NONLINEARITY IN         STRUCTURAL DYNAMICS         Detection, Identification and Modelling         K Worden and G R Tomlin...
­ IOP Publishing Ltd 2001         c         All rights reserved. No part of this publication may be reproduced, stored    ...
For Heather and MargaretCopyright © 2001 IOP Publishing Ltd
‘As you set out for Ithaka              hope your road is a long one,              full of adventure, full of discovery.  ...
Contents             Preface                                                           xv         1   Linear systems      ...
viii           Contents                      2.4.2 Vibration exciter problems                                 59          ...
Contents          ix         4   The Hilbert transform—a practical approach                          127             4.1 I...
x            Contents                    6.3.2 Parameter uncertainty                       235                    6.3.3 St...
Contents          xi             7.6   System identification using optimization                           355              ...
xii           Contents                     9.3.2 Frequency-domain characteristics of the bilinear beam   518              ...
Contents   xiii                   F.5.2 Convergence to solutions                           586                   F.5.3 Uni...
Preface         Nonlinearity is a frequent visitor to engineering structures which can modify—         sometimes catastrop...
apparently random response. In contrast, a linear system always responds to a         periodic excitation with a periodic ...
the fundamental measured quantities like the impulse response function              (IRF) and the frequency response funct...
complete description in this book of the effects of measurement noise and              the need for rigorous model validit...
A book like this does not spring into being without a lot of help from a         lot of people. It is a pleasure to thank ...
Chapter 1         Linear systems         This chapter is provided more or less as a reminder of linear system theory. It i...
2             Linear systems                                          k                             Free body diagram of t...
Continuous-time models: time domain                 3              The solution of (1.7) is elementary and is given in any...
4           Linear systems         of motion. Such a system is said to have three degrees-of-freedom and would         be ...
Continuous-time models: time domain                            5                    y(t)                                  ...
6           Linear systems                   y(t)                                                                         ...
Continuous-time models: time domain                       7         response of the solution.               For linear sys...
8           Linear systems                       Figure 1.5. SDOF system gain as a function of frequency .               T...
Continuous-time models: time domain               9                         φ(ω)                             π            ...
10              Linear systems         Bode plot of an actual SDOF system,                                               Ý...
Continuous-time models: frequency domain                          11         the equation, i.e.                     ·½    ...
12          Linear systems                Figure 1.8. Nyquist plot for system Ý · ¾¼Ý · ½¼   Ý   ܴص—receptance.         ...
Impulse response             13                 Figure 1.9. Nyquist plot for system Ý · ¾¼Ý · ½¼   Ý   ܴص—mobility.     ...
14           Linear systems               Figure 1.10. Nyquist plot for system Ý · ¾¼Ý · ½¼       Ý     ܴص—accelerance. ...
Impulse response              15                                                  x(t)                                  ε ...
16             Linear systems                 Now, according to equation (1.45), the system response to a Æ -function inpu...
Discrete-time models: time domain                              17         more rigorous approach to evaluating ´Øµ is simp...
18             Linear systems         representation defines the motion at all times. In reality, most observations of     ...
Discrete-time models: time domain        19         Ü  together with values for Ý ½ and ݾ . The specification of the first ...
20          Linear systems               By way of illustration, consider the SDOF system (1.30) again.         Equation (...
Classification of difference equations         21         One point about these equations is worth noting. The expressions ...
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72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy
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72268096 non-linearity-in-structural-dynamics-detection-identification-and-modelling-copy

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