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

Volume 4
1989


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

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Allen, J. J. A component synthesis method using Lanczos vectors. 4
(2):33-38; Apr 1989.

ABSTRACT - A component synthesis technique has been developed, which
uses a combination of constraint modes and fixed-interface Lanczos
vectors.  The sequence of Lanczos vectors is obtained via a recursion
equation similar to inverse iteration and mass orthonormalized to the
previously derived vectors.  The static solution of a problem of interest or
a set of random vectors can be used as the initial Lanczos vector in the
sequence.  The fixed interface Lanczos method produces a statically
complete model for a given load, if the static solution is the first vector
in the sequence.  The subsequent Lanczos vectors, X(sub)i, in the sequence
can be interpreted as being generated using the dynamic error K(super)-1
MX(sub)i-1 of the previous vector, including constraint modes for the
boundary degrees of freedom retains physical degrees of freedom of the
boundary, which allows the component to be incorporated into the system
by direct matrix assembly.  The convergence characteristics of the
fixed-interface Lanczos method is studied using static and transient
analysis.  Various criteria are examined for evaluating the convergence.
The results of the fixed-interface Lanczos method will be compared to the
component-mode synthesis method developed by Hurly.



Bernasconi, O.; Ewins, D.J.  Modal strain/stress fields. 4(2):68076; Apr
1989.

ABSTRACT - The concept of a strain/stress field associated with a mode
of a vibrating structure is studied.  The notion of massnormalized modal
strain field is clearly defined and the general expression of the strain
frequency-response function is derived.  The correspondence between
computed and measured massnormalized modal strain fields is
demonstrated on a simple model structure.  Strategies for determining
modal and dynamic strains and stresses in areas of concentration are
proposed, including a simple modal substructuring method involving the
finite-element method.  This paper gives a theoretical basis for obtaining
normalized modal strains, which are intrinsic modal parameters as are
the displacement mode shapes, and which can be used for further
computation of accurate time-dependent strain/stress fields.



Billings, S.A.; Tsang, K.M.; Tomlinson, G.R. Application of the NARMAX
method to nonlinear frequency-response estimation.  4(3):97-102; Jul
1989.



ABSTRACT - The NARMAX method of identifying the frequency-domain
characteristics of nonlinear systems is illustrated by computing the
first,second and third order generalized frequency-response functions of a
heat exchanger.



Cooper, J.E.  Comparison of some time-domain-system   identification
techniques using approximate data correlations.  4(2):51-57; Apr 1989.

ABSTRACT - Most time-domain methods used for modal analysis perform a
curve fit to impulse-response data and use the least-squares method as an
integral part of their formulations.  It is well know that when the data are
corrupted, least squares leads to biased parameter estimates, with the
damping values being especially sensitive.  A number of noniterative
techniques that attempt to eliminate the bias--instrumental matrix with
delayed observations, double least squares, correlation fit and total least
squares--are compared with least squares in terms of the approximate
data autocorrelations used in the curve fit.  The theoretical comparison is
complemented by statistical comparisons upon simply simulated systems.
As well as the ability of the methods to reduce the bias on damping
estimates, ease of implementation and computational requirements are
also investigated.



Cudney, H.H.; Inman, D.J. Determining damping mechanisms in a composite
beam by experimental modal analysis.  4(4):138-143; Oct 1989.

ABSTRACT - A method of estimating the distributed damping parameters
of a beam based on measured modal parameters (frequency and damping
ratios) is derived.  Three different mathematical models were used to
model  the damping mechanism of a quasi-isotropic pultruded cantilevered
beam.  These three models were (1)viscous (air) damping, (2)strain-rate
damping, and (3) both viscous and strain-rate damping.  Values were
obtained for each of the damping models as well as the modulus of
elasticity of the beam.  It is found that the two-parameter damping model
provides the best fit to measure modal data.  However, the two-parameter
damping model can only reproduce the measured damping ratios to within
85 percent.



Ebersbach, P.; Irretier, H.  On the application of modal-parameter
estimation using frequency-domain algorithms.  4(4):109-116; Oct 1989.

