MS15.10 - Nonlinear Dynamics and Dynamic Stability

In this work, modelling of non-smooth dynamics of an Anti Stick–Slip Tool (ASST) is carried out. ASST is used to protect a drill-string from a severe form of torsional vibrations known as stick-slip. A drill string is an essential component of any downhole drilling process and it exhibits a highly complex dynamic behaviour due to strong geometrical and material nonlinearities present in the system. To protect the drill-string and to maximize the rate of penetration, the stick-slip phenomenon should be suppressed. One of proposed solutions is to employ Anti Stick-Slip Tool, which is a mechanical device designed to control torsional vibrations by converting the excessive external torque into the axial movement of the bit allowing to avoid unwanted stick phase. In this paper the ASST is considered as a non-smooth dynamic system, where the presented modelling accounts for switching between Activated and Non-Activated states and proposes quantitative conditions for observing each state. The internal friction between coupled components contributes to the conversion of excessive loads to a relative motion of two coupled parts. The proposed models describe the effect of internal friction forces on the operation of the tool whilst the tool is subject to nonlinear cutting forces from bit–rock interactions. Prescribed kinematics imposed on the tool allows to simplify of the model of the entire system and provide insight into the complex behaviour of the tool. Nonlinear responses of the developed model for a range of system parameters were numerically simulated to explore the dynamic behaviour of the ASST. Various external loadings are considered including scenarios when the tool is activated and de-activated during the operation. This allows the tool to be tested and its performance to be optimised.

A novel type of structure-dependent integration methods has been developed for time integra-tion and pseudo-dynamic testing. The feasibility of this type of integration methods has been numerically affirmed by numerical tests and experimentally validated by pseudo-dynamic test-ing. It is generally recognized that structure-dependent integration methods can generally com-bine unconditional stability and explicit formulation together. Hence, they are promising for either time integration or pseudo-dynamic testing. An explicit pseudo-dynamic algorithm is generally preferred over an implicit pseudo-dynamic algorithm since the implementation of an implicit pseudo-dynamic algorithm is very complex due to an iteration procedure and it may lead to incorrect results. Both the Chang explicit method and CR explicit method (proposed by Chen and Ricles) have been shown to have desired numerical properties, such as unconditional stability, explicit formulation and second-order accuracy. However, they have a different per-formance in the step-by-step solution of high frequency initial value problems. This is because that Chang explicit method has no weak instability while CRM has this adverse property. It is recognized that a weak instability might lead to inaccurate solutions or numerical explosions. The root cause of weak instability was analytically investigated and numerically illustrated. In addition, a series of pseudo-dynamic tests were conducted by using both integration methods. Several hot-rolled steel beams with the cross section of H 100x100x6x8 and a length of 1.5 m were adopted for the serial tests. The test setup for each steel beam was like a cantilever beam. The steel beam was loaded in its minor axis to avoid any instability or local buckling. In addi-tion, some two-story steel frames were also fabricated for the pseudo-dynamic tests. Test results revealed that Chang explicit method can generally lead to reliable test results while CR explicit methods resulted in incorrect test results if there existed high frequency responses.

This research examines the influence of the two main types of earthquake mechanisms (i.e., subduction and crustal) on the seismic response of steel moment frames (SMFs). Nonlinear time history analyses are conducted on five archetypes SMFs (varying in height) using two suites of 500 carefully selected unscaled recorded ground motions. The first suite consists of records from subduction earthquakes, while the second suite consists of unscaled crustal ground motions that are spectrally equivalent to the subduction ground motion suite. The differences between the two seismic environments are analyzed by conducting a sensitivity analysis of the seismic response of the SMFs against ground motion intensity measures. The results indicate that peak floor accelerations and inter-story drift ratios under subduction earthquakes are statistically higher than their counterparts from crustal earthquakes. On average, peak floor accelerations and inter-story drifts of the SMFs are amplified by 1.43 and 1.13, respectively, when subjected to ground motions from subduction sources. Moreover, the sensitivity analysis results demonstrated that the behavior of SMFs is more prone to the duration of subduction ground motions than the duration of crustal ground motions.