José Viriato Araújo dos Santos | Instituto Superior Técnico (original) (raw)

Papers by José Viriato Araújo dos Santos

Research paper thumbnail of On the use of finite differences for vibration-based damage localization in laminated composite plates

Purpose-Laminated composite materials are a staple of modern material development, with extremely... more Purpose-Laminated composite materials are a staple of modern material development, with extremely strong fibers being combined with resins to form versatile and efficient engineering structures. However, the advancements in material development must be accompanied by equally advanced methods for damage detection, localization and quantification, as these materials develop inherently unique failure modes. This paper aims to further the study of the use of modal shapes and their spatial derivatives to localize damage in laminated composite rectangular plates. Exploring different damage scenarios and models, as well as different orders of mode shape derivatives of laminated plates.

Design/methodology/approach-ANSYS® Parametric Design Language (APDL) is used to perform finite element analysis of plates with several damage scenarios and damage mechanics models. MATLAB® is used to post-process these simulation results, namely by calculating the derivatives using finite differences, applying three distinct sets of damage indices, including one that is presently proposed. To mimic experimental conditions and test the resilience of the derivative orders, different noise levels are introduced into the results of the finite element analysis. A quality index is employed to quantitatively evaluate the solutions, mainly regarding the response to the introduced noise.

Findings-The results show that the applied damage localization methods have comparable results in terms of quality. These results also show that the quality of the damage localizations is higher when the damaged areas coincide with high displacement/curvature areas of the mode shapes and that higher noise levels have a more noticeable negative impact when employing higher-order derivatives.

Originality/value-Exploring different damage scenarios and models, as well as different orders of mode shape derivatives of laminated plates. The influence of a specific damage layer on the order of derivatives of modal response is evaluated, showing promising results concerning its identification.

Research paper thumbnail of Damage Identification in Beams by Post-processing Modal Displacements and Rotations with Haar Wavelet

Lecture Notes in Civil Engineering, 2021

A study on the post-processing of modal displacements and modal rotations with the Haar wavelet i... more A study on the post-processing of modal displacements and modal rotations with the Haar wavelet is presented in this paper. A free-free aluminum beam is chosen as a structure to be analyzed and its modal displacements and rotations in both undamaged and multiple damagedstates are computed with the finite element method. Three sets of damageindicators are proposed: (1) wavelet transform of damaged modal displacements or modalrotations, (2) wavelet transform of differences in modal displacements or modal rotations, and (3) ratio of wavelet transform of differences in modal displacements or modal rotations to wavelet transform of undamaged modal displacements or modal rotations. The study shows that post-processing modal displacements with the Haar wavelet leads to poor damageidentifications. On the other hand, if one applies the same type of wavelet to modalrotations, the damage indicators (2) and (3) clearly pinpoints the location of the damage. Although the set of damage indicators (1) and (2) are prone to the boundary effect, where high values of wavelets coefficients are present, the third set of damageindicators does not present this problem. Furthermore, for large values of damage, this damage indicators shows the presence of damagein all scales of the wavelet scalogram. The present study clearly shows that by post-processing modalrotations with the simplest wavelet one can obtain reliable identifications of multiple damage.

Research paper thumbnail of Improvement on modal curvatures methods for multiple damage identification in beams

Multidiscipline Modeling in Materials and Structures, 2021

PurposeThe purpose of this paper is to present a study on the application of four damage factors ... more PurposeThe purpose of this paper is to present a study on the application of four damage factors to several single and multiple damage scenarios of aluminium beams. Each one of these damage factors is defined by the information given by modal curvatures of the beams.Design/methodology/approachThe methodology consisted of a first experimental stage in which the modal rotations were measured with shearography and a subsequent numerical analysis in order to obtain the modal curvatures. To this end, three finite difference formulae were applied. The modal curvatures were then used to calculate the damage factors.FindingsIt was found that the profile of the damage factors varies according to the finite difference formula used. In view of the findings, the differences among the damage factors analysed are highlighted and some final recommendations to improve damage identifications via modal curvature-based are presented.Originality/valueTo the best of the authors’ knowledge, the applicati...

Research paper thumbnail of Application of spline interpolation to speckle shearography measurements for damage identification

Procedia Structural Integrity, 2019

This paper aims to explore a new technique for structural damage identification using cubic splin... more This paper aims to explore a new technique for structural damage identification using cubic spline interpolation. The method is based on the interpolation of modal rotations measured with speckle shearography. In order to locate the damaged areas, we make use of the analytical derivative of the cubic spline function to compute the modal curvature, which is known to be very sensitive to damage. A comprehensive parametric study of the spatial sampling interval is carried out to find its influence on noise filtering. Furthermore, the identification quality dependency on the mode shape and respective noise is also examined. The results obtained with the proposed method show the consistency of the localizations. Additionally, the challenging tasks of identifying small and multiple damage are tackled, yielding a good performance.

