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

Volume 6, Number 2
April 1991


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Maia, N. M. M., Technical University of Lisbon
 
6 (2): 69-80;  Apr. 1991
 
REFLECTIONS OF SOME SINGLE-DEGREE-OF-FREEDOM (SDOF) MODAL ANALYSIS
METHODS
 
ABSTRACT - In the present paper, some of the most important
single-degree-of-freedom (SDOF) methods of modal analysis are
described and compared, based on experience gained while applying
them to both theoretical and experimental cases.  The work is
descriptive, as the main objective is to stress and explore the
concepts involved and the existing similarities.  It is believed
that a contribution is made in the sense of providing a deeper
understanding of Dobsons method relating it to the inverse method.
 
 
 
Mioduchowski, A., University of Alberta and W. Nadolski, Polish
Academy of Sciences
 
6(2): 81-88; Apr. 1991
 
ON TORSIONAL RESONANT DEFORMATIONS OF SIMPLIFIED NONHOMOGENEOUS
DRIVE SYSTEMS
 
ABSTRACT - In this paper the one-dimensional discrete - continuous
model of a simple nonhomogeneous drive system is considered.  The
system consists of three rigid disks and two torsionally
deformable shafts of different materials, but such that torsional
wave speeds in both shafts are equal.  Damping is taken into
account by means of an equivalent external damping of the viscous
type and an equivalent damping of the Voigt type.  Numerical
results for the amplitude - frequency curves for selected cross-
sections are presented in graphical form.
 
 
 
Wright, J. R., University of Manchester and M. A. Al-Hadid,
Scientific Studies and Research Centre
 
6(2):  89-103; Apr. 1991
 
SENSITIVITY OF THE FORCE-STATE MAPPING APPROACH TO MEASUREMENT
ERRORS
 
ABSTRACT - In this paper the application of the force-state
mapping approach to the identification of nonlinear systems is
considered.  In particular, the sensitivity of the basic method to
systematic amplitude and phase errors, and to random errors, in
the measurements is investigated analytically using a linear
single degree of freedom system subject to steady state
excitation.  It is shown that the identified damping estimates are
very sensitive to small systematic errors in the phase of the
measured or integrated signals when the system itself is lightly
damped, and that significantly biased results can be obtained.
Other forms of error are far less important.  The study highlights
the need for extremely accurate instrumentation if this
identification approach is to be used successfully in practice.
 
 
 
Jara-Almonte, J., Clemson University and L. D. Mitchell, Virginia
Polytechnic Institute and State University
 
6(2): 105-115; Apr. 1991
 
A HYBRID EIGENPROBLEM FORMULATION USING THE FINITE ELEMENT METHOD;
PART I: THEORY
 
ABSTRACT - A hybrid technique to reduce the size of finite-
element-method based eigen problems is presented in this paper.
Numerical examples using this method are presented in Part II.  In
this hybrid method, a continuum transfer matrix beam element is
used as an exact dynamical element.  The exact element is
incorporated into a finite element model, and is used as a
substructure, resulting in smaller matrices.  The terms in the
exact dynamical representation are functions of frequency.  Thus
the ensuing eigenproblem is a transcendental eigenproblem.  A
frequency-scan extraction algorithm is employed to find the
eigenvalues.  The eigenvectors can be reconstructed for both
finite and exact elements; however, the exact formulation yields
eigenvectors with virtually any desired spatial precision.
 
One result of this hybrid, finite element and transfer matrix,
method is smaller matrices, albeit with a transcendental
eigenvalue problem.  Another result is that the hybrid method has
the ability to extract higher eigenfrequencies as easily and as
accurately as lower eigenfrequencies.  Moreover, the formulation
allows the extraction of an average of six
eigenfrequencies/vectors for every degree of freedom in the model.
In contrast, the finite element method models usually require four
or more degrees of freedom per accurate eigenfrequency (within 5%
of the true eigenvalue).
 
 
Jara-Almonte, J., Clemson University and L. D. Mitchell, Virginia
Polytechnic Institute and State University.
 
6(2): 117-130; Apr. 1991
 
A HYBRID EIGENPROBLEM FORMULATION USING THE FINITE ELEMENT METHOD;
PART II: EXAMPLES
 
ABSTRACT - This paper contains numerical examples of the method
presented in Part I , which dealt with the theory.  The proposed
method incorporates continuum transfer matrices into a finite
element discretization for substructuring purposes.  The two
examples presented in this paper, a portal arch and Vierendeel
truss, show that the proposed method reduced the number of degrees
of freedom of the finite element models and at the same time
improved the accuracy of the predicted higher eigenvalues.  These
improvements came at the expense of having to solve a
transcendental eigenproblem.  The implementation and solution of
the hybrid model is also presented.
 
 
 
McConnell, K. G., Iowa State University and Rogers, J. D., Sandia
National Laboratories
 
6(2): 131-145; Apr. 1991
 
TUTORIAL: TRANSDUCER REQUIREMENTS FOR USE IN MODAL ANALYSIS
 
ABSTRACT - The art of Experimental Modal Analysis starts with the
transducers and system components used in making the required
measurements.  Many different instrument systems can be used.  The
objective of the first set of four papers in this tutorial series
is to understand instrumentation requirements and measurement
system characteristics as applied to experimental modal analysis.
A second set of tutorial papers will explore the requirements for
understanding and using frequency analysis.  A third set of papers
will explore the art of pulling it all together in order to obtain
the natural frequencies, mode shapes, structural damping, etc.
These tutorial papers are based on a series of yearly seminars
given at the spring meetings of the Society of Experimental
Mechanics as well as current research and experience of the
authors.
 
The first paper is limited to the general measurement requirements
and beginning definitions used in instrumentation systems.  It
addresses several topics necessary for the understanding of modal
analysis measurements.  The first section gives a very brief
overview of the concepts of modal analysis.  The next two sections
deal with transducer characteristics.  The last five sections
discuss background material on measurements systems, operational
amplifiers, and convenient methods for dealing with complex
values.  Each section was written independently from the others to
provide for convenient review as reference material.  Thus, some
readers may find it more beneficial to read the background
material first, while others may choose to skip that material
entirely.
 

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