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