Research paper thumbnail of Identification of multiple damage using modal rotation obtained with shearography and undecimated wavelet transform

Mechanical Systems and Signal Processing, 2019

Due to its high spatial resolution measurements and flexible and contactless experimental setup, ... more Due to its high spatial resolution measurements and flexible and contactless experimental setup, shearography, as a non-destructive testing technique, provides effective structural damage identifications. However, this effectiveness can be increased by applying postprocessing algorithms to experimentally measured modal rotation fields. In this paper, the authors present a novel method, consisting of shearographic non-destructive testing and 2D undecimated wavelet transform as a post-processing tool. The studies covered tests of the proposed method on simulated modal data of a damaged plate, as well as a validation on real data obtained from shearographic experiments. The results show the high sensitivity of the proposed method to either single or multiple damage, including its edges and its various configurations.

Research paper thumbnail of A Review and Study on Ritz Method Admissible Functions with Emphasis on Buckling and Free Vibration of Isotropic and Anisotropic Beams and Plates

Archives of Computational Methods in Engineering, 2017

Research paper thumbnail of Numerical study on damage identification using shearography with different shearing amounts

Procedia Structural Integrity, 2017

During their operation, modern aircraft engine components are subjected to increasingly demanding... more During their operation, modern aircraft engine components are subjected to increasingly demanding operating conditions, especially the high pressure turbine (HPT) blades. Such conditions cause these parts to undergo different types of time-dependent degradation, one of which is creep. A model using the finite element method (FEM) was developed, in order to be able to predict the creep behaviour of HPT blades. Flight data records (FDR) for a specific aircraft, provided by a commercial aviation company, were used to obtain thermal and mechanical data for three different flight cycles. In order to create the 3D model needed for the FEM analysis, a HPT blade scrap was scanned, and its chemical composition and material properties were obtained. The data that was gathered was fed into the FEM model and different simulations were run, first with a simplified 3D rectangular block shape, in order to better establish the model, and then with the real 3D mesh obtained from the blade scrap. The overall expected behaviour in terms of displacement was observed, in particular at the trailing edge of the blade. Therefore such a model can be useful in the goal of predicting turbine blade life, given a set of FDR data.

Research paper thumbnail of Influence of shearing amount and vibration amplitude on noise in shearography

Procedia Structural Integrity, 2017

During their operation, modern aircraft engine components are subjected to increasingly demanding... more During their operation, modern aircraft engine components are subjected to increasingly demanding operating conditions, especially the high pressure turbine (HPT) blades. Such conditions cause these parts to undergo different types of time-dependent degradation, one of which is creep. A model using the finite element method (FEM) was developed, in order to be able to predict the creep behaviour of HPT blades. Flight data records (FDR) for a specific aircraft, provided by a commercial aviation company, were used to obtain thermal and mechanical data for three different flight cycles. In order to create the 3D model needed for the FEM analysis, a HPT blade scrap was scanned, and its chemical composition and material properties were obtained. The data that was gathered was fed into the FEM model and different simulations were run, first with a simplified 3D rectangular block shape, in order to better establish the model, and then with the real 3D mesh obtained from the blade scrap. The overall expected behaviour in terms of displacement was observed, in particular at the trailing edge of the blade. Therefore such a model can be useful in the goal of predicting turbine blade life, given a set of FDR data.

Research paper thumbnail of A damage localisation method based on higher order spatial derivatives of displacement and rotation fields

Journal of Physics: Conference Series, 2011

ABSTRACT This paper presents the development of a damage localisation method based on low and hig... more ABSTRACT This paper presents the development of a damage localisation method based on low and higher order spatial derivatives of displacement and rotation fields. The method relies on the Timoshenko beam theory, the Hamilton's principle and the Ritz method, allowing the computation of an approximate analytical solution of natural frequencies, displacement and rotation fields. Since these fields are expressed analytically, through a series expansion, the spatial derivatives are also obtained analytically. Besides the usual curvature difference and damage index, which are based on comparisons of second order spatial derivative of the displacement field of a beam in the undamaged and damaged states, other damage indicators are proposed. These new indicators rely on spatial derivatives of rotation fields. The indicators are applied to the localisation of various cases of damages in beams and a comparison among them is carried out. It is found that, for relatively thick beams, the values of the indicators based on rotation fields spatial derivatives are, in general, lower than those based on displacement fields. It is also observed that these differences are negligible for beams with high length to thickness ratio.

