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In total, ten different CFS channel cross-section prototypes are considered in the optimisation process.

The classification trees are then used to efficiently generate candidate member cross-section prototypes for subsequent refined local optimization.

The aim is to optimize a cross-section prototype shape with restrictions on its geometry attending to manufacturing feasibility and assembly constraints.

Fig. 3 Cross-section image of control valve prototype Fig. 4 FEM result of deformation mode of the prototype Fig. 5 Components of prototype Fig. 6 Assembled prototype.

The prototype is designed to improve the previous model using a bolt-clamped Langevin type transducer (BLT) and Fig. 3 shows a cross section of the prototype whose mechanism can generate large acceleration at the orifice plate [30].

The cross section of the prototype column is 4000 × 400 mm while the cross section of the scaled column is 500 × 50 mm according to the 1/8 scaled ratio.

a TEM cross-section image.

In addition, Fig. 9c shows the comparison between the cross section of the PFC3D model and the prototype CT image.

Open image in new window Fig. 9 Comparison between the selected cross section of the PFC3D model and the prototype CT image, a the cross section truncated from the constructed PFC3D model, b the prototype CT image of the selected cross section, c comparing the rock gravels that are represented in PFC3D model with the real ones that are shown in the CT image.

The prototype had a special X-shaped (Tresca) cross section to minimise the effects of torsional strain during length comparisons.

Parameters of the prototype is as follow: length of 34 mm, cross section of 10.5 mm × 10.5 mm, weight of 7.0 g, working frequency of 54.2 kHz, maximum no-load speed of 392 mm/s and maximum thrust of 1.2 N.