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An analytical form of the characteristic equation for a vertically mountedcantilever beam with an end rigid body is obtained and solved for theeigenvalues of the structure. The effect of the weight of the structure istaken into consideration by estimating the load as a function of the length ofthe beam. The mass, rotary inertia and eccentricity of the end rigid body aredemonstrated to considerably affect the eigenvalues of the structure.

Eigenvalues of an axially loaded cantilever beam with an eccentric end rigid body