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Missouri University of Science and Technology

Machinery -- Vibration<br />Machinery -- Vibration -- Computer simulation<br />Machinery -- Testing -- Mathematical models<br />Structural dynamics -- Mathematical models

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## Full-Text Articles in Mechanical Engineering

Vibration Of A Rotating Cantilever Beam With An Independently Rotating Disk On The Free End, Darrell Blaine Crimmins

#### Vibration Of A Rotating Cantilever Beam With An Independently Rotating Disk On The Free End, Darrell Blaine Crimmins

*Masters Theses*

"This thesis provides a vibration analysis of a rotating cantilever beam with an independently rotating thin circular disk on the free end. The exact differential equations of the system as defined by classical Bernoulli-Euler beam theory are written using the methods of the calculus of variations. The exact equations are not solved, but two different approximations are found by assuming a cubic polynomial deflection curve and applying the equation of Lagrange. The solutions are restricted to small deflections of the beam and a shaft stiffness which permits a deflection in only a single plane. Nonlinear differential equations result in the ...