Annamaria Pau

Numerical and experimental detection of concentrated damage in a parabolic arch by measured frequency variations

The dynamics of a parabolic arch is studied in its undamaged and damaged states. The damage consists of a notch that reduces the height of the cross section at a given abscissa. A damage identification technique, based on the minimization of an objective function measuring the differences between numerical and experimental variations of natural frequencies for undamaged and damaged states, is used. The uniqueness of the solution in different damage configurations is investigated using pseudo-experimental data and the reliability of the identification procedure is assessed. The identification procedure is then applied to an experimental case, where frequencies are obtained by impulsive tests on a prototype arch. The minimum number of experimental data needed to identify damage parameters is defined and the sensitivity of the identification algorithm to different possible choices of sets of data is analyzed.

Nonlinear guided wave propagation in prestressed plates

The measurement of stress in a structure presents considerable interest in many fields of engineering. In this paper, the diagnostic potential of nonlinear elastic guided waves in a prestressed plate is investigated. To do so, an analytical model is formulated accounting for different aspects involved in the phenomenon. The fact that the initial strains can be finite is considered using the Green Lagrange strain tensor, and initial and final configurations are not merged, as it would be assumed in the infinitesimal strain theory. Moreover, an appropriate third-order expression of the strain energy of the hyperelastic body is adopted to account for the material nonlinearities. The model obtained enables to investigate both the linearized case, which gives the variation of phase and group velocity as a function of the initial stress, and the nonlinear case, involving second-harmonic generation as a function of the initial state of stress. The analysis is limited to Rayleigh-Lamb waves propagating in a plate. Three cases of initial prestress are considered, including prestress in the direction of the wave propagation, prestress orthogonal to the direction of wave propagation, and plane isotropic stress.

Wave propagation in one-dimensional waveguides for damage characterization

The waveguide geometry of numerous structures used in civil and mechanical engineering can be exploited for the use of guided waves in damage detection. The present study examines the response of a bar to an impulsive force along its axis and points out the differences in the damaged bar. Relationships between the damage parameters and the amplitude and time-delay of the reflected and transmitted waves are exploited to formulate a damage characterization procedure. This procedure is analytically and experimentally tested in different damage configurations. The results are compared to those obtained from conventional methods based on frequency variations.

Reciprocity principle for scattered fields from discontinuities in waveguides.

This study investigates the scattering of guided waves from a discontinuity exploiting the principle of reciprocity in elastodynamics, written in a form that applies to waveguides. The coefficients of reflection and transmission for an arbitrary mode can be derived as long as the principle of reciprocity is satisfied at the discontinuity. Two elastodynamic states are related by the reciprocity. One is the response of the waveguide in the presence of the discontinuity, with the scattered fields expressed as a superposition of wave modes. The other state is the response of the waveguide in the absence of the discontinuity oscillating according to an arbitrary mode. The semi-analytical finite element method is applied to derive the needed dispersion relation and wave mode shapes. An application to a solid cylinder with a symmetric double change of cross-section is presented. This model is assumed to be representative of a damaged rod. The coefficients of reflection and transmission of longitudinal waves are investigated for selected values of notch length and varying depth.

Dynamic Characterization and Damage Identification

This chapter presents selected cases of modal parameter evaluation and damage identification, privileging the applied aspects. The identification of modal parameters is discussed through three experimental cases of masonry structures: a civil building, a monumental structure and a nineteenth century railway bridge. Modal parameters are response quantities that are sensitive to damage, whose variation with respect to an undamaged state can be exploited in view of damage detection and identification. Moreover, the variations of modal quantities can be used for updating the structural model, leading to the best estimate of model mechanical parameters in the undamaged and damaged conditions. This provides information on the damage location and severity. The technique of damage identification based on model updating is applied to laboratory experimental tests on a steel arch.

Elements of Experimental Modal Analysis

Fundamental concepts for the characterization of the dynamical response of SDOF and NDOF systems are provided. A description is given of the main techniques to represent the response in the frequency domain and its experimental characterization. Two classical procedures of modal parameter identification are outlined and selected numerical and experimental examples are reported.

Modal Analysis of a Beam with Radiation Damping: Numerical and Experimental Results

In large structures, the excitation energy produced by an impact force may not be sufficient to spread throughout the structure and excite global modes. Thus, one may be interested in the dynamic characterization of the excited part of the structure by taking into consideration the wave propagation through its boundaries. This radiation damping is a source of local damping and, as a consequence, causes modal complexity. The spectral element method is adopted here to describe the modal characteristics of a system with radiation damping. A semi-infinite Euler-Bernoulli beam, whose span is interrupted by a spring with translational and rotational stiffness, is used as an example to illustrate the main features of the phenomenon characterized by modal complexity and to obtain a simple but meaningful experimental confirmation. This method could be useful in the modal characterization of a part of a structure.

Health Monitoring of Cultural Heritage Using Ambient and Forced Vibrations

The main results of a campaign of experimental dynamic tests involving three important monuments of Rome, the Colosseum, the Traian Column and the Aurelian Walls are presented in this paper. The structural dynamic response due to ambient excitation and to impact force tests was investigated. The damage risk because of the vibrations induced by road and railway traffic was assessed according to international standards. Natural frequencies and mode shapes were determined and compared to numerical ones, which were obtained by a finite element model. Measuring the evolution of these quantities, which are representative of the structural conditions, allows for health monitoring of monuments.

Interaction of Shear and Rayleigh–Lamb Waves with Notches and Voids in Plate Waveguides

This paper investigates the interaction of different shear- and Rayleigh–Lamb-guided waves in plates with a discontinuity such as a notch or an internal void. The problem was solved numerically using a finite element model and by exploiting an analytical solution obtainable for the double sharp changes of the cross-section that served as a reference. We aimed to elucidate the relation between the size and shape of the discontinuity and the reflection and transmission coefficients of the scattered field. Different sizes and profiles of the discontinuity were considered, with the shapes ranging from step changes of the height to ellipses, both symmetric and nonsymmetric. Regimes related to low and high values of the product frequency multiplied by the height of the plate were investigated. These showed how the mode conversion was related to the symmetry between the incident mode and the discontinuity, and to the actual existence of multiple propagating modes. The analysis presented was motivated by the need to set up procedures that exploit propagating waves not only to detect the presence of a notch, but also to characterize its size and shape.

DAMAGE CHARACTERIZATION IN WAVEGUIDES WITH ULTRASONIC SHEAR WAVES

Damage can be viewed as a continuum discontinuity. In order to identify and quantify damage, the present study investigates the dependence of reflection and transmission coefficients from a discontinuity in a waveguide using a finite element model. A parametric study of a fiber reinforced polymer laminate beam is presented with five different ratios of reduced cross-section with two different kinds of geometry: symmetric and asymmetric, in three discontinuity lengths. What is more, finite element results are compared with the corresponding results of a semianalytical model based on the principle of reciprocity in elastodynamics. The analysis shows that: a) depending on the kind of discontinuity, the diagnostic potential of the used guided wave depends on the mode existence and on the magnitude of its wavelength in relation to the discontinuity extension, b) reflection and transmission coefficients can be used to identify and characterize damage both in symmetrical and asymmetrical damaged cross sections.