smart technologies for safety engineering

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(a) (b) (c) Figure 3.27 (a) Screw connection, (b) actuator, (c) sensors (a) (b) actuator sensor strain amplifier conditioning amplifier 0.05 0.025 activation line detection line function generator oscilloscope computer P(t) Figure 3.28 (a) Measuring system, (b) excitation signal 0 –0.025 Table 3.3 Comparison of eigenfrequencies obtained in the experiment and numerical analysis Eigenfrequency Experimental Numerical 1 5.00 5.05 2 29.70 29.36 3 70.60 73.27 4 140.00 129.05 5 199.00 199.30 0 0.04 intact, experimental intact, VDM damaged, experimental damaged, VDM time [s] 0.08 0.12 Figure 3.29 Numerical versus experimental results for the cantilever beam t
62 Smart Technologies for Safety Engineering 3.3.3 Identification of Delamination 3.3.3.1 Formulation of an Off-Line Problem Depending upon the application, the important problem of defect identification can be handled in an off-line (post factum) or on-line (real-time) procedure. This section is devoted to the problem of off-line identification of delamination by employing VDM-based gradient optimization. Within the framework of VDM, an analytical sensitivity analysis can be effectively performed. Therefore the inverse problem of identification can be solved using classical optimization tools, i.e. gradients of the objective function with respect to a design variable. Usually, frequencies and mode shapes obtained via modal analysis enter the objective function in the inverse problem of identification. In the presented approach, strains have been chosen for the purpose. The reason is that on the one hand strains can be easily modeled in the VDM (cf. Equation (8) in Chapter 2) and on the other they can be measured by piezoelectric sensors. One more advantage is that the variation of strains in dynamics is relatively smooth (compared to accelerations for instance), which is convenient from the signal processing point of view. Thus, the identification task is posed as a standard nonlinear least squares minimization problem, with the objective function expressed as follows: F(μ) = ε beam k − εbeamM k ε beamM k The function (33) collects responses from selected k sensors placed in beam elements, where flexural strains are measured. Note that the measurements are taken in horizontal beam elements (see Figures 3.14 and 3.16), whereas modifications to the structure are introduced only in truss elements A, B, C of the contact layer. This is an important distinction, which implies building an extended influence matrix Dext kj , collecting not just the interrelations within the contact layer but also the influence of the truss members on the connected beam members. The axial strain εi in truss elements (of type A, B or C) depends nonlinearly upon the modification coefficient μi (see Equation (17) in Chapter 2), which is further used as a variable in optimization. Natural constraints are imposed on the modification coefficient μi, which is nonnegative by definition: 2 (33) μi ≥ 0 (34) If delamination has been identified, the constraints (34) are active. Another formal constraint has to be imposed on μi, related to structural degradation: μi ≤ 1 (35) Using Equation (8) in Chapter 2 and building the extended influence matrix, the gradient of the objective function (33) with respect to the optimization variable μi is expressed as ∂ F ∇ Fi = = ∂μi ∂ F ∂ε beam k ∂ε beam k ∂ε 0 j ∂ε 0 j ∂μi = 2 (εbeamM k ) 2 ε beam k ∂ε 0 j ext − εbeamM k D kj ∂μi (36)
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SMART TECHNOLOGIES FOR SAFETY ENGIN
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Copyright C○ 2008 John Wiley & So
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vi Contents 2.7 Versatility of VDM
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viii Contents 6 VDM-Based Remodelin
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Preface The contents of this book c
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xiv About the Authors The team of s
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Organization of the Book The book h
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1 Introduction to Smart Technologie
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Introduction to Smart Technologies
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Page 24 and 25: Introduction to Smart Technologies
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5 Adaptive Impact Absorption Piotr
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Adaptive Impact Absorption 163 Figu
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Adaptive Impact Absorption 171 of t
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Adaptive Impact Absorption 177 of t
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Adaptive Impact Absorption 179 F VD
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Adaptive Impact Absorption 181 forc
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Adaptive Impact Absorption 183 Tabl
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Adaptive Impact Absorption 185 Curr
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Adaptive Impact Absorption 187 (a)
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Adaptive Impact Absorption 189 Vect
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Adaptive Impact Absorption 191 wher
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Adaptive Impact Absorption 193 (a)
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Adaptive Impact Absorption 195 time
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Adaptive Impact Absorption 199 towe
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Adaptive Impact Absorption 201 Tabl
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Adaptive Impact Absorption 205 5.6.
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Adaptive Impact Absorption 207 Unkn
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Adaptive Impact Absorption 209 Figu
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7 Adaptive Damping of Vibration by
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Adaptive Damping of Vibration 253 x
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Adaptive Damping of Vibration 255 t
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Adaptive Damping of Vibration 257 K
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Adaptive Damping of Vibration 259 M
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Adaptive Damping of Vibration 261 w
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Adaptive Damping of Vibration 263 1
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Acknowledgements Parts of Section
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Acknowledgements 325 Parts of Chap
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328 Index Control strategy (Continu
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330 Index Modification coefficient
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332 Index System analogies, 29, 68,
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