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
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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