Research paper thumbnail of A new technique to optimize the use of mode shape derivatives to localize damage in laminated composite plates

Composite Structures, 2014

Damage localization in laminated composite structures is a very active area of research due to th... more Damage localization in laminated composite structures is a very active area of research due to the role that these kind of structures play in the transport industries. The mode shape derivatives, like rotations (first derivative), curvatures (second derivative) and, more recently, third and four derivatives, have been used to localize damage in composite plates. The most used method to compute these derivatives is the application of finite differences. However, finite differences present several well-known problems, such as the error propagation and amplification. The magnitude of the error associated with the computed derivative is not easy to estimate, mainly because the numerical error associated with finite differences depends on the values of derivatives of higher order than the order of the derivative that one wants to compute. A new technique based on the Ritz method to estimate this error is proposed in this paper. The optimal spatial sampling for the numerical differentiation of the mode shapes are defined based on the minimization of the total error. The good performance of the optimal sampling is shown by applying it to the damage localization in a laminated composite plate.

Research paper thumbnail of Free Vibration and Buckling Analysis of Beams with a Modified Couple-Stress Theory

International Journal of Applied Mechanics, 2012

A model based on a modified couple stress theory for the free vibration and buckling analyses of ... more A model based on a modified couple stress theory for the free vibration and buckling analyses of beams is presented. The model also incorporates the Poisson's effect and allows the analysis of Timoshenko beams with any arbitrary end boundary condition. The natural frequencies and buckling loads are computed using the Ritz method. Parametric studies show that, while the natural frequencies and the buckling loads increase monotonically with the increase of the material length scale, they present a minimum in certain values of the Poisson's ratio. A study relating the classical elasticity and the couple stress strain energies is also presented. By establishing this relation, explicit formulas to obtain the natural frequencies and buckling loads, in which the couple stress and Poisson's effects are accounted for, in terms of the buckling loads of the classical elasticity are found. These formulas, which are valid when the shear strain and stress are zero, allow an expedite c...

Research paper thumbnail of Nonlocal material properties of single-walled carbon nanotubes

International Journal of Smart and Nano Materials, 2012

Natural frequencies of single-walled carbon nanotubes (SWCNTs) obtained using a model based on Er... more Natural frequencies of single-walled carbon nanotubes (SWCNTs) obtained using a model based on Eringen's nonlocal continuum mechanics and the Timoshenko beam theory are compared with those obtained by molecular dynamics simulations. The goal was to determine the values of the material constant, considered here as a nonlocal property, as a function of the length and the diameter of SWCNTs. The present approach has the advantage of eliminating the SWCNT thickness from the computations. A sensitivity analysis of natural frequencies to changes in the nonlocal material constant is also carried out and it shows that the influence of the nonlocal effects decreases with an increase in the SWCNT dimensions. The matching of natural frequencies shows that the nonlocal material constant varies with the natural frequency and the SWCNT length and diameter.

Research paper thumbnail of Damage Localisation in Beams using the Ritz Method and Speckle Shear Interferometry

Proceedings of the Tenth International Conference on Computational Structures Technology

A novel numerical-experimental technique is developed in order to minimise some of the difficulti... more A novel numerical-experimental technique is developed in order to minimise some of the difficulties exhibited by others damage localisation approaches. The present technique relies on the computation of undamaged rotation fields using the Ritz method and the Timoshenko beam theory, while the measurement of damaged rotation fields is performed by speckle shear interferometry. Two damage localisation indicators are also presented, which, instead of being based on the second derivative of displacement fields, are based on the first spatial derivative of rotation fields. These damage localisation indicators, the modified curvature difference (MCD) and the modified damage index (MDI), were applied successfully in the localisation of damage in two clamped-clamped aluminium beams.

Research paper thumbnail of Efficiency assessment of wavelet transforms and wavelets for damage localization in beams using shearography

Diagnostyka

Non-destructive testing of engineering structures and elements in operation is one of the crucial... more Non-destructive testing of engineering structures and elements in operation is one of the crucial steps in recently introduced design philosophies: damage tolerance and condition-based maintenance. Therefore, it is important to provide effective non-destructive testing methods, which are able to detect and identify a possible damage in early stage of its development. One effective testing method, which still gains its popularity in various industrial applications, is shearography. Although, shearography is sensitive to various types of structural damage and flaws, this sensitivity can be significantly improved by applying advanced post-processing algorithms to raw data obtained from measurements. An excellent candidate for such an improvement is the wavelet analysis, due to its very high sensitivity to smallest signal disturbances. This study presents results of comparative analysis of various wavelet transforms and various wavelets in order to analyse their sensitivity to damage. The improvement in damage detectability is verified using experimental data.

