Solving Vibration Equations for Rigid Jeffcott Rotor Supported by Elliptical Bearings

Solving vibration equations for rigid Jeffcott rotors supported by elliptical bearings using MATLAB enables more detailed analysis and precise results. The implementation incorporates the Capone model for calculating bearing oil film forces, which accurately characterizes fluid flow behavior through numerical integration of Reynolds equation with proper boundary conditions. The algorithm typically involves solving second-order differential equations using ODE solvers like ode45, with proper initialization of rotor position and velocity parameters. Through this computational approach, trajectory plots of the disk center can be generated using MATLAB's plotting functions (plot, comet, or animatedline), providing clear visualization of rotor dynamics during operation. This methodology allows for comprehensive study of vibration parameters including amplitude and frequency characteristics through FFT analysis (using fft function) and time-domain response evaluation. Further investigation of this model can yield deeper insights into bearing design optimization, including parameter sensitivity studies and stability analysis using eigenvalue computation techniques.