Encapsulated by critical drilling factors such as hydraulic power, weight-on-bit (WOB), drill-bit rotary velocity, and circulating fluids, conventional drilling operations urgently demand for alternative, reliable performance enhancing techniques capable of simultaneously reducing catastrophic events and operational time. Extensive [conventional] rotary drilling assessments regarding assembly vibration irregularities, bit-wear, fatigue, buckling, whirling, well-bore damage, and equipment failure invade scholastic and industrial spheres, targeting phenomenological characterization as a medium to augment rate-of-penetration (ROP). Recent investigational trends elucidate reasonable ROP increments centered on vibration-assisted drilling (VAD) methodology, where a transferring of high-frequency low-amplitude excitation into low-frequency high-amplitude response transpires by superimposing an axial vibratory source on the drill-string. The proposed rig-suspended dynamical model subjected to monochromatic deterministic and stochastic excitations, and exposed to a variety of material and geometric nonlinearities, captures the response (ROP) for any established downhole condition and formation type upon integrating percussion VAD technology; a two-step process deliberately percolates – proper mathematical representation of drill-string, VAD source, and rock-formation apprehending predominant physical attributes; and delineating appropriate [vibratory] source position within the drill-string, which warrants maximal penetration rates and eliminates tuning of mass near the natural frequency. Hypothetically formulating adequate physical parameters for the equation of motion implies incorporating finite element techniques, where the flexibility of the drill-string and elastic characteristics of the well-bore/formation are accounted along the axial and lateral directions. Modeling drill-string dynamics, nonetheless, postulates executing advanced numerical simulation techniques, particularly during the integration of the two thousand-degree-of-freedom oscillator exposed to mass, damping, and stiffness nonlinearities. In synthesizing compatible time histories through the adaptation of Kanai-Tajimi power spectrum, auto-regressive-moving-average (ARMA) filter is constituted. The method of Statistical Linearization and the method of Monte Carlo simulation are included within the stochastic vibration analyses.