Research paper thumbnail of Damage identification by wavelet analysis of modal rotation differences

In this paper, a novel damage identification approach based on differences in modal rotation fiel... more In this paper, a novel damage identification approach based on differences in modal rotation fields obtained from shearographic measurements of structures and post-processed with the 2D continuous wavelet transform-based algorithm is presented. It is shown that the baseline approach, which assumes analysis of differences in modal rotation fields, allows to improve the sensitivity of a method to damage, making it possible to identify smaller damage with respect to the baseline-free approach. Moreover, a new approach for the reduction of the boundary effect is presented, which allows for the improvement visualization of the resulting maps using the proposed damage identification method. The proposed method was tested with eight damage scenarios, which allowed to prove repeatability of the obtained results, as well as to define a detectability threshold which is on the level of 3.5% of the thickness reduction.

Research paper thumbnail of Improvement in Damage Localisation using Speckle Shearography

Research paper thumbnail of Enhancement of shearography-based damage identification using best tree wavelet packet analysis

MATEC Web of Conferences

Shearography found many industrial applications as a nondestructive testing method due to its hig... more Shearography found many industrial applications as a nondestructive testing method due to its high spatial resolution and contactless measurements. However, to detect small structural damage, shearography should be enhanced by applying advanced signal processing methods to results of experimental testing. In this paper, the authors present an enhanced method based on the best tree wavelet packet analysis, which allows for extraction of the most informative nodes from the 2D wavelet packet decomposition tree. The proposed method is more effective than typical wavelet transforms due to its ability of adaptive selection of the best basis. The efficiency of the method was verified experimentally on damaged plates. The obtained results clearly show high sensitivity to the introduced small damage, which make the method attractive for industrial applications.

Research paper thumbnail of Improvement in Damage Localisation using Speckle Shearography

Proceedings of the Eleventh International Conference on Computational Structures Technology, 2012

Research paper thumbnail of Damage Identification in Beams by Post-processing Modal Displacements and Rotations with Haar Wavelet

A study on the post-processing of modal displacements and modal rotations with the Haar wavelet i... more A study on the post-processing of modal displacements and modal rotations with the Haar wavelet is presented in this paper. A free-free aluminum beam is chosen as a structure to be analyzed and its modal displacements and rotations in both undamaged and multiple damagedstates are computed with the finite element method. Three sets of damageindicators are proposed: (1) wavelet transform of damaged modal displacements or modalrotations, (2) wavelet transform of differences in modal displacements or modal rotations, and (3) ratio of wavelet transform of differences in modal displacements or modal rotations to wavelet transform of undamaged modal displacements or modal rotations. The study shows that post-processing modal displacements with the Haar wavelet leads to poor damageidentifications. On the other hand, if one applies the same type of wavelet to modalrotations, the damage indicators (2) and (3) clearly pinpoints the location of the damage. Although the set of damage indicators (1) and (2) are prone to the boundary effect, where high values of wavelets coefficients are present, the third set of damageindicators does not present this problem. Furthermore, for large values of damage, this damage indicators shows the presence of damagein all scales of the wavelet scalogram. The present study clearly shows that by post-processing modalrotations with the simplest wavelet one can obtain reliable identifications of multiple damage.

Research paper thumbnail of Optimal Finite Difference Schemes for Multiple Damage Identification in Beams

This paper presents an experimental and numerical study on multiple damage localization in a beam... more This paper presents an experimental and numerical study on multiple damage localization in a beam. The modal rotations of an aluminum beam were measured with shearography and post-processed to obtain the modal curvatures. The modal curvatures, which are computed by finite differences, are used as damage indicators. In most approaches available in the literature, the modal curvatures are defined from the modal displacements, requiring the computation of the second order derivate. In the present approach, since the modal rotations are available, the curvatures are obtained by computing only the first order derivative, reducing the propagation of measurement errors. Optimal samplings for both the forward and the central finite difference schemes, the latter with three and five points formulas, are derived. The results of applying these three finite difference formulas are compared, showing that both central finite differences allow for a better representation of the experimental modal curvature. Therefore, the perturbations on the modal curvatures are better identified, thus clearly indicating the damage presence.

