Abstract
Flexible structure, such as beam or thin plate, would be unstable for some external forces. For example, in-plane excitation causes parametric resonance, and out of plane excitation causes forced resonance. In this study, dynamics of both horizontally and vertically excited slender cantilever beam was analyzed. The beam is assumed inextensible Euler-Bernoulli beam. Governing equation of motion has nonlinear elastic term and nonlinear inertia term. Applying Galerkin's method for the first bending mode, forced Mathieu's equation is derived. Frequency response is obtained by harmonic balance method, and its stability is investigated by phase plane method.
