Eigenvalues of an axially loaded cantilever beam with an eccentric end   rigid body
  An analytical form of the characteristic equation for a vertically mounted cantilever beam with an end rigid body is obtained and solved for the eigenvalues of the structure. The effect of the weight of the structure is taken into consideration by estimating the load as a function of the length of the beam. The mass, rotary inertia and eccentricity of the end rigid body are demonstrated to considerably affect the eigenvalues of the structure. 
S. Amir Mousavi Lajimi, Glenn R. Heppler
math.AP physics.class-ph