Mathematical Modeling and Analysis of Drill String Longitudinal Vibration with Lateral Inertia Effect

<table class="table-group" id="tab6"><tr><td><table class="table"><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr class="thead"><td class="align_left">Boundary conditions</td><td class="align_center">Without lateral inertia</td><td class="align_center">Lateral inertia</td></tr><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr><td class="align_left">The first-order natural frequency (rad/s)</td><td class="align_center">0.03</td><td class="align_center">0.04</td></tr><tr><td class="align_left">The second-order natural frequency (rad/s)</td><td class="align_center">0.05</td><td class="align_center">0.06</td></tr><tr><td class="align_left">The third-order natural frequency (rad/s)</td><td class="align_center">0.07</td><td class="align_center">0.09</td></tr><tr class="table-tr"><td colspan="3"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

The free vibration natural frequency in different conditions.

Shock and Vibration

tab6

Table 6

Table 6: Mathematical Modeling and Analysis of Drill String Longitudinal Vibration with Lateral Inertia Effect 