a, Mutual interference of two actuators at different relative angles α at 200 Hz. Two representative cases were studied, with one actuator (no. 1) positioned along (left) or perpendicular to (right) the bisector of the other actuator (no. 2). Here, only actuator 1 was actuated. The amplitude ratio, that is, the amplitude of actuator 2 over the amplitude (induced by mutual interference) of actuator 1, shown in the table demonstrates that α = 45°, 90° and 270° result in relatively small mutual interference for both representative cases simultaneously. b, Mutual interference of two small actuators at different relative angles α at their resonant frequency of 200 Hz. The size of the actuators and the distance between them were scaled to 1/10 of the original design as shown in a, that is, the distance between two actuators was 2.1 mm rather than 21 mm. Here the thickness of the PI disk was set at 1.8 μm to enable the resonant frequency for the small actuator to be 200 Hz. Two representative cases were studied, with one actuator (no. 1) positioned along (left) or perpendicular to (right) the bisector of the other actuator (no. 2). Here only actuator 1 was actuated. The amplitude ratios (actuator 2 to actuator 1) due to mutual interference are shown in the table. c, Optimization of the actuators’ arrangement. The mutual interference among actuators was studied for α = 0°, α = 45° and a combination of 90°/270° referring to the simulation results in a, and for representative cases when actuators A (around the centre), B (near the boundary) and C (near the corner) are actuated separately. The results show that α = 90°/270° yields the smallest mutual interference (see tables under). The number gives the amplitude ratio due to the mutual interference among the actuators—that is, the amplitude of all actuators over the amplitude of the activated actuator—where 1 represents the activated actuator.