PSI - Issue 44

Mauro Mazzei et al. / Procedia Structural Integrity 44 (2023) 1212–1219 Mauro Mazzei et al. / Structural Integrity Procedia 00 (2022) 000 – 000

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While the natural frequencies of bridges are among the fundamental properties of bridges, the natural frequencies of most bridges remain unknown. Identifying natural frequency by measuring acceleration with sensors installed on bridges is not practical when studying large numbers of bridges. Indirect methods of detecting frequencies from the acceleration responses of a vehicle passing over bridges, on the other hand, still present difficulties. Vehicle responses contain various components, making it difficult to distinguish the bridge frequency from other frequency components. As suggested by T. Nagayama et Al., the common vibration component among multiple vehicle responses can be extracted through signal processing involving cross-spectrum estimation. Numerical analyses using a vehicle-bridge interaction model (VBI) are conducted. bridge (VBI) to examine the performance of the algorithm under various conditions. The first natural frequency of the bridge was identified under various combinations of speed of driving, demonstrating the performance of the proposed approach. In that specific case, they derived a typical resonance frequency of 2.17 Hz. Typically, to adequately address this type of topic, it is necessary to exploit high resolution in the sub-Hertz regime. This cuts out most miniaturized MEM devices that due to their nature of construction and the limited size of the suspended accelerating mass prof, can only address frequencies well above the Hz regime. In the framework of the best capacitive accelerometer ever designed we have at the top the ISA (Italian Spring Accelerometer) experiment recently carried out on the ESA Bepi Colombo Mission, Iafolla et al. (2011), that perfectly addresses this sub-Hertz regime ISA in particular is a three-axis accelerometer dedicated to measuring the nongravitational acceleration of Mercury Planetary Orbiter (MPO), knowledge of which is important to take full advantage of the quality of tracking data. ISAs have an inherent noise level of 10 − 9 m/s 2 / √Hz in the 3 · 10 − 5 Hz to 10 − 1 Hz. Even if we want to draw inspiration from this excellent Italian example, we should not forget the millions of euros it cost. Even using cheaper and unsophisticated components would still leave a hundred kEuro class of instruments in its reduced version, not allowing the establishment of a large sensor network at limited cost. However, very significant savings can be directed to both the mechanical design of the suspended test masses and the electronics. In this sense, ISA is a tool that stems from a discrete component design approach thought up several decades ago. Technology has since taken a huge step forward by offering in one small integrated circuit most of the functionality would be implemented by multiple stacked boards. See below our design approach. 4.2. Concept of measurement The general idea is to implement a capacitive differential configuration like the one shown in Figure 2.

Fig. 2. Differential capacitive configuration.

The two varying CAPs shown in the above figure correspond to the modulated capacitance as exploited when the proof mass by the effect of its acceleration moves toward or get farer from two different polarized plate whch go to feed namely the CIN1(+) and CIN1(-) inputs. Providing the proper excitation to the CAPs their accurate value may be derived Vs time and its value may be directly correlated to the displacement the proof mass is undergone be the effect of the acceleration. As shown the part may benefit of an active shield polarization which minimize the effect of the cabling. As shown by Benmessaoud et al. (2013) , the differential ΔC = C1 -C2 is the differential capacitance measured value and it may be used as: Δ C = 2 C0 (x/d0) or x = d0 Δ C/ 2 C0