ABSTRACT - The aim of this paper is to give a review and comparison of
two applied MDOF methods for identification of modal parameters from
measured frequency-response date in the form of experimental results.
The first method is a nonlinear iterative algorithm based on linearizing
the frequency-response function by the first terms of a Taylor series
(1,2).  Starting with initial values for the modal parameters, the error
between the measured values and the calculated frequency will be
minimized iteratively.  The second method is a modification of a
noniterative algorithm, known as a linearized rational polynomial
algorithm (3,4).  The modification of this algorithm is a new definition of
the error function (5), whereby the iteration procedure becomes iterative.
In contrast  to the first method, this algorithm has a better behavior in
the iteration.  After the calculation of the poles, the residual terms of the
frequency-response function can be calculated directly from the
numerator of the polynomial, whereas normally in this method a following
linear least-squares algorithm is used.

Both estimation methods work with residual terms to compensate for the
influence of modes outside the measured frequency range.  They are
implemented at a HP deskcomputer at the Institute of Mechanics,
University of Kassel, and are applied successfully for estimation of modal
parameters from measured data.  Experimental results are given from the
testing of a turbine blade (impact excitation) and of a circular plate
(magnetic exciter with random excitation).



Ewins, D.J.; Vakakis, A.F.  An alternative method of SDOF modal analysis.
4(4):1440149; Oct 1989.

ABSTRACT - An analytical method of Modal Analysis is presented.  The
method takes advantage of the frequency distribution of the receptance
points in the complex plane and results in the so-called    plots.  From
these plots the modal parameters are extracted with improved accuracy
and the effects of nearby modes can be quantified.  The limitations of the
method are discussed and the analysis is applied to both theoretical and
experimental data.



Fullekrug, U. Structural-dynamics identification in the time
domain:estimation of modal parameters based on forced vibrations.
4(2):58-67;Apr 1989.

ABSTRACT - The objective this paper is to present a method for
structural-dynamics identification.  The proposed method operates in the
time domain and utilizes discrete time histories of both the excitation
forces and the dynamic responses.  Equations are derived for
eigenfrequencies, modal damping, eigenvectors and components of the
left-hand eigenvectors at the excitation points.  The method is applied to
a simulated vibrating structure with eleven degrees of freedom.



Hoff, C.; Natke, H.G. Correction of a finite-element model by input-output
measurements with application to a radar tower.  4(l):1-7; Jan 1989.

ABSTRACT - The mathematical model of a radar tower is improved by
input-output measurements.  Two experiments are performed: a free
vibration after unloading within the low-frequency range and a forced
vibration from impulsive loading with the high-frequency range.  The
tower itself is modeled with finite elements.  The fundament consists of
a circular ground plate with piles.  These support conditions are the most
uncertain quantities of the computational model.  The identification
method is applied to improve the displacement and torsional spring rate of
the foundation in a lumped-parameter model.  A least-squares fit with
modal residuals and input-output residuals is used to correct the
computational model.  The results show that the applied identification
methods are able to provide improved estimates of the foundation
characteristics.



Janter, T.; Heylen, W.; Sas, P. A comparison between model-optimization
procedures based on the model-optimization parameter set.  4(3):93-96,
Jul 1989.

ABSTRACT - This paper intends to make a profound comparison between
model-optimization procedures based on the selection of the
model-optimization parameters.  Emphasis is placed on the difference in
approach depending on whether we use individual mass and stiffness
matrix elements, structural submatrices, or more physically interpretable
design parameters such as the finite-element input parameters.
Advantages and disadvantages of these approaches, as well as the
consequences of the choice of the parameters are discussed.  Especially
aspects of interpretability, application fields, compatibility,
controllability of the model and numerical considerations are treated.



Jones, J.D.; Fuller, C.R.  Reduction of interior sound fields in flexible
cylinders by active vibration control.  4(2):45-50; Apr 1989.

ABSTRACT - An analytical model of a thin, flexible shell is evaluated to
study the mechanisms of interior sound reduction by the active control of
the shall vibrational response.  A single exterior acoustic monopole is
used as the primary noise source while the secondary controller is
represented as a single point force applied directly to the shell wall.  The
complex amplitude of the acoustic monopole is specified a prior;however,
the complex amplitude of the point controller is initially unknown.  The
control-force amplitude is evaluated such that the line-weighted mean
square pressure is minimized along the shell wall in the excitation plane.
The active control model is evaluated for harmonic excitation.  Results
indicate spatially averaged noise reductions in excess of 20 dB over the
source plane for acoustic resonant conditions within the cavity.  Modal
response of the shell and the coupled interior pressure field indicate
substantial control spillover in the shell due to control-force excitation;
however, control spillover is predominantly constrained to the shell and
thus does not contaminate the contained acoustic field.



