Superharmonic resonances of nonlinear forced bending vibrations of moderately large curvature of nonuniform cantilever beams of rectangular cross section and a sharp end are reported. Cantilevers of constant width and parabolic thickness variation are considered in this paper. