## On the motion of rotating shafts including an approximate solution for the case of constant angular acceleration |

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ahaft deflection angular speeds angular velocity aooelerated approaches zero APPROXIMATE SOLUTION arbitrary assumption becomes infinite boundary conditions center line CO^Oc CONSTANT ANGULAR ACCELERATION constants become CORNELL UNIVERSITY critical speed differential equation disc diso ehaft equation 40 equation 62 equations 24 equations 38 equations 9 ffiven Figure VII firet flection given an initial Graduate graph hence hich igure initial conditions Initial Curvature initial deflected form initially curved shaft initially straight Let the initial maximum deflection occurs Mechanical Engineering motion ie motion is unstable oase obtain oritical speed problem remains straight rlane ROTATING SHAFTS s^eed satisfy equation 46 satisfy the boundary seen from equation shaft is initially shaft remains SHAFT ROTATING solution of equation sreed stable motion stable solution stable vibration steam turbine straight position straight shaft substituting tangent theory of bend thesis thie thiF uniform acceleration uniformly accelerated values vith weightless shaft whirling