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

Volume 3
1988


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

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Abrahamsson, T.  Modal-parameter extraction for nonproportionally
damped linear structures.  3(2):62-68; Apr 1988.

ABSTRACT - An efficient dynamic analysis of a built-up structure can
often be performed setting out from the modal parameters of each of its
substructures.  Some of these sets of modal parameters of each of its
substructures.  Some of these sets of modal parameters can be
experimentally measure; others have to be extracted from a analytically
determined behavior of a substructure in the frequency domain.  This paper
advances a method for extracting the modal parameters of the latter type
of (sub)structure.  This structure may be composed of various types of
continuous and discrete elements.  The damping over the structure may be
nonproportionally distributed.  Poles and eigenvectors are found by solving
the nonlinear eigenvalue problem associate with the transcendentally
frequency-dependent stiffness matrix of the structure.  Starting with the
poles of the corresponding undamped structure, as found by use of the
Wittrick-Williams algorithm, the poles of the damped structure are found
by use of an algorithm which replaces the nonlinear problem with  a
sequence of linear problems.   Residues at poles are derived from the
calculated poles and eigenvectors and from the given mass and damping
properties of the structure.  Two numerical examples are included.
 
 
 
Abrahamsson, T.; Lundblad, M. Transient vibration analysis of
nonproportionally damped linear structures using modal parameters.
3(3):108-114;Jul 1988.
 
ABSTRACT - The modal parameters (generally complex) from a known
eigensolution are used to transform the coupled differential equations of
motion of a structure into a set of uncoupled first-order differential
equations.  Solutions for forcing functions whose dependence on time is
piece wise polynomial, exponential, or sinusoidal (or a product of these)
are given by exact explicit expressions.  Initial modal displacements are
fitted to a given set of physical initial displacements and velocities
(nonzero) through use of a weighted minimum two-norm method.  The
contribution to the structural response from truncated high-frequency
modes is approximately accounted for by adding residual flexibility terms
into the transient solution.  Three numerical examples are included.  Both
discrete and continuous structures are treated.
 
 
 
Braccesi, C.; Carfagni, M.; Rissone, P.  Using vibratory and modal analysis
to reduce vibrations and noise in an automotive engine.  3(3):89-95; Jul
1988.
 
ABSTRACT - An investigation was undertaken to determine mechanical
noise in an internal-combustion engine.  Noise detection was carried out
by characterizing the transmission paths of piston slap and
bearing-crankshaft impacts; the characterization was then recontraucted
by modal analysis.  Thereafter,using the structural modification
technique, it was possible to modify the engine block and thus achieve a
5-dB(A) reduction in overall engine-noise level.
 
 
 
Carne, T.G.; Lauffer, J.P.; Gomez, A.J.; Benjannet, H.  Modal testing an
immense flexible structure using natural and artificial excitation.
3(4):117-122; Oct 1988.
 
ABSTRACT - Modal testing of immense and very flexible structures poses
a number of problems.  It requires innovative excitation techniques since
the modal frequencies of these structures can be quite low.  Also,
substantial energy must be input to the structure to obtain reasonable
levels of response.  In this paper, results are presented from a modal test
of the 110-m tall EOLE wind turbine which had four modal frequencies
below l.0 Hz. Step-relaxation and wind were used to excite the structure.
 
 
 
Carne, T.G.; Lobitz, D.W.; Nord, A.R.; Watson, R.A.  Finite-element analysis
and modal testing of a rotating wind turbine.  3(l):32-41; Jan 1988.
 
ABSTRACT - A finite-element procedure which includes geometric
stiffening, and centrifugal and Coriolis terms resulting from the use of a
rotating coordinate system, has been developed to compute the mode
shapes and frequencies of rotating structures.  Special application of this
capability has been made to Darrieus, vertical-axis wind turbines.  In a
parallel development effort, a technique for the modal testing of a
rotating vertical-axis wind turbine has been established to measure modal
parameters directly.  Results from the predictive and experimental
techniques for the modal frequencies and mode shapes are compared over a
wide range of rotational speeds.
 
 
 
Cobb, R.E.; Mitchell, L.D.  A method for the unbiased estimate of system
FRFs in the presence of multiple-correlated inputs.  3(4):123-128; Oct
1988.
 
ABSTRACT - The two currently used frequency-response-function (FRF)
estimates, (super)1 H(hat) and (super)2 H(hat), product biased estimates
when there is uncorrelated content present in the measurement system.
Multiple-input FRF estimates have been based on (super)1 H(hat).  Such
estimates are biased in the presence of noise.  An unbiased estimate,
(super)c H(hat), have been developed for single input/output systems using
a third channel of data and is computed by forming a ratio of cross
spectra.  This paper presents the application of this method to obtain
unbiased FRF estimates in multiple input/output systems.  Computer
simulations illustrate the strengths of this method.  Good estimates of
FRFs have been obtained where the inputs are 99.8-percent correlated.  In
addition, good estimates have been obtained when coherence is less than
0.05!
 
FRF-estimate notation becomes complicated in a multiple input/output
system.  This paper proposes a system of notation for FRF specification
where the type of estimator, number of averages, input location, and
output location are clearly indicated.  The new notation is used in the
beginning of this abstract.
 
 
 
Dimas, D.J.; Pardown, G.C. Extrapolation of modal-analysis techniques to
nonlinear damped systems.  3(3):81-88; Jul 1988.
 
ABSTRACT - The resistive forces of objects that move through fluids in
mechanical systems can be proportional to their velocity raised to powers
other then one.  This type of resistive force, that is generically termed
Nth power velocity damping, yields a governing differential equation
which is nonlinear.  This investigation considered the effects of the
damping nonlinearities by numerically integrating the equation of motion
for a nonlinear one-DOF system subjected to a series of harmonic forcing
functions.  The results of these analyses were displayed in the frequency
domain by a series of three-dimensional response surfaces using
interactive graphics software(PATRAN).  The numerical-integration
results were (a) curve fit in the frequency domain using a rational
fraction polynomial technique to estimate the one-DOF modal parameters
and (b) compared to the actual values used in the numerical integrations.
The conclusions provide bounds on the salient parameters for this type of
nonlinear system in which the results of traditional modal-analysis
procedures can be extrapolated.
 
 
 
Doyle, J.F.  A spectrally formulated finite element for longitudinal wave
propagation.  3(1):1-5; Jan 1988.
 
ABSTRACT - By recasting the dynamics of rods in spectral terms and using
the FFT for inversion, a description emerges that requires information
only at the end points.  This description is eminently suited for a
finite-element formulation because the chosen length of the element can
be large.  This affords a substantial reduction in the size of the system of
equations to be solved.
 
 
 
Henried, A.G.; Lau, K.S.  Dynamic response of secondary systems in
structures subjected to earthquake excitation.  3(1):2025; Jan 1988.
 
ABSTRACT - The dynamic response of lightweight equipment (secondary
system) attached to a heavier structure (primary system) which is
subjected to earthquake ground motion is investigated.  A recently
developed technique for the determination of secondary subsystem
response, which avoids the shortcomings of either a numerical integration
of the combined system equations or various ad hoc approaches is
summarized.  The results of an intensive series of numerical experiments
on several primary-secondary systems subjected to earthquake excitation
are presented.  These numerical experiments shed new light on the
dynamic response of secondary systems in structures subjected to
earthquake excitation as well as on the proposed technique for the
determination of this response.
 
 
 
Huang, T.C.; Huang, X.L. Fixed-interface substructural modal perturbation
method.  3(1):6-11; Jan 1988.
 
ABSTRACT - By combining the modal-perturbation technique and
substructural modal analysis, a new substructural-modal-perturbation
method is developed.
 
 
 
Huo, Q.Z.; Zhang, D.J.  Application of impact testing in the modal analysis
of a large structure.  3(2):57-61; Apr 1988.
 
ABSTRACT - In order to use less equipment in the modal testing of a large
structure, an excitation method based on a random series of impacts was
studied analytically and experimentally.  The divisional excitation and
measurement technique was also considered.  The methods were
successfully applied in the modal testing of a diesel-locomotive body.
The first seven normal modes and other modal parameters were obtained.
 
 
 
Lee, G.M.; Trethewey, M.W.  Modal-parameter quality assessment from
time-domain data.  3(4):129-136; Oct 1988.
 
ABSTRACT - This paper will explore the application of digital filtering
methods for the evaluation of modal-parameter quality for the
finite-difference least-squares time-domain modalidentification method.
The approach uses a comparison of the modal-model response to the actual
response in a family of band-limited frequency regions.  The band-limited
responses are generated through the application of finite impulse
response filters to both the measured and modal model time series.  The
calculation of root mean square error between the series provides a
quantitative measure of the modal parameter  quality in narrow band
frequency regions.  The fundamentals of the approach are presented along
with practical details of its implementation.  The approach is applied to
both simulated and experimental structural-vibration data to examine the
utility of the approach.  The results illustrate that the approach can
quantitatively evaluate the modal-parameter quality for modes either
with a low-level response or which are masked by extraneous background
noise.
 
Leonard, F. ZMODAL: a new modal-identification technique. 3(2):69-76; Apr
1988.
 
ABSTRACT - This paper describes a new tool for modal identification and
proposes a novel approach for evaluating the real mode-shape accuracy.
The Z-plane modal-analysis  (ZMODAL) algorithm is based on topological
characteristics of amplitude and phase in the Z plane of the Z transform of
damped sinusoids.  Since damping is a dimension of the signal
representation space, it is easy to disassociate frequency modes that are
close but have different damping coefficients.  In the Z-plane
representation space, poles corresponding to modes have less energy
coupling between them than the frequency lobes in Fourier representation
space.  This, together with the use of spectral windows, improves
mode-energy separation.  In this context of good cross-modal rejection
(pole energy versus coupling energy with another pole).  MDOF and SDOF
algorithms give similar results although for this study the latter was
selected for its shorter CPU time, robustness and simplicity of
implementation.  Like the lbrahim time-domain (ITD) algorithm, it is
based on free-decay responses and does not call for force inputs.  The
algorithm has been tested for different experimental and analytical
results and shows good agreement with ITD results.  The paper also
proposes a method for quantitative evaluation of the real mode-shape
accuracy based on the phase output; the phase standard deviation.  The
mathematical demonstration of this significant new tool is given and
comparisons based on it are presented.
 
 
 
Mitchell, L.D.  A  perspective view of modal analysis.  3(2):45-48; Apr
1988.
 
ABSTRACT -  Historically, experimental modal analysis (EMA) grew to
prominence because the engineering community was incapable of properly
analyzing the dynamics of commercially significant structures.  As
experimental modal analysis developed the capacity to generate
mathematical models from experimental data, the
finite-element-analysis (FEA) community established significant
dynamic-analysis capability.  Accelerated development in both fields
followed.  Experimental modal analysis had the new task of verifying
analytical-modal-analysis (AMA) results.  The trend now is toward using
EMA to help pinpoint the modeling inadequacies in FEA.  Activity in sales
of, equipment for, and new horizons in experimental modal analysis seem
to have hit a plateau.  This paper traces these developments, relates its
connection to the CAD/CAM/CAE revolution, overviews the roadblocks,
assesses the current state, and probes the future.  Computer-aided
engineering (CAE), in general, and experimental/analytical modal analysis,
in particular, face a series of challenges.  When met, these challenges will
form the base for a major expansion of the technology and its application.
Moreover, merging experimental and analytical modal analysis will
solidify the contribution of modal analysis to the betterment of the
overall engineering-design process.  An improved and more efficient
design process will serve society for years to come.
 
 
 
Mitchell, L.D.; Cobb, R.E.; Deel, J.C.; Luk, Y.W.  An unbiased
frequency-response-function estimator. 3(1):12-19; Jan 1988.
 
ABSTRACT - In the past several years a number of alternative methods
have been introduced for the estimation of frequency-response functions
(FRF) of structures using averaged auto and cross spectra of the force and
response signals.  All of these methods coincide in the noise-free
environment, but each produce a biased estimate unless certain
assumptions about the force and response signal-to-noise ratios are
satisfied.  Since these noise characteristics are frequency dependent and
are generally unknown, it has been difficult to properly apply these
methods in practice.  This paper develops a little-known FRF estimate,
denoted by H(hat) (super)c , which avoid these problems.  Because this
estimate is compute entirely from averaged cross spectra, it avoids the
errors which uncorrelated sources produce in the autospectra used in all
the other currently available FRF estimates.  Examples are presented that
compare H(hat) (super)c with other estimates computed from exactly the
same date.  The effect of averaging on the convergence of |H(hat) (super)c|
is investigated.
 
 
 
Nariboli, G.A.; McConnell, K.G.  Curvature coupling of catenary cable
equations. 3(2):49-56; Apr 1988.
 
ABSTRACT - Not currently available
 
 
 
Olausson, H. L.; Torby, B.J.  Turbine design using complex modes and
substructuring.  3(4):148-157; Oct 1988
 
ABSTRACT - This paper presents a complex modal-analysis method for
studying the behavior of a turbine near its design speed.  In this method
gyroscopic moments as well as non-symmetric bearing effects are
accounted for in the modal calculations.  The complex mode shapes that
are found here more accurately describe steady-state orbital motion than
planar modes.  Transient motion, induced by some disturbance from a
dynamic equilibrium state, is formulated through a series expansion of the
complex normal-coordinate terms associated with these mode shapes.
The ensuing equations of motion can then be integrated and the solution
brought back to the problem's original generalized coordinates.  Since in
normal-coordinate description no distinction can be made between modes
obtained mathematically and those found experimentally, the paper also
describes how the latter mode shapes can easily be coupled to the system
equation when they are considered as substructure component modes.  This
use of component-mode synthesis allows the turbine model to incorporate
several rotors turning at different speeds, and even torsional motion.
Results are given from typical calculations performed for a 650 MW ASEA
STAL turbine installation.
 
 
 
Park, Y.S.; Park,, H.S.; Lee, S.S. Weighted-error-matrix application to
detect stiffness damage by dynamic-characteristic measurement.
3(3):101-107; Jul 1988.
 
ABSTRACT - A nondestructive method to detect stiffness damages in a
structure is studied.  The method is based on the fact that dynamic
characteristics vary depending on the locations of stiffness defect.  Close
examinations of measured dynamic characteristics enable us to study the
defects.  First the error-matrix method was tested.  Since the error
matrix originates from the differences of measured natural frequencies,
and mode shapes, before and after damages, it is generally influenced by
measurement errors and the number of measurable modes.  The
error-matrix method was applied to two sample structures to search for
damaged areas.  The method was found useful when the stiffness changes
were large.  But cracks and small defects in structures most often cause
only small changes in local stiffness.  The error matrix method is thus not
effective for searching out small local defects.  Next, the
weighted-error-matrix (WEM) method was tested to magnify the effect of
small stiffness loss in the error matrix.  The idea of WEM is to magnify
the damaged area in the error matrix by adding the information from the
eigenproperties'changing patterns through sensitivity analysis.  Applying
the WEM to the two same sample structures, it was found that WEM is a
far better method for identifying defects than the error-matrix method,
especially when the defect is small.  A step by step method is suggested
in order to locate the defects in a large structure economically.  First the
structure is divided into a few numbers of large elements and the damage
is studied by WEM techniques.  Next only the probable damaged element,
which is found in the first step, is divided into finer elements, and the
damage is studies within the narrow-downed element. Applying the step
by step method to a plate structure, it was found that the method is an
economical way to study the damaged areas.
 
 
 
Patton, M.E.; Trethewey, M.W.  External-intensity-modulated fiber-optic
sensors for structural-vibration measurements.  3(4):137-147; Oct 1988.
 
ABSTRACT - External-intensity-modulated fiber-optic systems have
gained considerable use recently for the measurement of dynamic
mechanical phenomena.  The systems posses many outstanding
characteristics.  However, their principle of operation makes them
susceptible to a variety of measurement errors if proper care is not
exercised in the experimental setup and data interpretation.  The
objective of this paper is to examine the transducer's characteristics and
present procedures for their proper implementation for modal-analysis
applications.  The paper examines several potential errors associated with
these sensors and discusses the effect on experimental data.
Specifically, the difficulties examined are positioning accuracy,
target-reflectivity differences, target curvature, nonlinear sensor
response, and inherent dynamic-range effects of displacement-based
modal data.  Each of these topics is investigated to examine the effects
which these errors have on the sensitivity, linearity, and data
consistency.  Procedures to either eliminate or minimize the effects of
the errors are described.
 
 
 
Starkey, J.M.; Durchholz, A.M.  A dynamic substructure algorithm to
investigate the feasibility of adaptable engine mounts.  3(1):26-31; Jan
1988.
 
ABSTRACT - This paper presents a technique for predicting the effects of
variable engine-mount properties on the natural frequencies and mode
shapes of a light-truck engine/chassis structure.  Modal testing was used
to develop chassis models and to validate the substructuring procedure.
Engine-mount sensitivity studies indicate that engine mounts with
adjustable damping and stiffness can significantly reduce chassis
vibrations at idle.
 
 
 
Steffen. V., Jr.; Marcelin, J.L.  On the optimization of vibration frequencies
of rotors.  3(3):77-80; Jul 1988.
 
ABSTRACT - At the design stage of construction of rotating machinery,
the natural frequencies and critical speeds much be optimized in such a
way that the operating speeds must be optimized in such a way that the
operating speed of rotation is safely far from the criticals.  This can be
performed by manipulating design variables taking into account
technological constraints.  This paper presents an optimizing program
coupled to a rotor-dynamics finite-elements code to perform the
optimization of rotors.  Three different applications for which natural
frequencies optimization were performed are presented.
 
 
 
Unlusoy, Y.S.  Mobility analysis of helical coil springs. 3(3):96-100;Jul
1988.
 
ABSTRACT - Dynamic behavior of helical compression springs as
represented by their point-mobility functions is investigated.  Mass and
stiffness matrices for the springs are obtained using straight-beam finite
elements with six degrees of freedom at each end.  The effects of static
axial load (i.e., preload) on the dynamic behavior are also taken into
account.  The eigenvalue problem is solved by the subspace iteration
method.  The undamped natural frequencies together with the
corresponding modal vectors are determined.  Theoretical point-mobility
functions are then calculated by the mode superposition method for
excitation in the direction of longitudinal spring axis at one end of the
spring while the other end is fixed.  The calculated and experimentally
obtained point-mobility functions for three automobile suspension
springs, drawn in the frequency range from 3 to 200 Hz, display fairly
good agreement.  The shapes of the first ten modes are also plotted and
the major categories of vibration modes are identified.  The effects of
preload on the natural frequencies corresponding to each category of
modes are identified.  The results allow an assessment of the
applicability of the widely used distributed-parameter spring model
which considers longitudinal spring vibrations only.
 
 

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