Problems in Structural Identification and Diagnostics: General Aspects and Applications: MURST Project n. MM08342598 — COFIN 2000

251 Pages·2003·23.871 MB·English

by  Cesare Davini, Erasmo Viola (eds.)

CISM COURSESAND LECTURES
Series Editors:
The Reetars
Manuel Garcia Velarde -Madrid
Mahir Sayir -Zurich
Wilhelm Schneider -Wien
The Secretary General
Bernhard Schrefler -Padua
Former Secretary General
Giovanni Bianchi -Milan
Executive Editor
Carlo Tasso- Udine
The series presents lecture notes, monographs, edited works and
proceedings in the field of Mechanics, Engineering, Computer Science
and Applied Mathematics.
Purpose of the series is to make known in the international scientific
and technical community results obtained in some of the activities
organized by CISM, the International Centre for Mechanical Sciences.
INTERNATIONAL CENTRE FOR MECHANICAL SCIENCES
COURSESAND LECTURES- No. 471
PROBLEMS IN STRUCTURAL
IDENTIFICATION AND DIAGNOSTICS:
GENERAL ASPECTS AND APPLICATIONS
MURST Project n. MM08342598 - COFIN 2000
EDITEDBY
CESARE DAVINI
UNIVERSITY OF UDINE, ITALY
ERASMO VIOLA
UNIVERSITY OF BOLOGNA, ITALY
i
Springer-Verlag Wien GmbH
This volume contains 131 illustrations
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© 2003 by Springer-Verlag Wien
Originally published by Springer-Verlag Wien New York in 2003
SPIN 10970591
In order to make this volume available as econornically and as
rapidly as possible the authors' typescripts have been
reproduced in their original forms. This method unfortunately
has its typographicallirnitations but it is hoped that they in no
way distract the reader.
ISBN 978-3-211-20492-4 ISBN 978-3-7091-2536-6 (eBook)
DOI 10.1007/978-3-7091-2536-6
PREFACE
The dynamic techniques as a tool for structural identification and diagnostics
have a consolidated tradition. They owe their appeal to the ability to convey a
great mass of information with relatively modest experimental burden and, over
all, to the fact that this can be done without suspending machines or structures
from service. Thus, a direct assessment of their integrity is possible. Of course,
these techniques have become a viable tool of structural analysis because of the
remarkable progress in the acquisition and treatment of experimental data that
has characterized the final decades of the last century.
By all these reasons the dynamic techniques have long since attracted the
interest of engineers in various areas, ranging from the aeronautical to civil ap
plications, and with various purposes, including e.g. model validation, failure
detection, noise analysis, vibration control, etc.. Today there are many journals
and conferences dedicated to the subject. Some, such as the The International
Seminar of Modal Analysis organized by the Katholieke Universiteit of Leuven,
have become institutional occasions where to periodically compare work and ex
perience or to share expertise gained in doing things. In Zooking at the research
activity which has been developed along the years, one is surprised by the huge
amount of work done, but he also notices a progressive improvement in the level
of awareness of the subtleties involved in this kind of problems. Scientific curios
ity, interest for the power of the techniques and need of clarity, that at least some
of us felt as a primary issue, were the motivation of the research project to which
the present volume is dedicated and also of those that, in preceding years, have
involved the same group of researchers.
Attention was constantly addressed to the fact that the identification prob
lems present pathology and difficulties typical of the inverse problems, and this
obstructs a blind use of the above mentioned techniques. The presence of non~
uniqueness, the lack of stability estimates, etc., make it difficult to renounce to
aside information or assumptions in analyzing a specific problem, and to exten~
the analysis to generat situations without discernment. It's not sur:prising that,
especially at the beginning, in the national and international Literature the at
tention was mainly devoted to the study of model problems and to data either
simulated or coming from laboratory tests, where measures can be performed un
der well controlled conditions. Studies of complex structures are rare and often
give results that are not easy to interpret. Thus, it's fair to say that the distance
between the pieces of information that these techniques can provide and those ex
pected by engineers still is noticeable and deeper understanding of both generat and
applied aspects of the discipline is needed. The long term objective of the project
was in jact to reduce such a distance by bringing tagether researchers interested
in the two aspects.
Gur research has been developed along two lines. On one side, we cultivated
the study of the generat properties of the identification problems, with specific
regard to the sensitivity of the natural frequencies to damage, the sensitivity of
the identification techniques to the accuracy of the data and of the interpretation
model, the determination of "minimal sets" of data needed for the reconstruc
tion of localized damages (mainly for one dimensional structural elements), the
determination of suitable darnage indicators, etc.. On the other side, we tried
to maintain the focus on the experimental aspects in the attempt to confront the
objective difficulty of making and interpreting the measures, especially when per
formed on complex systems and in real conditions. In fact, our research broadened
a little so as to include the identification of material properties and the use of both
static and dynamic methods for the scope.
The present volume collects papers illustrating the work of the various re
search units with special emphasis on their most recent achievements. The papers
were presented at a workshop held in Bologna on July 15-16, 2002, under the pa
tronage of the Study and Research Centre for the Identification of Materials and
Structures (CIMEST)-"M. Capurso". They cover the following themes: effects of
the modeling errors on the identification techniques; darnage identification from
the measurement of a couple of frequencies in rods and beams; node shifting and
darnage detection; identification of damping and elastic constants in orthotropic
plates; use of advanced techniques of signal theory in structural identification;
structural identification of non linear dynamical systems under random excita
tion and applications to bridge structures; dynamical modeling, tests and property
identification of building foundations on piles. As is seen, the papers encompass
a rather broad spectrum. Some work includes experimentation on full scale struc
tures andin situ tests on monumental buildings (units of Catania and Torino),
or tests on small scale models of bridge structures (unit of Palermo), all aiming
at the study and monitaring of manufacts of great public interest. But we wish
to stress that the experimental aspect, namely, the care that the theoretical results
can be carried over to practical experimental techniques, is also present in other
works that have a more methodological character. So, we believe that the project
has kept its original goal of contributing to reduce the gap between theory and
practice in the field.
Cesare Davini
Erasmo Viola
CONTENTS
Identification of Elastic Constants by Bayesian Approach
by I. Bartoli, A. Di Leo and E. Viola............................... 1
Problems Concerning the Elastic Constants Determination of Isotropie
and Orthotropic Plates
by I. Bartoli and E. Viola . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Effects of Darnage on the Response of Euler-Bernoulli Beams Tra
versed by a Moving Mass
by C. Bilello . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Dynamic Behaviour and Modelling of RC Beams Retrofitted with
CFRP Sheets
by B. Bonfiglioli and G. Pascale.................................... 47
Identification of Modal Parameters with Unknown Input
by M. De Angelis, V. Sepe and D. Capecchi......................... 59
Assessment of Historical Buildings via Ambient Vibration Measure
ments: Experiences on Bell-Towers
by A. De Stefano and R. Ceravolo.................................. 73
On Darnage ldentification in Vibrating Beams from ChangesinNode
Positions
by M. ·Dilena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Darnage Identification of Beams Using Static Test Data
by M. Di Paola and C. Bilello...................................... 101
A Novel Approach for the ldentification of Material Elastic Constants
by E. Ferretti, A. Di Leo and E. Viola. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
Computational Aspects and Numerical Simulations in the Elastic Con
stants Identification
by E. Ferretti, A. Di Leo and E. Viola. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
On the Three-Dimensional Vibration Analysis of Reetangular Plates
by C. Gentilini and E. Viola. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
The Crack Detection Problem in Vibrating Beams
by A. Morassi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
Formulation and Identification Problems for Cracked Orthotropic
Plates
by P. Ricci, E. Viola, A. Piva and L. Nobile........................ 179
Interaction of BEM Analysis and Experimental Design on Pile-Soil
Systems
by F. Vinciprova, O.Maeso Fortuny, J.J. Aznarez and G. Oliveta... 195
A Device for Static and/ or Dynamic Identification Tests on Pounda-
tion Piles
by G. Oliveto, G. Buda and P. Sciacca.............................. 229
ldentification of elastic constants by Bayesian
approach.