Research paper thumbnail of On the use of finite differences for vibration-based damage localization in laminated composite plates

Purpose-Laminated composite materials are a staple of modern material development, with extremely... more Purpose-Laminated composite materials are a staple of modern material development, with extremely strong fibers being combined with resins to form versatile and efficient engineering structures. However, the advancements in material development must be accompanied by equally advanced methods for damage detection, localization and quantification, as these materials develop inherently unique failure modes. This paper aims to further the study of the use of modal shapes and their spatial derivatives to localize damage in laminated composite rectangular plates. Exploring different damage scenarios and models, as well as different orders of mode shape derivatives of laminated plates.

Design/methodology/approach-ANSYS® Parametric Design Language (APDL) is used to perform finite element analysis of plates with several damage scenarios and damage mechanics models. MATLAB® is used to post-process these simulation results, namely by calculating the derivatives using finite differences, applying three distinct sets of damage indices, including one that is presently proposed. To mimic experimental conditions and test the resilience of the derivative orders, different noise levels are introduced into the results of the finite element analysis. A quality index is employed to quantitatively evaluate the solutions, mainly regarding the response to the introduced noise.

Findings-The results show that the applied damage localization methods have comparable results in terms of quality. These results also show that the quality of the damage localizations is higher when the damaged areas coincide with high displacement/curvature areas of the mode shapes and that higher noise levels have a more noticeable negative impact when employing higher-order derivatives.

Originality/value-Exploring different damage scenarios and models, as well as different orders of mode shape derivatives of laminated plates. The influence of a specific damage layer on the order of derivatives of modal response is evaluated, showing promising results concerning its identification.

Research paper thumbnail of Damage Identification in Beams by Post-processing Modal Displacements and Rotations with Haar Wavelet

Lecture Notes in Civil Engineering, 2021

A study on the post-processing of modal displacements and modal rotations with the Haar wavelet i... more A study on the post-processing of modal displacements and modal rotations with the Haar wavelet is presented in this paper. A free-free aluminum beam is chosen as a structure to be analyzed and its modal displacements and rotations in both undamaged and multiple damagedstates are computed with the finite element method. Three sets of damageindicators are proposed: (1) wavelet transform of damaged modal displacements or modalrotations, (2) wavelet transform of differences in modal displacements or modal rotations, and (3) ratio of wavelet transform of differences in modal displacements or modal rotations to wavelet transform of undamaged modal displacements or modal rotations. The study shows that post-processing modal displacements with the Haar wavelet leads to poor damageidentifications. On the other hand, if one applies the same type of wavelet to modalrotations, the damage indicators (2) and (3) clearly pinpoints the location of the damage. Although the set of damage indicators (1) and (2) are prone to the boundary effect, where high values of wavelets coefficients are present, the third set of damageindicators does not present this problem. Furthermore, for large values of damage, this damage indicators shows the presence of damagein all scales of the wavelet scalogram. The present study clearly shows that by post-processing modalrotations with the simplest wavelet one can obtain reliable identifications of multiple damage.

Research paper thumbnail of Improvement on modal curvatures methods for multiple damage identification in beams

Multidiscipline Modeling in Materials and Structures, 2021

PurposeThe purpose of this paper is to present a study on the application of four damage factors ... more PurposeThe purpose of this paper is to present a study on the application of four damage factors to several single and multiple damage scenarios of aluminium beams. Each one of these damage factors is defined by the information given by modal curvatures of the beams.Design/methodology/approachThe methodology consisted of a first experimental stage in which the modal rotations were measured with shearography and a subsequent numerical analysis in order to obtain the modal curvatures. To this end, three finite difference formulae were applied. The modal curvatures were then used to calculate the damage factors.FindingsIt was found that the profile of the damage factors varies according to the finite difference formula used. In view of the findings, the differences among the damage factors analysed are highlighted and some final recommendations to improve damage identifications via modal curvature-based are presented.Originality/valueTo the best of the authors’ knowledge, the applicati...

Research paper thumbnail of Application of spline interpolation to speckle shearography measurements for damage identification

Procedia Structural Integrity, 2019

This paper aims to explore a new technique for structural damage identification using cubic splin... more This paper aims to explore a new technique for structural damage identification using cubic spline interpolation. The method is based on the interpolation of modal rotations measured with speckle shearography. In order to locate the damaged areas, we make use of the analytical derivative of the cubic spline function to compute the modal curvature, which is known to be very sensitive to damage. A comprehensive parametric study of the spatial sampling interval is carried out to find its influence on noise filtering. Furthermore, the identification quality dependency on the mode shape and respective noise is also examined. The results obtained with the proposed method show the consistency of the localizations. Additionally, the challenging tasks of identifying small and multiple damage are tackled, yielding a good performance.

