|
xvii
Chapter
q
CONCLUSIONS
8.1
IDENTIFICATION OF STRUCTURAL NONLINEARITY ...................... 5
0
8.2 LOCATION OF STRUCTURAL NONLINEARITY ............................... 2 5 2
8.3
............
8.4 SUGGESTION FOR FURTHER STUDIES ......................................... 2 5 5
APPENDICES
Appendix I: Singular Value Decomposition (SVD) ................................... 257
Appendix II: Derivation of Eigenderivatives ........................................... 261
REFERENCES
CHAPTER
INTRODUCTION
1.1 GENERAL INTRODUCTION
In current engineering practice, the emphasis placed on safety, performance and reliability
of structural systems is becoming more and more demanding due to the continuous
challenges from real life. For example, any design inadequacy in an aircraft might lead to
huge loss of human life. In order to design a structural system which, after being
manufactured, will satisfy the prescribed safety performance and reliability criteria, it is
essential that dynamic analysis be carried out at the design stage as well as at the
prototype stage and, subsequently, a mathematical model which can accurately represent
the dynamic characteristics of the structure be established. Such a mathematical model is
needed for response and load prediction, stress and stability analysis, structural
modification and optimisation etc.
For simple structural components, such as uniform beams and plates, mathematical
models (and analytical solutions) which accurately describe their dynamic characteristics
are readily available. However, due to the complexity of most engineering structures,
analytical solutions are often impossible to obtain (if they exist at all) and numerical
approximations have to be pursued. In structural mechanics, the most commonly
employed numerical method is the so-called Finite Element Analysis
method. In
Introduction
2
FEA, a continuous structure is discretised into many ‘small’ elements (the size of the
element depends on the analysis accuracy required) called ‘finite elements’ and then,
based on the theory of dynamics (e.g., Newton’s law, Lagrange equation) and mechanics
of deformable bodies (e.g., stress-displacement equations, stress-strain relations), a
mathematical model of the structure is derived. This is often referred as the ‘analytical
model’ as compared with the ‘experimental model’ which is derived from dynamic
testing. Once a mathematical model (spatial model in terms of mass, stiffness and
possibly damping matrices of the structure) has been formulated, the next step of the
analysis is to solve the differential equations to obtain the dynamic response. However,
due to the approximations and idealisation involved, lack of knowledge about the
structure and even sometimes mismodelling of structural joints and boundary conditions,
it is inevitable that the mathematical model thus established will not always adequately
represent the actual behaviour of the real structure.
Apart from the analytical approach to achieve a mathematical model for the study of
vibration characteristics of a dynamic system, another major approach is to establish an
experimental model for the system by performing a vibration test and subsequent analysis
on the measured data. This process, including the data acquisition and the subsequent
analysis, is now known as ‘Modal Testing’. The theoretical basis and practical
applications of modal testing have been discussed in detail in
The most significant
application of modal testing is perhaps to compare and eventually to validate an analytical
model using measured vibration test data. Apart from this, mathematical models derived
from measured data (referred to as ‘experimental models’ which can be in the form of
response, modal or spatial models) are frequently used in structural modification analysis,
structural coupling, force determination etc. It is usually believed that provided sufficient
care is given to the experimental procedures, the results from measurement are those that
should be regarded as the most correct.
In
a
typical engineering design process, both analytical prediction and experimental modal
testing procedures are involved in an iterative way. They have complementary roles for
the complete description and understanding of the dynamic behaviour of a structure and
one cannot be substituted for the other. In the present work, we shall be dealing mainly
with the experimental side of the problem of evaluating the dynamic characteristics of
mechanical structures (mainly nonlinear structures), although analytical models are often
needed and are assumed to be available in the studies of location of structural
nonlinearities and mathematical modelling of nonlinear structures.
Introduction
3
Do'stlaringiz bilan baham: |
