A time-domain model-based crack diagnostic methodology using vibration data is presented. Most of the damage detection methods proposed to date are based on modal parameters and are limited by the loss of information caused by data reduction and by the implicit assumption of linearity. The use of time domain information permits the direct inclusion of the nonlinear behavior due to crack opening-closure cycles. In addition, very little information is lost, since no signal processing or parameter identification steps are involved. The proposed method is based on a continuous model for the transverse vibrations of beams consisting of partial differential equations of motion with varying coefficients to account for the presence of damage. In order to provide accurate representation of the structure's behavior over a broader frequency range, a new continuous cracked beam model including shear effects and rotatory inertia is developed using the Hu-Washizu-Barr variational method. The resulting equations of motion are discretized by a Galerkin method using local B-splines as test functions. The crack is assumed to be either fully open or fully closed, resulting in a bilinear system. The simultaneous identification of crack location and depth is performed by minimizing the norm of the differences between the numerical and experimental time responses to multiple excitations. Impact, low frequency sinusoidal and Schroeder--phased multisine inputs are investigated as potential excitation methods. The cost function to be minimized presents several local minima that are shown to be related to the length of the response records. A genetic algorithm is used to overcome the multimodal nature of the objective function. The methodology is validated through simulated identifications of several damage scenarios. The importance of the inclusion of the nonlinear behavior is addressed, and the effects of model uncertainties and measurement noise are quantified in terms of minimum identifiable crack size. / Ph. D.

Establishing dynamic characteristics of structures is a challenging area of research. The dynamic characteristics of structures, such as natural frequencies, modeshapes, response levels and damping characteristics play an important role in identifying the condition of the structures. The assumed modes method is a particular analytical method used to estimate the dynamic characteristics of a structure. However, the eigenfunctions used in the assumed mode method often led to ill-conditioning due to the presence of hyperbolic functions. Furthermore, a change in the boundary conditions of the system usually necessitates a change in the choice of assumed mode. In this thesis, a set of Alternative Admissible Functions (AAF), along with penalty functions, are used to obtain closed form solutions for an Euler-Bernoulli beam with various boundary conditions. A key advantage of the proposed approach is that the choice of AAF does not depend on the boundary conditions since the boundary conditions are modelled via penalty functions. The mathematical formulation is validated with different boundary conditions, Clamped-Free (CF), Simply-Supported (SS), and Clamped-Clamped (CC). A specific relation between the penalty function and the system parameters are established for CF, SS and CC boundary conditions to obtain appropriate values of penalties. Validation of results with the reported literature indicates excellent agreement when compared with closed-form Euler-Bernoulli beam values. The AAF approach with penalties is extended to a beam with a shallow crack to estimate the dynamic characteristics. The crack is modelled as a penalty function via a massless rotational spring. This model has the advantage of simplifying parametric studies, because of its discrete nature, allowing easy modification in the crack position and depth of the crack. Therefore, once the model is established, various practical applications may be performed without reformulation of the problem. Validation of results with the reported literature on beams with shallow cracks indicates the suitability of the proposed approach.

The thesis presents a novel computational method for analysing the static and dynamic behaviour of a multi-damaged beam using local and non-local elasticity theories. Most of the lumped damage beam models proposed to date are based on slender beam theory in classical (local) elasticity and are limited by inaccuracies caused by the implicit assumption of the Euler-Bernoulli beam model and by the spring model itself, which simplifies the real beam behaviour around the crack. In addition, size effects and material heterogeneity cannot be taken into account using the classical elasticity theory due to the absence of any microstructural parameter. The proposed work is based on the inhomogeneous Euler-Bernoulli beam theory in which a Dirac's delta function is added to the bending flexibility at the position of each crack: that is, the severer the damage, the larger is the resulting impulsive term. The crack is assumed to be always open, resulting in a linear system (i.e. nonlinear phenomena associated with breathing cracks are not considered). In order to provide an accurate representation of the structure's behaviour, a new multi-cracked beam element including shear effects and rotatory inertia is developed using the flexibility approach for the concentrated damage. The resulting stiffness matrix and load vector terms are evaluated by the unit-displacement method, employing the closed-form solutions for the multi-cracked beam problem. The same deformed shapes are used to derive the consistent mass matrix, also including the rotatory inertia terms. The two-node multi-damaged beam model has been validated through comparison of the results of static and dynamic analyses for two numerical examples against those provided by a commercial finite element code. The proposed model is shown to improve the computational efficiency as well as the accuracy, thanks to the inclusion of both shear deformations and rotatory inertia. The inaccuracy of the spring model, where for example for a rotational spring a finite jump appears on the rotations' profile, has been tackled by the enrichment of the elastic constitutive law with higher order stress and strain gradients. In particular, a new phenomenological approach based upon a convenient form of non-local elasticity beam theory has been presented. This hybrid non-local beam model is able to take into account the distortion on the stress/strain field around the crack as well as to include the microstructure of the material, without introducing any additional crack related parameters. The Laplace's transform method applied to the differential equation of the problem allowed deriving the static closed-form solution for the multi-cracked Euler-Bernoulli beams with hybrid non-local elasticity. The dynamic analysis has been performed using a new computational meshless method, where the equation of motions are discretised by a Galerkin-type approximation, with convenient shape functions able to ensure the same grade of approximation as the beam element for the classical elasticity. The importance of the inclusion of microstructural parameters is addressed and their effects are quantified also in comparison with those obtained using the classical elasticity theory.