Research paper thumbnail of Identification of multiple damage using modal rotation obtained with shearography and undecimated wavelet transform

Mechanical Systems and Signal Processing, 2019

Due to its high spatial resolution measurements and flexible and contactless experimental setup, ... more Due to its high spatial resolution measurements and flexible and contactless experimental setup, shearography, as a non-destructive testing technique, provides effective structural damage identifications. However, this effectiveness can be increased by applying postprocessing algorithms to experimentally measured modal rotation fields. In this paper, the authors present a novel method, consisting of shearographic non-destructive testing and 2D undecimated wavelet transform as a post-processing tool. The studies covered tests of the proposed method on simulated modal data of a damaged plate, as well as a validation on real data obtained from shearographic experiments. The results show the high sensitivity of the proposed method to either single or multiple damage, including its edges and its various configurations.

Research paper thumbnail of A Review and Study on Ritz Method Admissible Functions with Emphasis on Buckling and Free Vibration of Isotropic and Anisotropic Beams and Plates

Archives of Computational Methods in Engineering, 2017

Research paper thumbnail of Numerical study on damage identification using shearography with different shearing amounts

Procedia Structural Integrity, 2017

During their operation, modern aircraft engine components are subjected to increasingly demanding... more During their operation, modern aircraft engine components are subjected to increasingly demanding operating conditions, especially the high pressure turbine (HPT) blades. Such conditions cause these parts to undergo different types of time-dependent degradation, one of which is creep. A model using the finite element method (FEM) was developed, in order to be able to predict the creep behaviour of HPT blades. Flight data records (FDR) for a specific aircraft, provided by a commercial aviation company, were used to obtain thermal and mechanical data for three different flight cycles. In order to create the 3D model needed for the FEM analysis, a HPT blade scrap was scanned, and its chemical composition and material properties were obtained. The data that was gathered was fed into the FEM model and different simulations were run, first with a simplified 3D rectangular block shape, in order to better establish the model, and then with the real 3D mesh obtained from the blade scrap. The overall expected behaviour in terms of displacement was observed, in particular at the trailing edge of the blade. Therefore such a model can be useful in the goal of predicting turbine blade life, given a set of FDR data.

Research paper thumbnail of Influence of shearing amount and vibration amplitude on noise in shearography

Procedia Structural Integrity, 2017

During their operation, modern aircraft engine components are subjected to increasingly demanding... more During their operation, modern aircraft engine components are subjected to increasingly demanding operating conditions, especially the high pressure turbine (HPT) blades. Such conditions cause these parts to undergo different types of time-dependent degradation, one of which is creep. A model using the finite element method (FEM) was developed, in order to be able to predict the creep behaviour of HPT blades. Flight data records (FDR) for a specific aircraft, provided by a commercial aviation company, were used to obtain thermal and mechanical data for three different flight cycles. In order to create the 3D model needed for the FEM analysis, a HPT blade scrap was scanned, and its chemical composition and material properties were obtained. The data that was gathered was fed into the FEM model and different simulations were run, first with a simplified 3D rectangular block shape, in order to better establish the model, and then with the real 3D mesh obtained from the blade scrap. The overall expected behaviour in terms of displacement was observed, in particular at the trailing edge of the blade. Therefore such a model can be useful in the goal of predicting turbine blade life, given a set of FDR data.

Research paper thumbnail of A damage localisation method based on higher order spatial derivatives of displacement and rotation fields

Journal of Physics: Conference Series, 2011

ABSTRACT This paper presents the development of a damage localisation method based on low and hig... more ABSTRACT This paper presents the development of a damage localisation method based on low and higher order spatial derivatives of displacement and rotation fields. The method relies on the Timoshenko beam theory, the Hamilton's principle and the Ritz method, allowing the computation of an approximate analytical solution of natural frequencies, displacement and rotation fields. Since these fields are expressed analytically, through a series expansion, the spatial derivatives are also obtained analytically. Besides the usual curvature difference and damage index, which are based on comparisons of second order spatial derivative of the displacement field of a beam in the undamaged and damaged states, other damage indicators are proposed. These new indicators rely on spatial derivatives of rotation fields. The indicators are applied to the localisation of various cases of damages in beams and a comparison among them is carried out. It is found that, for relatively thick beams, the values of the indicators based on rotation fields spatial derivatives are, in general, lower than those based on displacement fields. It is also observed that these differences are negligible for beams with high length to thickness ratio.

