Parametrically excited transverse oscillations of columns are studied. The amplitude of the response is taken to be small, but finite; hence, stretching of the neutral axis is significant. Nonlinear strain-displacement relationships are used. A general method of analysis is first described and then used to solve two numerical examples—one without and one with internal resonances. The results show that jump phenomena exist, that the same excitation can produce two rather different responses, and that, when there is an internal resonance, two rather different excitations can produce practically the same response.

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