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

Volume 2
1987


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

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Abu-Farsakh, G.; Nhader, N. A new triangular finite element for the
analysis of free vibration of plates. 2(3):136-143; Jul 1987.
 
ABSTRACT - A finite-element analysis was carried out using three
versions of the TNTE element (ten-node triangular element).  The
free-vibration problem of a rectangular plate with different boundary
conditions was studied.  The lowest four frequencies were obtained and
compared with the available results.  It is shown that reasonably
acceptable results can be obtained using the proper version of the
element, even with coarse mesh divisions.  In some cases, higher mode
frequencies were obtained.  They are compared with the corresponding
experimental and/or analytical values.
 
 
 
Ahme, I.; Tomlinson, G.R.  Reducing the effects of residual modes in
measured frequency-response data.  2(3):113-120; Jul 1987.
 
ABSTRACT - A procedure is described for ameliorating the effects of
mass and stiffness residuals in measured frequency-response data.  The
procedure is applied to both simulated and experimental data.  It is shown
that the modified data set resembles a finite set of modes which can be
analyzed without resort to the inclusion of residuals normally used to
represent the low- and high-frequency modes.
 
 
 
Akgun, M.; Ju, F.D.  Diagnosis of fracture damage in frame structures (a
PI-circuit analogy). 2(4):155-162; Oct 1987.
 
ABSTRACT - The paper applies an aspect of modal analysis to the problem
of damage diagnosis in complex frame structures.  The criterion is based
quantitatively on the changes in modal frequencies as a result of
structural softening from fracture damages.  The analysis requires
accurate structural modelings for the pre- and post-damage structures.  A
II-circuit analogy is developed for the simulation of the complex frame
structure and for the subsequent simplification and formalization of
diagnostic analysis.  The analogous simulation is based on the algebraic
equivalence of the equations for a straight beam with a given shape
function and the Kirchhoff's law for a II-circuit.  The end moments and
rotations (slopes) are thus algebraically equivalent to the port currents
and voltages.  The moment equilibrium at a structural node is satisfied by
Kirchhoff's current law at the corresponding electrical node.  The rotation
(slope) continuation at the node is automatically defined by the modal
potential.  Moreover, the slope discontinuity at the cracked section
becomes the potential difference across an electrical impedance, which is
identified as a resistance, equivalent to the negative reciprocal of the
'fracture-hinge' spring constant.  The natural frequencies of the structure
are therefore those of the network of II-circuits.  Based on the II-circuit
network, the paper establishes a formalism procedure to construct the
matrices in the frequency equation without requiring the users of the
frequency equation   to draw the analog network.  The method is therefore
readily adaptable to computer programming.  Use of the method and the
fracture-damage diagnosis is illustrated with a two-story single-span
frame structure.
 
 
 
Akgun, M.; Ju, F.D.  Diagnosis of multiple cracks on a beam structure.
2(4):149-154; Oct 1987.
 
ABSTRACT - The paper explores the modal-frequency theory in diagnosis
of multiple cracks in a beam structure.  The damage functions based on the
change in modal frequencies are formulated for a beam with k number of
cracks, using the analogy of electrical T-circuits.  The modal analysis
using electrical analogy is fully developed, for which the individual beam
segments are represented by T-circuits while the cracks by resistors.
The paper addresses further the uncertainties in the application of the
modal-frequency theory for fracture diagnosis, especially for multiple
cracks.  The paper found that there exists a spacing limit of multiple
cracks, below which the modal change is indistinguishable from that of a
single crack.  Uncertainty could also arise from the tolerance limit in
measurement of frequency variations.  Then, if it could be ascertained
that there exists only a single major crack, the effect of minor cracks on
the frequency variations will be of small order.  Finally, the paper
considers the case that, when inadequate measurements are available,
valuable information can be extracted if a crack occurs at a peak-response
location of a modal shape.
 
 
 
Brandon, J.A.  Eliminating indirect analysis - the potential for receptance
sensitivities. 2(2):73-75; Apr 1987.
 
ABSTRACT - The approach currently dominant in sensitivity analysis for
structural dynamics is the use of modal-design sensitivities.  These
modal properties are often synthesized using receptance data (or other
force-response characteristics).  It is not unusual that, having evaluated
modal-design sensitivities, the analyst will then transform these back
into response characteristics.  The paper considers transformations which
produce receptance sensitivities directly from the experimental study
eliminating the need for the modal analysis stages of reanalysis.  Thus in
design problems where only specific force-response properties are of
interest, the indirect route appears unnecessary.
 