Ivan Bartoli + Antonio di Leo + and Erasmo Viola+
+ Faculty of Engineering, DISTART Department, University of Bologna, Italy
Abstract A combined numerical-experimental procedure for the identification of
the elastic material modulus of generally thin orthotropic plates is discussed in this
paper. This method makes use of experimental plate response data, corresponding
numerical predictions and Bayesian sensitivity analysis. The response data are a
set of natural frequencies of flexural vibration of the plate. The numerical model
is based on the Rayleigh Ritz method and the finite element method using a clas
sical plate theory displacement field. Statistical Bayesian estimation is applied in
an iterative scheme to direct the adjustments of material properties based on the
discrepancies between the analytical and experimental responses. The confidence
associated with frequencies and mechanical properties is incorporated into the re
vision procedure. The effects of the confidence associated with experimental and
numerical data and parameter estimates are numerically investigated. The validity
and efficiency of the present procedure is illustrated through several test cases.
1 Introduction
In this work, a numerical-experimental method for the identification of mechanical prop
erties of generally orthotropic plate is described. For this purpose, the experimental
results of the structure response are used. The dynamic free vibration behaviour of a
structure made of anisotropic materials depends on its geometry, density and boundary
conditions. The analytical model of the plate is obtained using Rayleigh-Ritz method
and finite element method. Since the plates discussed are thin the classical Iamination
theory is employed to describe dynamic behaviour. It is assumed that geometry, material
density and angle between edge and fibre direction are known in the identification ap
proach. Generally in order to obtain good esteems of experimental vibration frequencies
the plates are supposed to be with all boundary edges free. Introducing initial values of
material properties into the mathematical model one can obtain analytical eigenvalues
and eigenvectors. Frequently, this model does not initially produce mode shapes and nat
ural frequencies, which concur with test results agree. The present approach is founded
on an error function, which includes the differences between analytical and experimental
frequencies. This error function also considers the deviations of the revised mechanical
properties from their initial values based on some confidence limits. The unknown plate
rigidities are evaluated at every step by an estimator, which is achieved by the minimiza
tion of the error function. The estimator is based on measured values and initial estimates
2 I. Bartoli, A. Di Leo and E. Viola
vibrating
··s·Fiape·· ·· --·-::.--·
X
Figure 1. Orthotropic plate. Material (1, 2) and global (x, y) coordinate axis.
of the mechanical parameters. Sensitivity matrix is the most important operator of the
estimator. Derivatives of the analytical eigenvalues with respect to the various constants
constitute the elements of the matrix. The estimator also contains the uncertainties in
the initial estimates, and those associated with modeHing by two confidence matrices.
2 Numerical model
Figure 1 shows a reetangular plate of constant thickness h and plate dimensions l and b. A
Cartesian coordinate system (x, y, z) is located at the middle plane as shown. () represents
the angle between material fibres and x-axis. The maximumpotential energy expression
for the 2-D Iaminated plate model, including only the bending effects, is (Bartoli, 2001)
(2.1)
where the Dij are the conventional in-plane plate ftexural stiffnesses from classicallam
ination theory (which in turn are related to thein-plane engineering constants E1, E2,
G12 and v12) (Jones, 1975). W (x, y) is the plate deftection amplitude when an harmonic
motion
w (x, y) = W (x, y) eiwt (2.2)
is considered in which w is the frequency of vibration.
The maximum kinetic energy ignoring rotary inertia effects, is given by
(2.3)