Graduate Thesis Or Dissertation
 

Forced vibration of a beam-pendulum system

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  • These studies are concerned with the forced motion of a two-degree-of-freedom system consisting of a "flexible beam" supported by pendulum type hangers. Using an asymptotic method, an approximate solution to the nonlinear equations of motion was found. The solution takes the form of a series in powers of the amplitude of vibration ratio μ. A mechanical model was built and data were taken for purposes of verifying the analytical steady state solution. The results are presented in the form of maximum amplitude of pendulum swing and maximum "beam" deflection curves plotted as functions of the forcing frequency ratio. Experimental results were found to compare quite favorably with the analytically predicted solution except for several resonant peaks thought to be a part of the higher order approximations not analyzed here. As μ was made smaller, agreement was better. As a result of this work, some important phenomena have been been discovered which do not appear in the solution to the linearized equations of motion.
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