Abstract
The cross-orthogonality check (XOR) is a widely used correlation measure for validating finite element (FE) models, where the orthogonality between analytical and experimental mode shapes is measured as the inner product over the mass matrix. Ideally, this yields the identity matrix where any deviation from this matrix can be seen as a lack of correlation. One of the drawbacks of this measure is its sensitivity to noise on the experimental mode shapes, which can have a significant influence. The present paper presents a new way of calculating the XOR which provides robust results towards noise. The method, known as the principle of local correspondence (LC), is a mode shape-based technique for expanding experimental mode shapes using a unique linear combination of FE modes. The advantage of using the LC principle for calculating the XOR is that no reduced mass matrix is needed, and the influence towards noise on the mode shapes is reduced compared with other known techniques. In this paper, the method is validated using probabilistic numerical investigations. An FE model of a shell structure is used as a case study where Monte Carlo simulations are used to change the material properties and create a variety of different noise scenarios. The results are compared with similar simulations using Guyan and SEREP.
Highlights
Finite element (FE) models are some of the most important tools for engineers working with advanced civil structures subjected to dynamic loading. e FE models provide valuable information in the design phase where a wide variety of structural designs, materials, and advanced load scenarios can be tested
When focusing on the dynamic properties of the structure, the correlation can be determined using a variety of different measures such as the modal assurance criterion (MAC), the coordinate modal assurance criterion (COMAC), the frequency response assurance criterion (FRAC), and more [1]. e cross-orthogonality check (XOR) is popular as a correlation measure when comparing analytical and experimental mode shapes
This yields the identity matrix, whereas any off-diagonal element can be seen as a coupling of modes. e acceptable limits for the XOR are often dictated by large agencies such as NASA, United States Air Force, and ESA [2,3,4]. ese limits vary, but often diagonal terms above 0.95 and off-diagonal terms below 0.1 are considered acceptable
Summary
Finite element (FE) models are some of the most important tools for engineers working with advanced civil structures subjected to dynamic loading. e FE models provide valuable information in the design phase where a wide variety of structural designs, materials, and advanced load scenarios can be tested. The orthogonality between the experimental and analytical mode shapes is measured as the inner product over the mass matrix. This yields the identity matrix, whereas any off-diagonal element can be seen as a coupling of modes. E theory presented in this paper shows that the matrix describing the linear combination between experimental modes and analytical modes is equivalent to the XOR, which has the advantage that the XOR can be calculated without either expanding the mode shapes or reducing the mass matrix. Is technique is validated using a probabilistic approach where the main focus is on how noise on the experimental mode shapes affects the diagonal and offdiagonal elements when calculating the XOR. E proposed method is compared with similar analysis using SEREP and Guyan
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