Abstract
A multi-parameter approach for analysing drilling dynamics is developed. It is oriented to better understanding peculiarities of the process and optimising existing formulations. The procedure is specified for bending vibrations of a rotating elastic beam pre-stressed simultaneously by an axial compressive force and torque. The appropriately normalized ratio of the bending stiffness to the axial force magnitude is assumed to be small. Two other independent dimensionless parameters correspond to the vibration frequency and the relation between force and torque magnitudes. A classification, similar to that in thin shell theory, is established for free bending vibrations. The associated shortened equations are derived. The asymptotic results are validated by comparison with the dispersion curves calculated from the original full equation of motion. An example of a boundary-value problem for a drill string of a finite length is also presented.
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