 
 
Chua, K.H.; Rahman, M.; Mansur, M.A.  Performance evaluation of
machine-tool structures using modal analysis.  2(1):43-49; Jan 1987.
 
ABSTRACT - The use of experimental-modal-analysis technique in the
evaluation of machine-tool dynamic performance is discussed and
illustrated in this paper.  Two machine-tool structures made of different
materials, ferrocement and conventional cast iron, are studied.  The
dynamic performance of these two structures is evaluated and compared.
Both structures were designed to give the same static stiffness (1).
However, while carrying out modal analysis of these structures, it has
been found that the first resonance peak is observed for the cast-iron bed
at 125 Hz in the first torsional mode which goes undetected in normal
impact test, whereas the first resonance peak for ferrocement is observed
at 280 Hz in the first vertical bending mode.  The results obtained through
modal-analysis tests have further been verified through finite-element
analysis.  Moreover, the damping ratio of ferrocement, has been found to
be significantly higher than cast iron.  From the study, it is clear that
ferrocement is a very good replacement for cast iron for machine-tool
structures because of its good dynamic properties.
 
 
 
Craig, R.R., Jr.  A review of time-domain and frequency domain
component-mode synthesis methods. 2(2):59-72; Apr 1987.
 
ABSTRACT - Component-mode synthesis (CMS) is a form of substructure
coupling analysis frequently employed in structural dynamics.  The
dynamic behavior of each substructure is formulated as a superposition of
modal contributions.  The system model is formed by enforcing
equilibrium and compatibility along component interfaces.  Both
time-domain and frequency-domain approaches are reviewed in this paper,
since both may be employed to develop system models using experimental
data.  Time-domain methods of CMS may be divided into those for
undamped structures and those which apply to damped structures.
Methods may be further subdivided on the basis of the types of component
modes employed in the synthesis procedure, such as free-interface
component normal modes, constraint modes, inertia-relief attachment
modes, etc.  These component modes are described; and their availability
from component testing is discussed.  The use of state space descriptions
for systems with general viscous damping is briefly discussed, along with
the use of frequency-domain models for determining response.
 
 
 
Cunniff, P.F.; O'Hara, G.J.  Modal characteristics of structures from
transient-response data.  2(4):180-191; Oct 1987.
 
ABSTRACT - This paper examines the problem of extracting useful
information from measured-transient-response motion of structural
systems that have been shock excited.  The structural systems are
composed of two parts: the equipment/foundation combination which in
turn is attached to a supporting vehicle structure at a single point.  Use of
the Fourier transformation and manipulation of the transient-response
data permit the fixed-base natural frequencies, normal-mode shapes, and
modal effective masses to be calculated for the equipment/foundation
combination.  The normal-mode damping factors for multi-degrees of
freedom equipment/foundation combinations can also be approximated for
the case of lightly damped structural systems with proportional damping.
Finally, transfer functions can be found which allow the analyst to predict
responses of the structural systems to other possible shock excitations.
 
 
 
Hermanski, M.; Ostholt, H.  Linking finite elements with experimental
modal analysis.  2(3):144-147; Jul 1987.
 
ABSTRACT - A method for linking finite elements (FEM) with experimental
modal analysis is presented.  Lagrange polynomials and cubic spline
functions are used to approximate the rotational degrees of freedom
(RDOF) at the linking points in the modal data base.
 
 
 
Ibrahim, A.; Ismail, F.; Martin, H.R.  Modeling of the dynamics of a
continuous beam including non-linear fatigue crack.  2(2):76-82; Apr 1987.
 
ABSTRACT - Vibration testing is a fast means of detecting crack
development in structures.  In previous work by other authors, an
open-crack model was assumed and analytical expressions for the change
in the resonant frequencies were derived.  In this work, numerical
simulation is employed to investigate the dynamic behavior of a
cantilever beam including nonlinear fatigue crack.  This crack is assumed
to open and close depending on the vibration direction.  A bondgraph model
of the cantilever beam is developed in this work.  It is verified using the
finite-element method.  This model is then used in the numerical
simulation to obtain frequency-response functions of the cracked beam.
Results obtained in this work show that the frequency drop due to a
nonlinear fatigue crack is always smaller than that computed assuming an
open-crack model.  Also, the shape of the frequency-response function can
help identify the presence and nature of the crack.
 
 
 
Inman, D.J.; Jiang, B.L.  On damping ratios for multiple degree of freedom
linear systems.  2(1):38-42; Jan 1987.
 
