26 M. S. Bonney and D. Wagg Fig. 3.3 Experimental results for the fundamental frequency unique difficulties in the modelling procedure. In addition to the modelling fidelities, two general methodologies are used to model the thermal properties of each joint. These methods include using the built-in thermal expansion coefficients used in ABAQUS, and the second is a temperature-dependent stiffness of the joint connection. This calibrated stiffness is reasonable due to the nature of the digital twin correlation. Since a large amount of data is collected during the operation of a physical system, this calibration can utilise these real data to produce an accurate model. While this is not predictive, this can still give insight to a large range of environmental conditions that the physical system experiences. One aspect to note is that this modelling only accounts for the change in stiffness that produces the change in natural frequency. The future work will incorporate the temperature-dependent damping as well, and however, the accurate modelling of damping is also a current area of modern research. 3.4 Model Updating of FEA Models This system is comprised of two main metals, a stock rolled steel used for the structural supports and 6105-T5 extruded T-slot aluminium. These have nominal properties of Est =210GPa, ρst =7.89 g/cm3 and αst =1.17e−5 C−1 for the steel and Eal =71.3GPa, ρal =2.7 g/cm3 and αal =2.36e−5 C−1 for the aluminium. Since a rigid tie connection is typically used (and is used for the thermal coefficient method), an elastic contact can only produce a less stiff connection, thus lowering the natural frequencies. Because of this property, the nominal models are calibrated to the most stiff testing configuration, the test results for the lowest temperature tested of −15◦C. For the beam model, after doing a sensitivity study, it was found that the material property of the steel is orders of magnitude more significant than the aluminium. In hindsight, this makes sense since the frequencies of interest are the first three global bending modes. These consist of flexure in the steel supports and very slight flexure in the aluminium. Despite this, two attempts at model updated were performed. The first attempt was based on a non-informed decision to modify Young’s modulus for both materials. However, this resulted in more than doubling the strength of the aluminium and maintaining nearly nominal strength for the steel. This produced a maximum error of less than 1%. While this produced accurate natural frequencies, the change in the aluminium is deemed to be too excessive and not realistic. Because of this, the
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