30 S. Tincani et al. are present but significantly reduced in amplitude compared to the case without structural damping. As for the reduction achieved at fres, the peak attenuation is higher than that of the case without damping. This is in accordance with references [6], [19]. Considering the results of the system’s frequency response when TVAs are applied (ideal case, shown in Fig. 3) and the LRM solution (Fig. 9), it is possible to compare the width of the stopband, considered in this case as the frequency range for which the orange curve (in Fig. 3 representing the solution with 25 TVAs and in Fig. 8 the LRM solution without damping) is positioned below the black one (baseline case for both figures). The stopband obtained when the LRM concept is applied to the actual system turns out to be 92% of the solution that involves the 25 TVAs applied to the same system. It should be noted that, in the case of the simulation related only to the UCs and the computation of the dispersion curves, this percentage was around 94%. Therefore, the simulations conducted have demonstrated the feasibility of creating an LRM concept using designs that are practically manufacturable and whose behavior closely approximates the ideal case simulated in Section 3. 1 Normalized Frequency, f/f res [-] log 10 (average displacement), [m] Normalized Values Base LRM LRM (damped) 1 Normalized Frequency, f/f res [-] Phase Angle, [°] Normalized Values Base LRM LRM (damped) Fig. 9 The average of the directional displacement responses (amplitude and phase in normalized values) recorded on the upper face of the PCB. Frame without LRM concept (Base), LRM concept (LRM) and LRM concept with structural damping (LRM (damped)). Conclusions In the presented study, a solution involving LRM applicable to an electric drive PEU is investigated. The problem statement is defined in Section 2, such that an out-of-plane PCB mode, with a global assembly participation is targeted. Key challenges are the physical constraints due to the complex geometry of the component and the requirement to investigate a realizable solution. The LRM solution is compared to the effectiveness of a single TVA exploring the optimal solution applicable to the component keeping additional mass consistent. This comparison establishes the LRM concept as the superior solution and although the single TVA has an impact on the system, the reduction in component response is less than that achieved with the LRM concept. A comparable reduction is achievable with a single TVA however, this approach is impractical due to the excessive increase in mass on the system at a single location. The proposed optimal resonator is achievable through additive manufacturing technology and capable of being positioned on the frame, while respecting the geometric constraints of the structure. UC modeling is presented to evaluate initial designs, and different UCs with two types of realizable resonators are simulated and compared, also in relation to an idealized TVA. The Ring Resonator is selected as the optimal solution and its application to the component in a distributed sense is discussed. The results demonstrate its reproducibility in a real case using actual materials and manufacturing technologies.
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