Question: The composite rotor shown in Figure is supported on bearings that are modeled as linear displacement springs. Assume small motion (pitch and bounce) about tyhe rotor's equilibrium position. System properties are d1 = 6 in., D3 = 2 in., L1 = 20 in., D1 = 7.5 in., L2 = 18 in., D2 = 10.75 in., d2 = 6 in., kA = 750,000lb/in., and kB = 900,000 lb/in. The shaft D3 goes through the entire body and is amde of steel (ρs = 0.283lb/in.3). Disk D1 is made of steel, and disk D2 is made from brass (ρs = 0.283lb/in.3).
Tasks: (a) Select coordinates, develop the equations of motion for the system, and present them in matrix format.
(b) Obtain the eigenvalues and eigenvectors for the system.
(c) Draw mode shape plots for the eigenvectors.
(d) What are the natural frequencies?