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The uncertainty budget of Mixed-Numerical-Experimental-Techniques for the identification of elastic material properties from resonant frequencies

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The uncertainty budget of Mixed-Numerical-Experimental-Techniques for the identification of elastic material properties from resonant frequencies

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The elastic properties of homogeneous, linear-elastic materials can be identified using resonant vibration analysis. Several sources of uncertainty contribute to the combined uncertainty of the measured values. This paper presents a method to handle uncertainty budgets in vibration based mixed numerical-experimental identification techniques. The presented method is evaluated with two numerical test cases. The first example considers an isotropic material, and allows to compare the presented method with the method proposed in the UNCERT Code of Practice 13 [1]. The second example considers the uncertainty budget of the identification of a coated steel plate.
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... The identification of structural material properties by using the measured modal results was presented by Sol et al. [4]. Lauwagie et al. [5] proposed a method to estimate the uncertainty associated with the elastic properties identified with a Mixed-Numerical-Experimental-Technique (MNET). Elasticity and transverse shear modulus of beams were obtained from the measured flexural resonance frequencies using inverse method by Shi et al. [6] and Larsson [7]. ...
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Structural parameter identification based on the measured dynamic responses has become very popular recently. This paper presents structural parameter identification of fixed end beams by inverse method using measured natural frequencies. An added mass is used as a modification tool. The measurements of the flexural vibrations of a fixed end beam with and without added mass are performed by using experimental modal testing. The solution of free bending transverse vibration of the beam is obtained by solving the differential equation motion of Bernoulli-Euler beam. By introducing the natural frequencies from experimental measurements into the solution of differential equation, the structural parameters of the fixed end beam are calculated. It is seen from the results that the values of the mass distribution and elasticity modulus identified using the first natural frequency of the beam nearly close to the real values. Besides, the theoretical frequencies obtained using the identified structural parameters also close to the measured frequencies.
... Young's modulus measurement is not exact, and some unknown inaccuracy is always associated with it. According to GUM (Guide to the Expression of Uncertainty in Measurements), two main categories of uncertainty in measurement, A and B, should be evaluated [29,30,31]. ...
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In this paper we describe the construction of a laboratory-made resonant apparatus for the modulated force thermomechanical analysis (mf-TMA) and estimate the uncertainty of the measurement of Young's modulus of a porcelain sample. The porcelain sample was measured while increasing the temperature up to 1000 °C/5 °C/min. Thermodilatometry was performed to determine the actual dimensions of the sample in the same temperature regime. We assessed the influence of the repeatability of the directly measured values, the accuracy of the used measurers and different exceptions from the ideal experimental arrangement on the Young's modulus measurement uncertainties of types A and B. We found that the majority of the total uncertainty (80%) is determined at the room temperature. The remaining sources of uncertainty can be attributed to thermal expansion of the sample and inhomogeneity of the temperature field. The relative expanded uncertainty of the Young's modulus at the elevated temperatures was 1.1%.
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Many papers have already been presented about identification of 2D in plane elastic engineering constants E1, E2, v12 and G12 by inverse methods. Most of the described methods are based on measured resonance frequencies on plate specimens. Less attention has been paid to the identification of transverse shear moduli. Especially, validation of the obtained results and error bound estimations are often lacking. This paper presents an inverse method for the identification of the transverse moduli of test beams by measured flexural resonance frequencies. The procedure is first illustrated with numerically generated test data and next applied on experimentally measured results. The sensitivity of the flexural resonance frequencies for variations of the shear modulus is discussed as well as an estimation of the uncertainty intervals on the obtained moduli. The results are validated by using the obtained shear moduli for the prediction of torsional resonance frequencies.
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This work introduces a resonant-based, mixed numerical–experimental method for the determination of the in-plane elastic properties of the constituent materials of laminates. This non-destructive method identifies elastic properties from the resonant frequencies of beam-shaped layered specimens, using a set of finite element models. The method is demonstrated on a thermal barrier coating system made of NiCoCrAlY bondcoat and yttria-stabilised zirconia topcoat deposited by air-plasma spraying on stainless steel. The stainless steel was found to be elastically anisotropic, while both bondcoat and topcoat exhibited in-plane isotropy. Moreover, the topcoat Poisson's ratio approached zero, and the bondcoat properties varied with the coating thickness. Scanning electron microscopy was used to correlate the identified elastic properties with the coating microstructure.
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Sandwich structures are extensively used in engineering because of their high specific stiffness and strength. The modelling of sandwich structures has been studied extensively, but less attention has been paid to their material identification. This paper proposes an inverse method for the material identification of sandwich beams by measured flexural resonance frequencies. The procedure is illustrated with numerically generated test data and also applied on experimentally measured data taken out of literature. An error estimation procedure is conducted to discover and discuss the main error sources.
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Layered materials are becoming increasingly important for the production of high-performance components and constructions. Their stiffness properties are fundamental to assess stress fields during design calculations. Numerous analysis techniques to identify the elastic properties of materials exist, but in the case of layered materials, these techniques usually yield properties that are ‘averaged’ over the thickness of the test specimen. To assess the in-plane elastic properties of each individual layer, a new non-destructive testing method is developed. The proposed method derives the material properties from the resonance frequencies of a number of freely suspended test plates. A multi-model updating routine is used for this purpose. Finite element models of the different test plates are simultaneously updated. Once the Finite element models reproduce the measured frequencies, the updating procedure is halted, and the material properties of the different layers can be retrieved from the Finite element model's database. It is shown that the multi-model approach is necessary to ensure the uniqueness of the obtained properties.
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This paper compares results of three different methods to determine the in-plane elastic properties of sheet materials. Results obtained with standard resonant beam and tensile tests are used to assess a mixed numerical–experimental technique developed to determine the in-plane elastic properties of orthotropic plates from the resonance frequencies of rectangular plate samples (the so-called ‘Resonalyser’ technique). Test materials were selected on the basis of an expected low degree of elastic anisotropy in order to put the accuracy and sensitivity of the different techniques to assess anisotropic materials to a test. Therefore, aluminium alloy and stainless steel samples were prepared from hot-rolled plates, deliberately avoiding pronounced cold-rolling textures. The differences between the results obtained with the three experimental approaches are critically evaluated.In the case of very thin plates, the existing mixed numerical–experimental Resonalyser procedure succeeded in accurately identifying the elastic material properties. A slightly adapted procedure is proposed to extend the applicability of the Resonalyser procedure to thicker plates.
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