Dynamic Methods for damage Detection in Structures

Non-destructive testing aimed at monitoring, structural identification and diagnostics is of strategic importance in many branches of civil and mechanical engineering. This type of tests is widely practiced and directly affects topical issues regarding the design of new buildings and the repair and monitoring of existing ones. The load-bearing capacity of a structure can now be evaluated using well-established mechanical modelling methods aided by computing facilities of great capability. However, to ensure reliable results, models must be calibrated with accurate information on the characteristics of materials and structural components. To this end, non-destructive techniques are a useful tool from several points of view. Particularly, by measuring structural response, they provide guidance on the validation of structural descriptions or of the mathematical models of material behaviour. Diagnostic engineering is a crucial area for the application of non-destructive testing methods. Repeated tests over time can indicate the emergence of possible damage occurring during the structure's lifetime and provide quantitative estimates of the level of residual safety. Of the many non-destructive testing techniques now available, dynamic methods enjoy growing focus among the engineering community. Conventional diagnostic methods, such as those based on visual inspection, thermal or ultrasonic analysis, are local by nature. To be effective these require direct accessibility of the region to be inspected and a good preliminary knowledge of the position of the defective area. Techniques based on the study of the dynamic response of the structure or wave propagation, on the contrary, are a potentially effective diagnostic tool. These can operate on a global scale and do not require a priori information on the damaged area. Recent technological progress has generated extremely accurate and reliable experimental methods, enabling a good estimate of changes in the dynamic behaviour of a structural system caused by possible damage. Although experimental techniques are now well-established, the interpretation of measurements still lags somewhat behind. This particularly concerns identification and structural diagnostics due to their nature of inverse problems. Indeed, in these applications one wishes to determine some mechanical properties of a system on the basis of measurements of its response, in part exchanging the role of the unknowns and data compared to the direct problems of structural analysis. Hence, concerns typical of inverse problems arise, such as high nonlinearity, non-uniqueness or non-continuous dependence of the solution on the data. When identification techniques are applied to the study of real-world structures, additional obstacles arise given the complexity of structural modelling, the inaccuracy of the analytical models used to interpret experiments, measurement errors and incomplete field data. Furthermore, the results of the theoretical mathematical formulation of problems of identification and diagnostics, given the present state-of-knowledge in the field, focus on quality, while practical needs often require more specific and quantitative estimates of quantities to be identified. To overcome these obstacles, standard procedures often do not suffice and an individual approach must be applied to tackle the intrinsic nature of the problem, using specific experimental, theoretical and numerical methods. It is for these reasons that use of damage identification techniques still involves delicate issues that are only now being clarified in international scientific literature. The CISM Course "Dynamic Methods for Damage Detection in Structures" was an opportunity to present an updated state-of-the-art overview. The aim was to tackle both theoretical and experimental aspects of dynamic non-destructive methods, with special emphasis on advanced research in the field today. The opening chapter by Vestroni and Pau describes basic concepts for the dynamic characterization of discrete vibrating systems. Chapter 2, by Friswell, gives an overview of the use of inverse methods in damage detection and location, using measured vibration data. Regularisation techniques to reduce ill-conditioning effects are presented and problems discussed relating to the inverse approach to structural health monitoring, such as modelling errors, environmental effects, damage models and sensor validation. Chapter 3, by Betti, presents a methodology to identify mass, stiffness and damping coefficients of a discrete vibrating system based on the measurement of input/output time histories. Using this approach, structural damage can be assessed by comparing the undamaged and damaged estimates of the physical parameters. Cases of partial/limited instrumentation and the effect of model reduction are also discussed. Chapter 4, by Vestroni, deals with the analysis of structural identification techniques based on parametric models. A numerical code, that implements a variational procedure for the identification of linear finite element models based on modal quantities, is presented and applied for modal updating and damage detection purposes. Pseudo-experimental and experimental cases are solved. Ill-conditioning and other peculiarities of the method are also investigated. Chapter 5, by Vestroni, deals with damage detection in beam structures via natural frequency measurements. Cases of single, multiple and interacting cracks are considered in detail. Attention is particularly focussed on the consequences that certain peculiarities, such as the limited number of unknowns (e.g., locations and stiffness reduction of damaged sections), have on the inverse problem solution. The analysis of damage identification in vibrating beams is continued in Chapter 6 by Morassi. Damage analysis is formulated as a reconstruction problem and it is shown that frequency shifts caused by damage contain information on certain Fourier coefficients of the unknown stiffness variation. The rest of the chapter is devoted to the identification of localized damage in beams from a minimal set of natural frequency measurements. Closed form solutions for certain crack identification problems in vibrating rods and beams are presented. Applications based on changes in the nodes of the mode shapes and on antiresonant data are also discussed. Chapter 7, by Testa, is on the localization of concentrated damage in beam structures based on frequency changes caused by the damage. A second application deals with a crack closure that may develop in fatigue and the potential impact on damage detection. Chapter 8 proposes a paper by Cawley on the use of guided waves for long-range inspection and the integrity assessment of pipes. The aim is to determine the reflection coefficients from cracks and notches of varying depth, circumferential and axial extent when the fundamental torsional mode is travelling in the pipe. Chapter 9, by Vestroni and Vidoli, discusses a technique to enhance sensitivity of the dynamic response to local variations of the mechanical characteristics of a vibrating system based on coupling with an auxiliary system. An application to a beam-like structure coupled to a network of piezoelectric patches is discussed in detail to illustrate the approach