Abstract
The dynamic stability of a cantilever beam attached to a translational/rotational base is studied in this paper. Equations of motion for the simple flexure cantilever beam with a tip mass are derived by Hamilton's principle, and then transformed into a set of ordinary differential equations by applying variable transformation and the Galerkin method. Hsu's method is extended to investigate the instability regions of the non-homogeneous solutions. The main objective of this paper is to identify instability regions of the system for various combinations of the excitation frequencies and amplitudes of the oscillations. The instability regions of the system with and without tip mass and effects of the rotational angle velocities are compared and discussed by using Hsu's and Bolotin's methods.
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