On the Motion of Rotating Shafts Including an Approximate Solution for the Case of Constant Angular Acceleration |
Common terms and phrases
accelerated shaft angular speeds angular velocity assumption becomes infinite Bernoulli-Euler equations boundary conditions C₁ C₂ center line CONSTANT ANGULAR ACCELERATION constant speed CORNELL UNIVERSITY LIBRARY critical speed d²f₁ differential equation disc dt d²fz dt² dx² Ecuations Ecuations 11 end cross section equation 40 equations 38 equations 9 f₁ f₁(t f₂ f₂(t Figure III flection graph I₁ initial conditions Initial Curvature initial deflected form initially curved shaft initially straight shaft llo wa+w M₂ maintain any given maximum deflection occurs Norman Clifford Small p₁ P₂ particular solution problem rlane ROTATING SHAFTS satisfy equation 46 shaft is given shaft is initially shown in Figure solution of equation stable solution stable vibration steam turbine Substituting equation 24 t₂ thesis transient whirl uniform acceleration w=kt W=WC wc-w wc+co wc+w weightless shaft Zæp zép Zwc Zwc Ζωο