1,720,979 research outputs found
Estimating damage in a rod from changes in node positions
No full textThis paper is an analytical/experimental investigation of the effect of damage on the nodes of free vibration modes of a thin rod in longitudinal vibration. The damage, a notch, is simulated by a simple spring. It is shown that nodes move toward the notch. The direction and amount by which they move may be used to estimate the position and severity of the damage. Analytical results agree well with experimental tests
Dynamical Inverse Problems: Theory and Application
No full textClassical vibration theory is concerned with the determination of
the response of a given dynamical system to a prescribed input.
These are called direct problems in vibration and powerful
analytical and numerical methods are available nowadays for their
solution. However, when one studies a phenomenon which is governed
by the equations of classical dynamics, the application of the
model to real life situations often requires the knowledge of
constitutive and/or geometrical parameters which in the direct
formulation are considered as part of the data, whereas, in
practice, they are not completely known or are inaccessible to
direct measurements. Therefore, in several areas in applied
science and technology, one has to deal with inverse problems in
vibration, that is problems in which the roles of the unknowns and
the data is reversed, at least in part. For example, one of the
basic problems in the direct vibration theory - for infinitesimal
undamped free vibrations - is the determination of the natural
frequencies and normal modes of the vibrating body, assuming that
the stiffness and mass coefficients are known. In the context of
inverse theory, on the contrary, one is dealing with the
construction of a model of a given type (i.e., a mass-spring
system, a string, a beam) that has given eigenproperties.
In addition to its applications, the study of inverse problems in
vibration has also inherent mathematical interest, since the
issues encountered have remarkable features in terms of
originality and technical difficulty, when compared with the
classical problems of direct vibration theory. In fact, inverse
problems do not usually satisfy the Hadamard postulates of
well-posedeness, also, in many cases, they are extremely
non-linear, even if the direct problem is linear. In most cases,
in order to overcome such obstacles, it is impossible to invoke
all-purpose, ready made, theoretical procedures. Instead, it is
necessary to single out a suitable approach and trade-off with the
intrinsic ill-posedeness by using original ideas and a deep use of
mathematical methods {}from various areas. Another specific and
fundamental aspect of the study of inverse problems in vibration
concerns the numerical treatment and the development of ad-hoc
strategies for the treatment of ill-conditioned, linear and
non-linear problems. Finally, when inverse techniques are applied
to the study of real problems, additional obstructions arise
because of the complexity of mechanical modelling, the inadequacy
of the analytical models used for the interpretation of the
experiments, measurement errors and incompleteness of the field
data. Therefore, of particular relevance for practical
applications is to assess the robustness of the algorithms to
measurement errors and to the accuracy of the analytical models
used to describe the physical phenomenon.
The purpose of the CISM course entitled ``Dynamical Inverse
Problems: Theory and Application", held in Udine on May 25-29
2009, was to present a state-of-the-art overview of the general
aspects and practical applications of dynamic inverse methods,
through the interaction of several topics, ranging {}from
classical and advanced inverse problems in vibration, isospectral
systems, dynamic methods for structural identification, active
vibration control and damage detection, imaging shear stiffness in
biological tissues, wave propagation, computational and
experimental aspects relevant for engineering problems.
The course was addressed to PhD students and researchers in civil
and mechanic engineering, applied mathematics, academic and
industrial researchers.
In the first chapter Gladwell discusses matrix inverse eigenvalue
problems. He describes the classical inverse problems for in-line
systems, such as discrete models of rods in longitudinal vibration
and beams in flexural vibration. He illustrates the theory
governing the formation of isospectral systems, and describe how
it may be used to construct isospectral finite-element models of
membranes. Throughout the chapter, emphasis is placed on ways of
choosing data that lead to a realistic system. Morassi in the
second chapter describes some classical approaches to the
inversion of continuous second-order systems. Attention is focused
on uniqueness, stability and existence results for Sturm-Liouville
differential operators given in canonical form on a finite
interval. A uniqueness result for a fourth order Euler-Bernoulli
operator of the bending vibration of a beam is also discussed. The
next chapter by R\"{o}hrl presents a method to numerically solve
the Sturm-Liouville inverse problem using a least squares approach
based on eigenvalue data. The potential and the boundary
conditions are estimated {}from two sequences of spectral data in
several examples. Theorems show why this approach works
particularly well. An introduction to the Boundary Control method
(BC-method) for solving inverse problems is presented by Belishev
in the fourth chapter. In particular, the one-dimensional version
of the BC-method is used for two dynamical inverse problems. The
first problem is to recover the potential in a Sturm-Liouville
operator describing the transverse vibration of a semi-infinite
taut string with constant linear mass density by time-history
measurements at the endpoint of the string. The second problem
deals with a second-order vectorial dynamical system governing,
for example, the longitudinal vibration of two semi-infinite
connected beams having constant linear mass densities. An inverse
problem is to recover the matrix coefficients of the lower order
terms via time-domain measurements at the endpoint of the beam.
Connections between the BC-method and asymptotic methods in PDEs,
functional analysis, control and system theory, are especially
investigated in this chapter. In the fifth chapter Vestroni and
Pau introduce dynamic methods for dynamic characterization and
damage identification of civil engineering structures.
Indeterminacy and difficulties in modal identification and model
updating are discussed with reference to several experimental
cases of masonry structures. A damage identification procedure in
a steel arch with concentrate damage is also presented. Eigenvalue
assignment problems in vibration are presented by Mottershead,
Tehrani and Ram in the sixth chapter. Procedures are described for
pole placement by passive modification and active control using
measured receptances. The theoretical basis of the method is
described and experimental implementation is explained. The book
ends with the lectures by Oberai and Barbone on inverse problems
in biomechanical imaging. The authors briefly describe the
clinical relevance of these problems and how the measured data is
acquired. Attention is focused on two distinct strategies for
solving these problems. These include a direct approach that is
fast but relies on the availability of complete interior
displacement measurements. The other is an iterative approach that
is computationally intensive but is able to handle incomplete
interior data and is robust to noise
On isospectral rods, horns and strings
No full textThe free undamped vibrations of rods, horns and taut strings are governed by second-order differential equations. It is known that the inverse problem, namely the reconstruction
of such a system, e.g. the reconstruction of the cross-sectional profile of a rod, requires the
knowledge of two free vibration spectra corresponding to two different sets of end conditions.
This paper is concerned with families of second-order systems which have one spectrum in
common. The analysis is based on the reduction of the governing equation to the standard
Sturm-Liouville form, the use of the Darboux lemma, and the research of Trubowitz, Poschel,
Deift and others. In particular the paper establishes necessary and sufficient conditions for
isospectral flow from one rod to another rod with the same end conditions, using double Darboux transformation
Families of beams with a given buckling spectrum
No full textThis paper is concerned with constructing families of
Euler-Bernoulli beams which have exactly the same sequence of
buckling loads of a given beam. The result is valid under the
assumption of Pinned-Pinned, Pinned-Sliding and Sliding-Sliding
end conditions. The analysis is based on a reduction of the
buckling problem to an eigenvalue problem for a class of strings,
and on constructing isospectral strings via a Darboux lemma
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Full text linkWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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