral form.  This integral
is then solved to determine the forced response in Fourier-Bessel
series form.  The sudden change in radial position requires the
transient deflection of the plate to be included as well as the steady
state deflection due to the moving load at each of the constant radial
positions before and after the sudden change.  The transient and
maximum deflections are studied in detail.
 
 
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Zeng, Z., and Huang, T., Tianjin University, and J. F. Hamilton,
Purdue University
 
5(2):109-104; Apr. 1990.
 
AN EFFECTIVE APPROACH TO  DETERMINE  NATURAL FREQUENCIES  AND  MODE
SHAPES OF CONSTRAINED BEAMS USING LAGRANGE MULTIPLIERS
 
ABSTRACT - In this paper, an approach using Lagrange multipliers is
presented for determining the eigenfrequencies and eigenfunctions of
beams with a variety of elastic and rigid support conditions.  The
presented approach utilizes component modal synthesis and results in a
linear generalized eigenvalue problem which can be solved by standard
procedures.
 
 
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For back-issues, contact:
 
Society for Experimental Mechanics
7 School Street
Bethel, CT  06801
 
Phone: 203-790-6373
 
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DLA Ejournals | MODAL Home | Search MODAL and other ejournals | MODAL Access Data