Structure Borne Traveling Waves (SBTWs) have promise as a means of underwater propulsion and fluid pumping; however, there is minimal understanding of how to generate SBTWS favorable for these applications. SBTWs take advantage of a surface’s structural properties (mode shapes and natural frequencies) to deform the surface into continually propagating traveling waves. These SBTWs can be generated on any thin-walled surface, across a wide bandwidth, and with minimal actuation footprint. By combining these benefits with the ability to tailor the pattern (propagation direction, wave length, frequency), there is significant potential for use in propulsion and pumping applications. At the basic level, SBTWs are generated by harmonically exciting two actuators at the same frequency but with a phase offset between them. This phase offset causes adjacent mode shapes to combine and produce the propagating SBTW. However, the optimal phase offset varies with excitation frequency, and that relationship is poorly understood. In addition, the SBTW pattern is governed by which modes participate, and there is minimal understanding of which modes yield favorable SBTWs (uniform propagation direction and consistent amplitude).

This paper explains the (1) relationship between phase offset and frequency and (2) which mode shapes yield favorable SBTWs. Using a previously validated electro-mechanical model, SBTWs are generated on a two-dimensional (2D) plate using two piezoelectric actuators. The actuators are excited at combinations of frequency and phase offset and the plate response is captured for each condition. The traveling wave quality is then analytically evaluated and a quality metric calculated for each frequency/phase combination. Plotting the quality metric versus frequency and phase demonstrates there is an optimal phase offset at each frequency that maximizes SBTW quality. At the natural frequencies, the optimal phase offset is always 0 or pi radians. The mode shape and actuator placement determines whether each natural frequency is  0 or pi. At other excitation frequencies, the optimal phase follows the trend lines that connect the optimal phase offsets at the natural frequencies. Thus, the optimal phase difference at any frequency can be predicted by knowing the mode shapes and actuator locations.

To determine how the mode shapes govern the generation of favorable SBTWs, the SBTW patterns were evaluated across frequencies and mode shapes. The SBTW pattern is most favorable (uniform propagation and consistent amplitude) when the two participating modes have a different number of nodal lines in their mode shapes. Specifically, the higher frequency mode shape has one more node than the lower frequency mode (e.g. Mode 1 has 0 nodes and Mode 2 has 1 nodes). This is the default case for one-dimensional structures, but not for 2D surfaces; in 2D, nodal lines can be perpendicular and increasing mode shapes don’t always add node lines in the same direction. Thus, a 2D surface only has certain frequency regions that generate favorable SBTWs. These regions are easily visible on the plot of TW quality vs frequency and phase: favorable SBTW regions correspond with adjacent modes having opposite optimal phase offsets, \[0,pi\] or \[pi,0\].


Procedure for Tailoring Steady-State Traveling Waves for Underwater Propulsion and Solid-State Motion

Division / Sponsors: 
Aerospace Division

Paper Proceedings: https://asmedigitalcollection.asme.org/SMASIS/SMASIS2020/volume/84027

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