This paper reports the primary resonance of single mode forced, undamped, bending vibration of nonuniform sharp cantilevers of rectangular cross-section, constant width, and convex parabolic thickness variation. The case of nonlinear curvature, moderately large amplitudes, is considered. The method of multiple scales is applied directly to the nonlinear partial-differential equation of motion and boundary conditions. The frequency-response is analytically determined, and numerical results show a softening effect of the geometrical nonlinearities.
- Dynamic Systems and Control Division
On Nonlinear Forced Response of Nonuniform Beams
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Caruntu, DI. "On Nonlinear Forced Response of Nonuniform Beams." Proceedings of the ASME 2008 Dynamic Systems and Control Conference. ASME 2008 Dynamic Systems and Control Conference, Parts A and B. Ann Arbor, Michigan, USA. October 20–22, 2008. pp. 403-408. ASME. https://doi.org/10.1115/DSCC2008-2157
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