Kujath, M.R. Detection of sudden changes of modal parameters in
machinery. 4(4):131-137; Oct 1989.   

ABSTRACT - The paper deals with
operating machines' dynamic behavior which is monitored by measurement
of the forced response at various points on the machine structure.  The
topic of the paper is focused on abrupt changes of system modal
parameters which may indicate a system failure.  A method of processing
signals for obtaining the information about the presence and the extent of
the changes is introduced.  The input forces remain unknown during the
analysis, and the vibrations alone are used to provide details about the
system.  The calculation procedures include finding a usable relation
between a limited modal data and the system transfer function matrix.
The problem of the number of the parameters involved is discussed.
Results of a digital simulation support the theoretical analysis.



Lee, J.L.; Lee, S.Y.; Lee, H.  Vibration and chatter analysis of an NC lathe.

ABSTRACT - In order to investigate the influence of structural dynamics
on the chatter of machine tools, the dynamic characteristics of a newly
fabricated NC lathe are analyzed by using the finite-element method.  The
bed, the base body and the spindle-bearing system of the lathe are
analyzed separately and then the total dynamic characteristics are
obtained by a component-mode-synthesis method.  Also chatter
experiments were performed with tapered MTIRA (Machine Tool Industrial
Research Association,England) workpieces.  With this experimental setup,
both the direct cutting test and the excitation test can be performed.  The
component-mode synthesis along with the direct cutting/excitation test
is proposed as the powerful tool for design modification to improve
dynamic performance of machine tools.



Lee, S.Y.;Kao,J.J.  Flexural waves in beams with periodic, but piecewise
constant, impedance.  4(4):124-130; Oct 1989.

ABSTRACT - A systematic method is developed for studying the problem
of flexural wave propagation in a beam with periodic, but piecewise
constant, impedance.  Since several interesting relations between the
particularly chosen fundamental solutions of the corresponding eigenvalue
equation are found.  It is shown that the dispersion equation can be
simplified and factorized into product form and the dynamic nature of the
system is mainly dominated by a simple function.



Leung, A.Y.T. Dynamic stiffness and nonconservative modal analysis.
4(3):77-82; July 1989.

ABSTRACT - The dynamic stiffness method and the substructure method
predict more number of natural modes than the number of master
coordinates retained.  For nonconservative systems, the dynamic stiffness
matrix may be defective.  A general algorithm for response analysis is
presented.  Discrete finite-element system are discussed first and the
unwanted coordinates are eliminated.  As the number of elements
increases, the formulation approaches that of the continuum modeling.
Since harmonic and time responses are Fourier pair, initial discussion is
concentrated on harmonic analysis and the results are applied to time
response by replacing  = lw by d/df.  New features include the orthonormal
condition, the spectral decomposition of dynamic flexibility, the mixed
frequency dynamic derivative and the expansion theorem.



Moustafa, K.A.F.  On-line extraction of offshore tower vibration
parameters from response measurements.  4(3):83-88; July 1989.

ABSTRACT - A linear mathematical model representing the dynamics of
offshore towers is considered.  An on-line identification scheme is
proposed to estimate the modal parameters by using noisy response
measurements obtained during tower normal operation.  A technique is
presented to extract the damping and stiffness matrices required for
incipient failure detection from the identified modal parameters.  An
illustrative numerical example is presented.



O'Callahan, J.C.; Chou, C.M. Localization of model errors in optimized mass
and stiffness matrices using modal-test data.  4(1):8-14; Jan 1989.

