Sound vibration damping optimization with application to the design of speakerphone casings

We optimize the thickness distribution in a 1D beam model of an elastic plate, subject to forced vibration at one of its ends, in order to minimize the structural vibration in a given area of the plate. The optimization is carried out both in broadband and band-pass cases. Geometric constraints, weight constraints, and constraints on the static compliance are imposed in the optimization. A broadband optimization over 50 frequencies, evenly distributed in the 300–3400 Hz range, reduces the vibration by around 5–10 dB on average throughout the frequency range. When targeting only the higher end of the above frequency range, it is possible to achieve more dramatic results. Vibration reductions of 20 dB and more can be achieved in the 2300–2800 Hz region. In the latter case, the results suggest that a band-gap phenomenon occurs, similarly as for phononic band gap materials. To validate the results, the best-performing optimal shape for the clamped case was imported into a 3D computational structural model, and the resulting forced vibration response agreed well with the the beam-model computations. These results were first announced in a technical report by Lacis et al. [5]