Spectral Analysis of the Infinite-Dimensional Sonic Drillstring Dynamics

By deploying sonic drilling for soil structure fracturing in the presence of consolidated/ unconsolidated formations, this technique greatly reduces the friction on the drillstring and bit by using energetic resonance, a bit-bouncing high-frequency axial vibration. While resonance must be avoided, to our knowledge, drilling is the only application area where resonance is necessary to break up the rocks. The problem is that the machine's tool can encounter several different geological layers with many varieties of density. Hence, keeping the resonance of the tool plays an important role in drill processes, especially in tunnel or infrastructure shoring. In this paper, we analyze the sonic drillstring dynamics as an infinite-dimensional system from another viewpoint using the frequency domain approach. From the operator theory in defining the adequate function spaces, we show the system well-posedness. The hydraulic produced axial force that should preserve the resonant drillstring mode is defined from the spectrum study of the constructed linear operator guided by the ratio control from the top to tip boundary magnitudes.