A two-dimensional piezoelectric traveling wave generator using a multi-integer frequency, two-mode method (MIF-TM)

In this paper, we report a new method called a multi-integer frequency, two-mode (MIF-TM) to generate multi-directional traveling waves on a square plate. The uniqueness of this driving method is threefold. Firstly, as the two driving frequencies are at or near resonant frequencies of the two bending modes, the driving efficiency can be largely enhanced by using structural resonance. Secondly, as the two actuating areas can sufficiently induce traveling waves, each of them is driven by one of the two driving frequencies. It is possible to generate steady traveling waves by making the two driving frequencies possess a multi-integer relationship and with a phase difference. Thirdly, the direction of the traveling wave can be controlled to propagate toward either the x- or y-direction by designing the location and size of the actuating area. To assist in the design of the MIF-TM traveling wave generator, an analytical model was derived to depict the induction of the traveling waves. Using this analytical model, we designed a piezoelectric traveling wave generator with weight of 2.35 g, dimension of 45 × 45 × 0.4 mm piezoelectric bimorph with four designated electrode pairs. It was verified to be either in the positive or negative direction traveling wave as it was controlled by adjusting the phase difference between the two driving frequencies. Our experimental results demonstrated that the generated x-direction traveling wave can move a 0.3 g object at a speed of 1.48 mm s⁻¹, and the generated y-direction travel wave can move this same object at a speed of 1.36 mm s⁻¹. The design, numerical analysis, finite element analysis, and experimental studies are detailed in this paper.