Papers by Author: John E. Mottershead

Abstract: The term damage can be generally defined as a change introduced into a system that affects its performance. Its identification and characterization is a valid help in deciding amongst continuing the operation or performing a repair or replacement of the system. A valid support to this decision is based on the use of well-known measurement techniques from Non-Destructive Testing and Evaluation (NDT&E). A well-established correlation between damage and features extracted from the measured data makes these techniques capable of providing information about the extent of the damage. However the prediction of the remaining useful life of a system by comparing full-filed measurements techniques and FEM analysis results is the challenge of an increasing number of research studies. The need of a guide for enumerating the extent of the damage has been the thrust to perform this work. A common methodology developed for both numerical and experimental studies will be presented. It consists of three main parts: proper selection of the parameter capable of describing the damage in a quantitative manner; several approaches to obtain results from measurement techniques and FEM analysis; and damage assessment making use of a quantitative comparison of FEM results only, full-field experimental results only, or comparison of FEM to experimental results. A different approach in damage assessment will be also presented making use of Zernike moment descriptors from which the severity of the damage is inferred. An example to illustrate the methodology will be shown.

Abstract: For the analysis of vibrations and mode shape extraction in particular the use of optical full-field measurement techniques has grown during the last years. Beside techniques like Digital Speckle Pattern Interferometry, Moiré, Thermography or Photoelasticity the Digital Image Correlation techniques have already been successfully proven to be an accurate displacement analysis tool for a wide range of applications.

Abstract: Recent advances in measurement techniques, including digital image correlation, automated photoelasticity, electronic speckle pattern interferometry and thermoelastic stress analysis, permit full-field maps of displacement or strain to be obtained easily. They provide large volumes of mostly redundant data, which should be condensed to the essential information to permit straightforward processes such as validations of computational models or damage assessments. A way to do this is by image processing, an important aspect of which is the definition of an orthogonal basis (orthogonal kernel functions). Generally, this is problem dependent and requires some skill from the analyst if the number of image features (the coefficients of the orthogonal basis) is to be restricted to a suitably small number. Advantage may be taken of patterns of symmetry, for example cyclically symmetric patterns are well-suited to treatment by Zernike polynomials and rectangular patterns are well-suited to treatment by Fourier series. The Zernike and Fourier kernels are continuous polynomials with orthogonality properties that require integration and must be discretised. The discrete Tchebichef polynomials are ideal for the treatment of full-field information at multiple discrete data points. In many cases the data field is localised around a particular feature, such as local strain around a hole in a tension-test specimen. In this case, the polynomial basis should similarly be localised by various forms of scaling – this requires the application of the Gram-Schmidt procedure to maintain orthogonality. The image features (sometimes called shape features) are meaningful and may be used to identify particular patterns in the data – e.g. for detecting cracks or other forms of damage. When assembled in a feature vector, the distance between feature vectors from measured and numerical results are useful for refining numerical models. In this paper the principles of image analysis, as applied to full-field displacement/strain data are explained and experimental examples are used to illustrate the practical usefulness of the method. The applications include (i) vibration mode shapes of laminated honeycomb structures and, (ii) strain in an aluminium plate with a central hole in tension.

Abstract: Relative entropy has been employed, as an alternative to other regularization methods, in solving ill-conditioned linear inverse problems. Damage detection when treated as structural modification imparted by the damage leads to a linear inverse problem involving frequency response functions. This problem is amenable to ill-conditioning issues that could arise from the low frequency response values and noisy experiments. This article formulates and solves using the minimum relative entropy method the damage detection and localization problem on a simulated cantilever beam.

Abstract: The vibration of a beam excited by a moving simple oscillator is an extensively studied problem. However, the vibration of a beam excited by an elastic body with conformal contact has attracted much less attention. This is the subject of the present paper. The established model is a big improvement to the moving oscillator model and has many engineering applications. Because the moving body is flexible, the moving loads at the contact interface are not known a priori and must be determined together with the dynamics of the whole system. Considerable mathematical complication arises as a result, compared with the moving-oscillator problem, even if the contact is assumed to be complete. In this paper, the equation of motion of the beam and the moving body are established separately using an analytical-numerical combined approach. The equation for the moving loads is established through the displacement continuity at the contact interface. It is found from the simulated numerical results that the deflection of the beam displays several cycles of oscillation during the passage of the moving body and can exceed the maximum static deflection at moderate speeds, but is close to the static deflection when the speed is either very low or very high.

Abstract: Finite element model updating of a Westland Lynx XZ649 helicopter tail is presented. Eigenvalue sensitivities with respect to Young’s modulus and mass density are used. Large groups based on material input data were divided to form smaller subgroups so that those parts of the model responsible for errors in the predicted eigenvalues were located. A particular new development was the use of parameter clustering based on the similarity of different columns of the sensitivity matrix. Finally the finite element model was updated successfully with regard to the lower frequency tail-bending modes.