Abstract
This paper is concerned with the onset of parametric instability and the steady-state parametric response of a beam with variable cross-section resting on an elastic foundation. The problem is studied both theoretically and experimentally. The theoretical and experimental results show close agreement both for the boundaries of the principal and second temporal regions of instability and the steady-state response within the principal instability region. The experimental and theoretical results reveal that the slope factor of a beam with a linear variable cross-section has a pronounced effect upon the boundaries of the principal instability region. The effect of the elastic foundation is to decrease the width of the instability regions and the amplitude of the parametric response.
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