Irina Trendafilova

A phased array-based method for damage detection and localization in thin plates

A method for damage localization based on the phased array idea has been developed. Four arrays of transducers are used to perform a beam-forming procedure. Each array consists of nine transducers placed along a line, which are able to excite and register elastic waves. The A0 Lamb wave mode has been chosen for the localization method. The arrays are placed in such a way that the angular difference between them is 45° and the rotation point is the middle transducer, which is common for all the arrays. The idea has been tested on a square aluminium plate modeled by the Spectral Element Method. Two types of damage were considered, namely distributed damage, which was modeled as stiffness reduction, and cracks, modeled as separation of nodes between selected spectral elements. The plate is excited by a wave packet. The whole array system is placed in the middle of the plate. Each linear phased array in the system acts independently and produces maps of a scanned field based on the beam-forming procedure. These maps are made of time signals (transferred to space domain) that represent the difference between the damaged plate signals and those from the intact plate. An algorithm was developed to join all four maps. The final map is modified by proposed signal processing algorithm to indicate the damaged area of the plate more precisely. The problem for damage localization was investigated and exemplary maps confirming the effectiveness of the proposed system were obtained. It was also shown that the response of the introduced configuration removes the ambiguity of damage localization normally present when a linear phased array is utilized. The investigation is based exclusively on numerical data.

Analytical modeling and vibration analysis of partially cracked rectangular plates with different boundary conditions and loading

This study proposes an analytical model for vibrations in a cracked rectangular plate as one of the results from a program of research on vibration based damage detection in aircraft panel structures. This particular work considers an isotropic plate, typically made of aluminum, and containing a crack in the form of a continuous line with its center located at the center of the plate and parallel to one edge of the plate. The plate is subjected to a point load on its surface for three different possible boundary conditions, and one examined in detail. Galerkins method is applied to reformulate the governing equation of the cracked plate into time dependent modal coordinates. Nonlinearity is introduced by appropriate formulations introduced by applying Bergers method. An approximate solution technique-the method of multiple scales-is applied to solve the nonlinear equation of the cracked plate. The results are presented in terms of natural frequency versus crack length and plate thickness, and the nonlinear amplitude response of the plate is calculated for one set of boundary conditions and three different load locations, over a practical range of external excitation frequencies.

Vibration-based damage detection in structures using time series analysis

Abstract The paper considers some possibilities to use pure time series analysis for damage diagnosis in vibrating structures. It introduces the basics of the state space methodology and discusses a number of possible methods to extract damage sensitive features from the state space representation of the attractor of a vibrating system. The discussed methods can be divided into two groups: methods that use non-linear dynamics characteristics and methods based on the statistical characteristics of the distribution of points on the attractor. Each possible damage feature is introduced separately and the advantages and shortfalls of its application are discussed. The application of the suggested techniques is demonstrated on a test case of a reinforced concrete plate.

Delamination assessment in structures made of composites based on general signal correlation

This paper considers a vibration-based damage assessment approach which is based on the general idea for signal cross-correlation. Here the method is demonstrated and validated on a composite laminate beam and it is applied for the purposes of delamination assessment in composite structures. The method uses two measures of cross-correlation between two vibration signals measured in different points on the structure in order to diagnose the delamination. The linear cross-correlation as well as a new measure for nonlinear cross-correlation, the mutual information, are introduced and applied for the purposes of delamination assessment. The delamination assessment is based on the comparison of the measures for the healthy and the damaged state of the structure. In this study, the method is applied using the free decay responses of the beam. Two delamination indices are introduced and they are used for the purposes of delamination detection and localization.

A simple method for enhanced vibration-based structural health monitoring

This study suggests a novel method for structural vibration-based health monitoring for beams which only utilises the first natural frequency of the beam in order to detect and localise a defect. The method is based on the application of a static force in different positions along the beam. It is shown that the application of a static force on a damaged beam induces stresses at the defect which in turn cause changes in the structural natural frequencies. A very simple procedure for damage detection is suggested which uses a static force applied in just one point, in the middle of the beam. Localisation is made using two additional application points of the static force. Damage is modelled as a small notch through the whole width of the beam. The method is demonstrated and validated numerically, using a finite element model of the beam, and experimentally for a simply supported beam. Our results show that the frequency variation with the change of the force application point can be used to detect and in the same time localize very precisely even a very small defect. The method can be extended for health monitoring of other more complicated structures.

