Parametrically excited surface waves: Two-frequency forcing, normal form symmetries, and pattern selection

Motivated by experimental observations of exotic standing wave patterns in the two-frequency Faraday experiment, we investigate the role of normal form symmetries in the pattern selection problem. With forcing frequency components in ratio m/n, where m and n are co-prime integers, there is the possibility that both harmonic and subharmonic waves may lose stability simultaneously, each with a different wavenumber. We focus on this situation and compare the case where the harmonic waves have a longer wavelength than the subharmonic waves with the case where the harmonic waves have a shorter wavelength. We show that in the former case a normal form transformation can be used to remove all quadratic terms from the amplitude equations governing the relevant resonant triad interactions. Thus the role of resonant triads in the pattern selection problem is greatly diminished in this situation. We verify our general results within the example of one-dimensional surface wave solutions of the Zhang-Vinals model of the two-frequency Faraday problem. In one-dimension, a 1:2 spatial resonance takes the place of a resonant triad in our investigation. We find that when the bifurcating modes are in this spatial resonance, it dramatically effects the bifurcation to subharmonic waves in the case of forcing frequencies are in ratio 1/2; this is consistent with the results of Zhang and Vinals. In sharp contrast, we find that when the forcing frequencies are in ratio 2/3, the bifurcation to (sub)harmonic waves is insensitive to the presence of another spatially-resonant bifurcating mode

Wear Testing of a Mechanized Percussion Well Drilling System for Water Access in West Africa

The Mechanized Percussion Well Drilling (MPWD) Collaboratory project is assisting in the development of a mechanized well drilling system for drilling shallow water wells in West Africa. Our client, Mr. Joseph Longenecker with Open Door Development (ODD), desires to make water wells accessible to all in this region, but has experienced difficulty drilling through hard soil layers. To overcome this problem, the MPWD team has worked closely with Mr. Joseph Longenecker to develop a mechanized percussion well drilling rig using a rubber friction wheel drive system that is capable of drilling through these harder layers. Currently, the MPWD team is working to provide recommendations to improve the useful service life of our client’s new, mechanized rig design. The MPWD team’s most recent work includes the design and fabrication of a testing rig to simulate the operation of our client’s full-size rig. The testing rig will allow our team to conduct fatigue testing on a model of the driveline system to analyze the wear patterns on the rubber friction wheel and to estimate its expected service life. The team has also performed a series of finite element analyses on the mast design of our client\u27s rig to evaluate working stresses under static loading and buckling, along with fatigue analysis, to confirm safe operation of the rig and to identify any elements that might require upgrades. Funding for this work provided by The Collaboratory for Strategic Partnerships and Applied Research.https://mosaic.messiah.edu/engr2022/1010/thumbnail.jp