Research paper thumbnail of A new technique to optimize the use of mode shape derivatives to localize damage in laminated composite plates

Composite Structures, 2014

Damage localization in laminated composite structures is a very active area of research due to th... more Damage localization in laminated composite structures is a very active area of research due to the role that these kind of structures play in the transport industries. The mode shape derivatives, like rotations (first derivative), curvatures (second derivative) and, more recently, third and four derivatives, have been used to localize damage in composite plates. The most used method to compute these derivatives is the application of finite differences. However, finite differences present several well-known problems, such as the error propagation and amplification. The magnitude of the error associated with the computed derivative is not easy to estimate, mainly because the numerical error associated with finite differences depends on the values of derivatives of higher order than the order of the derivative that one wants to compute. A new technique based on the Ritz method to estimate this error is proposed in this paper. The optimal spatial sampling for the numerical differentiation of the mode shapes are defined based on the minimization of the total error. The good performance of the optimal sampling is shown by applying it to the damage localization in a laminated composite plate.

Research paper thumbnail of Free Vibration and Buckling Analysis of Beams with a Modified Couple-Stress Theory

International Journal of Applied Mechanics, 2012

A model based on a modified couple stress theory for the free vibration and buckling analyses of ... more A model based on a modified couple stress theory for the free vibration and buckling analyses of beams is presented. The model also incorporates the Poisson's effect and allows the analysis of Timoshenko beams with any arbitrary end boundary condition. The natural frequencies and buckling loads are computed using the Ritz method. Parametric studies show that, while the natural frequencies and the buckling loads increase monotonically with the increase of the material length scale, they present a minimum in certain values of the Poisson's ratio. A study relating the classical elasticity and the couple stress strain energies is also presented. By establishing this relation, explicit formulas to obtain the natural frequencies and buckling loads, in which the couple stress and Poisson's effects are accounted for, in terms of the buckling loads of the classical elasticity are found. These formulas, which are valid when the shear strain and stress are zero, allow an expedite c...

Research paper thumbnail of Nonlocal material properties of single-walled carbon nanotubes

International Journal of Smart and Nano Materials, 2012

Natural frequencies of single-walled carbon nanotubes (SWCNTs) obtained using a model based on Er... more Natural frequencies of single-walled carbon nanotubes (SWCNTs) obtained using a model based on Eringen's nonlocal continuum mechanics and the Timoshenko beam theory are compared with those obtained by molecular dynamics simulations. The goal was to determine the values of the material constant, considered here as a nonlocal property, as a function of the length and the diameter of SWCNTs. The present approach has the advantage of eliminating the SWCNT thickness from the computations. A sensitivity analysis of natural frequencies to changes in the nonlocal material constant is also carried out and it shows that the influence of the nonlocal effects decreases with an increase in the SWCNT dimensions. The matching of natural frequencies shows that the nonlocal material constant varies with the natural frequency and the SWCNT length and diameter.

Research paper thumbnail of Damage Localisation in Beams using the Ritz Method and Speckle Shear Interferometry

Proceedings of the Tenth International Conference on Computational Structures Technology

A novel numerical-experimental technique is developed in order to minimise some of the difficulti... more A novel numerical-experimental technique is developed in order to minimise some of the difficulties exhibited by others damage localisation approaches. The present technique relies on the computation of undamaged rotation fields using the Ritz method and the Timoshenko beam theory, while the measurement of damaged rotation fields is performed by speckle shear interferometry. Two damage localisation indicators are also presented, which, instead of being based on the second derivative of displacement fields, are based on the first spatial derivative of rotation fields. These damage localisation indicators, the modified curvature difference (MCD) and the modified damage index (MDI), were applied successfully in the localisation of damage in two clamped-clamped aluminium beams.

Research paper thumbnail of Efficiency assessment of wavelet transforms and wavelets for damage localization in beams using shearography

Diagnostyka

Non-destructive testing of engineering structures and elements in operation is one of the crucial... more Non-destructive testing of engineering structures and elements in operation is one of the crucial steps in recently introduced design philosophies: damage tolerance and condition-based maintenance. Therefore, it is important to provide effective non-destructive testing methods, which are able to detect and identify a possible damage in early stage of its development. One effective testing method, which still gains its popularity in various industrial applications, is shearography. Although, shearography is sensitive to various types of structural damage and flaws, this sensitivity can be significantly improved by applying advanced post-processing algorithms to raw data obtained from measurements. An excellent candidate for such an improvement is the wavelet analysis, due to its very high sensitivity to smallest signal disturbances. This study presents results of comparative analysis of various wavelet transforms and various wavelets in order to analyse their sensitivity to damage. The improvement in damage detectability is verified using experimental data.

Research paper thumbnail of Damage identification by wavelet analysis of modal rotation differences

In this paper, a novel damage identification approach based on differences in modal rotation fiel... more In this paper, a novel damage identification approach based on differences in modal rotation fields obtained from shearographic measurements of structures and post-processed with the 2D continuous wavelet transform-based algorithm is presented. It is shown that the baseline approach, which assumes analysis of differences in modal rotation fields, allows to improve the sensitivity of a method to damage, making it possible to identify smaller damage with respect to the baseline-free approach. Moreover, a new approach for the reduction of the boundary effect is presented, which allows for the improvement visualization of the resulting maps using the proposed damage identification method. The proposed method was tested with eight damage scenarios, which allowed to prove repeatability of the obtained results, as well as to define a detectability threshold which is on the level of 3.5% of the thickness reduction.

Research paper thumbnail of Improvement in Damage Localisation using Speckle Shearography

Research paper thumbnail of Enhancement of shearography-based damage identification using best tree wavelet packet analysis

MATEC Web of Conferences

Shearography found many industrial applications as a nondestructive testing method due to its hig... more Shearography found many industrial applications as a nondestructive testing method due to its high spatial resolution and contactless measurements. However, to detect small structural damage, shearography should be enhanced by applying advanced signal processing methods to results of experimental testing. In this paper, the authors present an enhanced method based on the best tree wavelet packet analysis, which allows for extraction of the most informative nodes from the 2D wavelet packet decomposition tree. The proposed method is more effective than typical wavelet transforms due to its ability of adaptive selection of the best basis. The efficiency of the method was verified experimentally on damaged plates. The obtained results clearly show high sensitivity to the introduced small damage, which make the method attractive for industrial applications.

Research paper thumbnail of Improvement in Damage Localisation using Speckle Shearography

Proceedings of the Eleventh International Conference on Computational Structures Technology, 2012

Research paper thumbnail of Damage Identification in Beams by Post-processing Modal Displacements and Rotations with Haar Wavelet

A study on the post-processing of modal displacements and modal rotations with the Haar wavelet i... more A study on the post-processing of modal displacements and modal rotations with the Haar wavelet is presented in this paper. A free-free aluminum beam is chosen as a structure to be analyzed and its modal displacements and rotations in both undamaged and multiple damagedstates are computed with the finite element method. Three sets of damageindicators are proposed: (1) wavelet transform of damaged modal displacements or modalrotations, (2) wavelet transform of differences in modal displacements or modal rotations, and (3) ratio of wavelet transform of differences in modal displacements or modal rotations to wavelet transform of undamaged modal displacements or modal rotations. The study shows that post-processing modal displacements with the Haar wavelet leads to poor damageidentifications. On the other hand, if one applies the same type of wavelet to modalrotations, the damage indicators (2) and (3) clearly pinpoints the location of the damage. Although the set of damage indicators (1) and (2) are prone to the boundary effect, where high values of wavelets coefficients are present, the third set of damageindicators does not present this problem. Furthermore, for large values of damage, this damage indicators shows the presence of damagein all scales of the wavelet scalogram. The present study clearly shows that by post-processing modalrotations with the simplest wavelet one can obtain reliable identifications of multiple damage.

Research paper thumbnail of Optimal Finite Difference Schemes for Multiple Damage Identification in Beams

This paper presents an experimental and numerical study on multiple damage localization in a beam... more This paper presents an experimental and numerical study on multiple damage localization in a beam. The modal rotations of an aluminum beam were measured with shearography and post-processed to obtain the modal curvatures. The modal curvatures, which are computed by finite differences, are used as damage indicators. In most approaches available in the literature, the modal curvatures are defined from the modal displacements, requiring the computation of the second order derivate. In the present approach, since the modal rotations are available, the curvatures are obtained by computing only the first order derivative, reducing the propagation of measurement errors. Optimal samplings for both the forward and the central finite difference schemes, the latter with three and five points formulas, are derived. The results of applying these three finite difference formulas are compared, showing that both central finite differences allow for a better representation of the experimental modal curvature. Therefore, the perturbations on the modal curvatures are better identified, thus clearly indicating the damage presence.