Analytical solution for primary resonances of a rotating shaft with stretching non-linearity
2008 ◽
Vol 222
(9)
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pp. 1655-1664
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Keyword(s):
In this paper, primary resonances of a simply supported rotating shaft with stretching non-linearity are studied. Rotary inertia and gyroscopic effects are included, but shear deformation is neglected. The equations of motion are derived with the aid of Hamilton's principle and then transformed to the complex form. To analyse the primary resonances, the method of multiple scales is directly applied to the partial differential equation of motion. The frequency—response curves are plotted for the first two modes. It is shown that these resonance curves are of the hardening type. The effects of eccentricity and the damping coefficient are investigated on the steady-state response of the rotating shaft.
Keyword(s):
2003 ◽
Vol 25
(2)
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pp. 251-265
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