On the Behavior of Superimposed Orthogonal Structure-Borne Traveling Waves in Two-Dimensional Finite Surfaces

Wave-driven motion is a phenomenon that has been observed in nature as a method for propulsion. Earlier studies replicated these traveling waves in finite structures to propel the structures itself or particles across the surface of the structure. Two-mode excitation has been introduced as an effective method to generate steady-state structure-borne traveling waves (SBTW). Two-mode excitation generates SBTW in finite structures by superimposing two standing waves in a structure with a prescribed phase offset. While the generation of STBW for propulsion and particle motion has been a topic of study for some time, most research has examined SBTW propagating along a single axis. This chapter expands on this method by using two pairs of actuators to simultaneously excite two SBTW orthogonal to one another. The superposition of these orthogonal waves results in a net SBTW that propagates in any desired direction. By controlling the direction of SBTW using only two pairs of actuators, an active surface could be made to drive motion in any direction without the need for a large number of actuators. It is shown that while the excitation frequency will determine the mode shapes that dominate the behavior of the SBTW, it is the geometry, boundary conditions, and the locations of actuators that will determine the possible combinations of SBTW that can be excited in the plate. It is found that adjusting the relative amplitude and phase between the two SBTW will influence the quality of the wave, in addition to affecting the overall direction of the superimposed SBTW. This motion is studied using simulations in a 2D Finite Element model that represents a plate using first-order shear deformation theory. The quality of the SBTW is calculated using a traveling index defined by the complex orthogonal decomposition of the wavefront. The direction of the wavefront in this study is interpreted by calculating a weighted average of the structural intensity (SI) field over the plate.