JSME International Journal Series C Mechanical Systems, Machine Elements and Manufacturing
Online ISSN : 1347-538X
Print ISSN : 1344-7653
ISSN-L : 1344-7653
Nonlinear Analysis of a Parametrically Excited Cantilever Beam : Effect of the Tip Mass on Stationary Response(Special Issue on Nonlinear Dynamics)
Hiroshi YABUNOYoshiro IDENobuharu AOSHIMA
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1998 Volume 41 Issue 3 Pages 555-562

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Abstract

For a parametrically excited cantilever beam the effect of the tip mass on the nonlinear characteristics of the frequency-response is theoretically presented.The equation of motion governing the system is formulated by Hamilton's pronciple, taking into account the inertia and curvature nonlinearities and a quadratic damping effect of the beam.Using the method of multiple scales and center manifold theory, the bifurcation points of the frequency-response curve are analyzed.It follows that there are two transcritical bifurcations, and in addition to these bifurcations there are two saddle-node bifurcations, in the cases when the tip mass is relatively light and heavy, respectively.Experiments are also performed and the results show good qualitative agreement with the theoretical ones.

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© The Japan Society of Mechanical Engineers
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