Patent ID: 9000941
Filing Date: 2015-04-07
Classification: E21B

Abstract:
1. A method for estimating a steady state response of a drill string disposed in a borehole penetrating at least one of the earth and another material, the method comprising: calculating a first displacement of the drill string in a frequency domain for a first excitation force frequency and a number of multiples of this frequency using an equation of motion of the drill string that is solved by a processor, the equation of motion having a static force component, an excitation force component, and a non-linear force component with respect to at least one of a deflection and a derivative of the deflection of the drill string; transforming the first displacement from the frequency domain into a time domain using the processor; calculating a non-linear force in the time domain based on at least one of the calculated displacement and a derivative of the calculated displacement using the processor; calculating a frequency domain coefficient derived from the calculated non-linear force in the time domain using the processor; and calculating a second displacement of the drill string in the frequency domain using the equation of motion and the frequency domain coefficient using the processor.