ABSTRACT - A commonly used parameter in both experimental and
analytical modal analysis is the damping ratio or percent of critical
damping.  For a single degree of freedom system this concept is clearly
defined and knowledge of a system's spring constant, damping rate and
mass allows the calculation of the damping ratio.  This concept is
extended here and defined for multiple degree of freedom systems.  The
damping-ratio matrix and a modal-damping-ratio matrix are defined in
terms of the mass matrix, damping matrix and stiffness matrix for a
multiple degree of freedom system of arbitrary dimension.  The definition
used for the damping-ratio matrix relies on the definition of critical
damping for lumped parameter systems provided previously.  The
definitions presented here offer a partial physical interpretation of
measured modal-damping ratios for nonproportionally damped systems.
 
 
 
Jones, D.I.G.; Muszynska, A.  Mechanical-structure improvement by dynamic
stiffness methods.  2(2):833-91; Apr 1987.
 
ABSTRACT - The relationship between the receptance and
dynamic-stiffness models of the dynamic response of structures is
described.  The transformation from receptance to dynamic-stiffness
models allows one to determine modifications needed to change the
response behavior in a desired manner.  Potential applications are
described for space structures., turbomachinery blading and extremely
large, one of a kind, structures.  A simple example is given to illustrate
the approach.
 
 
 
Juang, J.N.  Mathematical correlation of modal-parameter-identification
methods via system-realization theory.  2(1):1-18; Jan 1987.
 
ABSTRACT - A unified approach is introduced using system-realization
theory to derive and correlate modal-parameter-identification methods
for flexible structures.  Several different time-domain and
frequency-domain methods are analyzed and treated.  A basic
mathematical foundation is presented which provides insight into the
field of modal-parameter identification for comparison and evaluation.
The relation among various existing methods is established and discussed.
This report serves as a starting point to stimulate additional research
towards the unification of the many possible approaches for
modal-parameter identification.
 
 
 
Kammer, D.C.  Test-analysis-model development using an exact modal
reduction.  2(4):174-179; Oct 1987.
 
ABSTRACT - A new method for test-analysis-model (TAM) development
for use in test/analysis correlation and system identification utilizes the
finite-element-model (FEM) mode shapes to reduce the associated
analytical mass and stiffness matrices.  The reduced representation
exactly predicts all the FEM mode shapes and frequencies used in the
reduction process.  This method, termed modal reduction, offers a valuable
alternative to the Guyan reduction method in cases where a static
reduction requires a prohibitively large number of master degrees of
freedom to generate an accurate TAM.  It also eliminates all error
associated with the TAM reduction from test/analysis correlation and
system identification.  A numerical example is used to illustrate the
accuracy of the method.
 
 
 
Lembregts, F.; Snoeys, R.; Leuridan, J.  Application and evaluation of
multiple-input modal-parameter estimation.  2(1):19-31; Jan 1987.
 
ABSTRACT - This paper compares the frequency-domain
direct-parameter-identification method (FDPI) to the time-domain
least-squares complex exponential algorithm (polyreference) to estimate
the modal parameters (natural frequencies, damping values, mode shapes
and modal-participation factors) from a most general multiple-input
frequency-response-function measurement set.  Some practical tools for
the parameter-estimation process in general are referenced and/or
presented.  They deal with order estimation, accuracy of the extracted
parameters and rejection of computational modes.  Two experimental
tests have been carried out to show the use and applicability of these
tools as well as the excellent agreement between the two identification
methods.
 
 
 
McConnell, K.G.; Abdelhamid, M.K.  On the dynamic calibration of
measurement systems for use in modal analysis. 2(3):121-127; Jul 1987.
 
ABSTRACT - Proper calibration of measurement systems for use in modal
analysis should include sensitivity, as well as magnitude and phase
distortion in the frequency domain.  Force, acceleration, and strain are the
most frequently measured quantities in modal analysis.  Different
methods of calibration such as mass, free-free bar, long rod, and an
electronic method are discussed.  Two simple methods for time-delay
compensation are presented.
 
 
 
Natke, H.G.  Input and damping identification within the frequency domain.
2(2):92-98; Apr 1987.
 
ABSTRACT - Input-identification procedures are described using output
quantities of the system with a nonsturctured and a structured model of
the system including incomplete modal quantities.  With regard to the
latter, static correction due to the truncated modes is applied.  The
simultaneous identification of damping matrices is discussed in addition
to the input identification.  Examples demonstrate the procedures.
 
 
 
Pappa, R.S.; Juang, J. N.  Studies of modal-identification performance using
hybrid data.  2(2):99-108; Apr 1987.
 
ABSTRACT - Modal-identification accuracy can be affected significantly
in practice by high modal density and nonlinearities.  It may be difficult to
determine the true number of modes; many of the identified mode shapes
may be questionable.  Results can vary considerably using different
analysis techniques.  This paper introduces a new method for studying
modal-identification performance under such circumstances.  A difficult
set of test data from an erectable truss structure  was modified
numerically by adding two artificial modes with known parameters.  These
'hybrid data' were then analyzed with the polyreference technique and the
eigensystem realization algorithm (ERA).  Identification performance is
studied by comparing the identified modal parameters for the artificial
modes with their known values.
 
 
 
Patton, M.E.; Trethewey,  M.W.  A survey and assessment of
nonintrusive-modal-testing techniques for ultralightweight structures.
2(4):163-173; Oct 1987.
 
ABSTRACT - Lightweight delicate mechanical structures do not lend
themselves to typical modal-analysis procedures.  Either the application
of an artificial excitation or a response transducer may alter the system
sufficiently to preclude accurate modal-parameter extraction.  The
current work surveys experimental methods to identify suitable
excitation and transducer techniques for the nonintrusive modal analysis
of lightweight structures.  A total of eight response transducers and six
excitation techniques are presented.  The operating fundamentals of each
identified technique are briefly reviewed to illustrate their capabilities
and limitations for nonintrusive testing.  The operational specifications
of the various systems are compared to assess the current state of
technology.  The assessment indicates that many transducer techniques
are well suited for nonintrusive vibration measurement,whereas
nonintrusive excitation techniques are not as easily adapted or developed
for modal-analysis applications.  The assessment indicates that the
technology exists to perform effective nonintrusive modal analysis on
lightweight structures, but that careful consideration must be given to
the entire test-system compatibility.
 
 
 
Robertson, B.P.; Pilkey, W.D.  Limiting performance for the control of large
vibrating structures by a modal approach.  2(1):32-37; Jan 1987.
 
ABSTRACT - The absolute optimal response of a system for a given
performance index is referred to as the limiting performance.  In this
study, the limiting performance characteristics of large structures,
perhaps formed of substructures, subjected to transient disturbances, are
investigated using modal responses.  Equations of motion are developed
for both systems with imbedded control forces and systems with
generic-control-force connections between substructures.  A linear
programming formulation of the limiting performance problem is obtained
by discretizing in time a modal formulation of response variables.  The
limiting performance of a three-degree-of-freedom system is solved as
an example.
 
 
 
Wang, B.P.  Structural dynamic optimization using reanalysis techniques.
2(1):50-58; Jan 1987.
 
ABSTRACT - The problem of designing a structure with multiple
natural-frequency constraints is investigated in this paper.  Several
gradient-based methods are considered.  The salient feature of the current
approaches are the use of assumed-mode reanalysis method   for the
repeated solutions of eigenproblems during the iterative design process.
These approaches can be implemented readily with any general-purpose
finite-element-analysis program.  Two such implementations were
attempted.  Numerical experience with some real design problems
indicates that the combined assumed-mode reanalysis and numerical
optimization techniques can be a powerful tool in synthesizing structures
with multiple frequency constraints.
 
 
 
Wang, M.L.; Paez, T.L.; Ju, F.  System identification of nonlinear damaged
structure.  2(3):128-125; Jul 1987.
 
ABSTRACT - In structural engineering, it is necessary to design each
structured system to survive the inputs anticipated over its design life.
Although a structure may experience a variety of stresses, one important
type is strong motion which causes systems to execute nonlinear
responses.  This, in turn, may subsequently induce cumulative structural
damage.  Therefore the capability of modeling nonlinear responses and
using these to assess the damage level in a structure is essential for
structural design.  This paper discusses the development of this type of
approximate linear model that can simulate an inelastic system response
and can measure damage accumulation in a structure.  The paper also
discusses using the frequency-domain technique for identifying model
parameters, calculating techniques for energy dissipation during strong
motion and finally compares model prediction with results from actual
structures.  The results show that structural damage can be predicted
even in the presence of measurement noise.
 
 
 
Wicks, A.L.; Mitchell, L.D.  Methods for the estimation of
frequency-response functions in the presence of uncorrelated noise, a
review.  2(3):109-112; Jul 1987.
 
ABSTRACT - The estimation of frequency-response function (FRF) from
measured sources is fundamental to many areas of engineering
experimentation.  The quality of these estimates is dependent on
identifying the bias errors from the random errors, thus permitting
statistically meaningful estimates of the FRF.  In recent years a variety
of techniques has been developed to form this estimation from data
contaminated by noise.  This paper reviews the techniques available,
identifying the limitations of each in terms of the assumptions governing
the estimation model.  In addition, the coherence function is discussed
relative to each estimation procedure and its usefulness in identifying the
random-error content.
 

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