On approximate analytical solutions for vibrations in cracked plates

Recent NATO funded research on methods for detection and interpretation methodologies for damage detection in aircraft panel structures has motivated work on low-order nonlinear analytical modelling of vibrations in cracked isotropic plates, typically in the form of aluminium aircraft panels. The work applies fundamental aspects of fracture mechanics to define an elliptical crack, and the local stress field and loading conditions, arbitrarily located at some point in the plate, and then derives an analytical expression for this that can be incorporated into the PDE for an edge loaded plate with various possible boundary conditions. The plate PDE is converted into a nonlinear Duffing-type ODE in the time domain by means of a Galerkin procedure and then an arbitrarily small perturbation parameter is introduced into the equation in order to apply an appropriate solution method, in this case the method of multiple scales. This is used to solve the equation for the vibration in the cracked plate for the chosen boundary conditions, which, in turn, leads to an approximate analytical solution. The solution is discussed in terms of the perturbation approximations that have been applied and highlights the phenomenology inherent within the problem via the specific structures of the analytical solution.

A study on vibration-based damage detection and location in an aircraft wing scaled model

This study investigates the possibilities for damage detection and location using the vibration response of an aircraft wing. A simplified finite element model of an aircraft wing is used to model its vibration response. The model is subjected to modal analysis- its natural frequencies are estimated and the mode shapes are determined. Two types of damage are considered - localised and distributed. The wing model is divided into a number of volumes. The goal of the study is to investigate the possibility to use the vibration response of an aircraft wing and especially its modal characteristics for the purposes of damage detection. So we’ll be trying to find suitable features, which can be used to detect damage and restrict it to one of the introduced volumes. The sensitivity of the modal frequencies of the model to damage in different locations is studied. Some general trends in the behaviour of these frequencies with change of the damage location are investigated. The utilization of the modal frequencies for detecting damage in a certain part of the wing is discussed

State Space Modelling and Representation for Vibration-Based Damaged Assessment

This paper discusses the application of state-space representation of the structural vibration response for the purposes of structural health monitoring and damage detection. The offered methodology considers the changes in the state space and especially in the distribution of points on the attractor that are introduced by the initiation of damage and its accumulation. The probability density of this distribution represented using a basis of orthogonal functions is employed and the coefficients in this distribution are used to characterize the damage state of the structure. The method is applied to a simulated case study of an aluminium beam. The development of the coefficients is tracked with the initiation and the accumulation of damage in the structure. A damage feature based on the introduced coefficients is suggested to detect and quantify damage in the structure. The proposed damage feature is compared to similar ones, which however make use of the modal characteristics of the structure and its frequency response functions.

Multi-Phased Array for Damage Localisation

A method for damage localisation has been developed, which is based on the phased array idea. Four arrays of transducers, instead of only one, are used to perform a beam-forming procedure. Each array consists of nine transducers placed along a line, which are able to excite and register elastic waves. The arrays are placed in such a way that the angular difference between them is 45º and the rotation point is the middle transducer, which is common for all the arrays. The idea has been tested on a square aluminium plate modelled by the Spectral Finite Element Method. Two types of damage were considered, namely distributed damage, which was modelled as stiffness reduction, and cracks, modelled as separation of nodes in selected finite elements. The plate is excited by a wave packet (5-cycle sine modulated by the Hanning window). The whole array system is placed in the middle of the plate. Each phase array in the system acts independently and produces maps of a scanned field based on the beam-forming procedure. These maps are made of signals that represent the difference between the damaged plate signals and those from the intact plate. An algorithm was developed to join all four maps. This procedure eliminates the necessity to analyse each map individually and also gives the possibility to extract common features only. It allows to remove ambiguity and helps to localise damage more precisely than in the case of a single map. The problem for damage localisation was investigated and exemplary maps confirming the effectiveness of the system proposed were obtained. The investigation is based exclusively on numerical data.

A State Space Based Approach to Health Monitoring of Vibrating Structures

This study suggests the use of the probability density of points on the attractor of a dynamic system for the purposes of damage detection. This suggestion is based on the ergodic theorem, which relates the invariants of a dynamic system and the probability distribution of points on its attractor. The main assumption is that the geometric properties of the attractor will change at the introduction of damage. This assumption is theoretically based and the results from the case study as well as from previous studies come to justify it.