ABSTRACT - The mass and stiffness matrices of an analytical model can
be optimized using a generalized inverse technique on the measured modal
data.  A spatial representation of the structural-element properly changes
resulting from the model errors is generally preferred for engineering
applications.  This paper proposes a procedure to localize the model
errors using a least-squares approach.  The error matrices obtained from a
system optimization process are projected to the modal space and then
are equated to the summation of a series of element modal matrices.  The
unknown error coefficients associated with the element matrices are
formulated into a set of overspecified algebraic equations and are solved
using a least-squares method.  After having been weighted using the
element modal-participation factors, these error coefficients can be
directly utilized to quantify the spatial contributions of the mass and
stiffness errors in the model.

Numerical examples of a flawed cantilever beam model are used to
demonstrate the proposed error-localization procedure.



Sestieri, A.; D'Ambrogio, W.  Why be model:how to avoid the use of modes
in the modification of vibrating systems.  4(1):25-30; Jan 1989.

ABSTRACT - Modes and modal parameters are the magic and fundamental
means through which every linear problem of vibration is usually
developed.  No doubt that this is the reason for the existence of a large
number of codes performing curve-fitting procedures apt to determine
modal parameters from experimental transfer functions.  The field of
structural modification does not take exception to this rule.  However
modal identification often leads to significant errors.  Therefore, in order
to avoid the derived pitfalls, a procedure which performs optimal
structural modification without the use of modal parameters has been
developed.  Theoretical and experimental tests show the capability of the
method.



Song, T.X.; Zhang, P.Q.; Feng, W.Q., Huang, T.C.  Experimental strain modal
analysis by space-time regression method in the time domain.
4(1):15-18;Jan 1989.

ABSTRACT - Strain modal analysis has been of particular interest
recently.  This paper shows the possibility and advantage of using dynamic
strain signals as input date for strain modal analysis in the time domain,
a method developed by space and time regression.  Applications to
diagnosis and failure detection and prevention are the motivations.



Stanway, R.; Mottershead, J.E.  Experimental techniques for modeling
nonlinear stiffness and damping characteristics.  4(3):89-91;Jul 1989.

ABSTRACT - This paper describes the application of sequential filtering
to the estimation of parameters in nonlinear models of components in
mechanical vibrating structures.  The modeling strategy is outlined and
the choice of method is justified.  Experimental results are included  to
demonstrate one application of the technique: the identification of a
combined viscous plus quadratic damping model associated with an
electrorheological vibration damper.



Starkey, J.M.; Merrill, G.L.  On the ill-conditioned nature of indirect
force-measurement techniques.  4(3):103-108; Jul 1989.

ABSTRACT - Indirect measurement of excitation forces is necessary when
they are distributed or inaccessible.  The forces can then be inferred from
measurements of response if an accurate dynamic model is available; but
the computation tends to be ill conditioned.  This paper presents results
that indicate that the condition of the accelerance matrix is a good
indicator of errors in the force predictions.  Numerical simulations and
experimental results support this claim.



Tzou, H.S.  Nonlinear structural dynamics of space manipulators with
elastic joints.  4(4):117-123; Oct 1989.

ABSTRACT - Joint dynamic characteristics in flexible space manipulators
affect the manipulators' high-demanding operational performance and
accuracy.  In this paper, the structural dynamics of a flexible robotic
manipulator with elastic joints is studied using nonlinear theoretical and
finite-element methods.  Dynamic equations of a discretized multi-degree
of freedom system with initial joint gaps are derived.  Dynamic contacts
in an elastic joint are simulated by a nonlinear joint model represented by
a set of nonlinear springs and dampers.  A pseudo-force approximation
method is used in nonlinear finite-element analyses.  Nonlinear dynamic
contacts resulting from internal joint gap between two links in the
manipulator systems are studied.  Effect of joint gap size and surface
rigidity are evaluated in this paper.



Zhang, Q.; Wang, W.; Allemang, R.J.; Brown, D.L.  Prediction of mass
modification for desired natural frequencies.  4(2):39-44; Apr 1989.

ABSTRACT - In this paper a method is presented to predict the critical
amount(s) and the best location(s) of the mass modification to the
structure for certain dynamic requirements.  The analysis is made through
perturbation theory with the use of measured modal data (natural
frequency, damping factor and mode shape).  Also, a
best-approximation-subspace technique is introduced to find the best
combination of mass modifications from several possible measurement
points.  The method is illustrated by both analytical and experimental data
to show how the method handles real normal modes and complex modes.



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