66 S. Manzoni et al. of the rod’s material, cannot be skipped. Moreover, the not perfect matching between FEM model and experimental model must be taken in account. A numerical model might not rightly include the effects on the dynamic behaviour of the tie-rod, due to the presence of a screw shackle in the middle. The weight of the uncertainties due to all these variability can be reduced by means of a minimization process. The function chosen is based on the square deviation between the measured and the numerical values, such as (7.2): f .p/ DXm iD1 qi .vi wi / 2 (7.2) where p is a vector of input parameters, vi and wi are respectively the i-th numerical and measured value, qi is the weight of each quantity. The function is processed in Matlab and minimized by means of one of the algorithm available in Toolbox Optimtool. In the method developed, the target value to be optimized is obviously the axial load. The parameters taken into account as variables of the process are Young’s modulus and the mass per unit length, starting from the nominal values of the metal which the tie-rod is made, and a set of natural frequencies obtained respectively by means of numerical model and experimental measures. 7.3 Experimental Setup A system strongly resembling with a common tie-rods was assembled in the Mechanical Department’s laboratory. The model is a double connected beam with circular cross-section, joined by means of a screw shackle (Fig. 7.15). The constraints (Fig. 7.14) are composed of modular elements in order to give them a sort of yielding, by allowing a changing clamping along the grip span. Tie-rod and constraints are made in the same material, aluminium, in order to avoid differential thermal expansion which may change in time the behaviour of the clamping. Tensile axial load is changed by means of the screw shackle and is measured by strain gauges in full Wheatstone bridge configuration set for tensile strain sensitivity and for temperature compensation (Fig. 7.15). The strain gauge was calibrated by a load cell mounted along the beam as shown in Fig. 7.16. Vibration measurements are made by three piezoelectric accelerometers PCB 333B30, which metrological specifications are shown in Table 7.1. One of Fig. 7.14 The constraints on the ends of tie-rod
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