In this paper, the propagation of lateral waves in a drill-string are studied by using a new numerical method and a stability monitoring scheme is proposed. The drill-string is modeled as a linear beam structure under gravitational field effects. An iterative wavelet-based spectral finite element method (WS-FEM) model is developed to obtain a high fidelity response. Numerical simulations of the lateral impact wave propagation at the bottom-hole-assembly (BHA) are conducted and a time-frequency analysis technique is applied to the response in order to identify the relationship between the position of the transition point between positive and negative strain and the dispersive properties of the lateral wave. Based on the results, a new monitoring scheme is proposed to monitor the stability of the drill-string based on a combination of lateral impact wave analysis at the BHA and the axial acoustic telemetry technique.

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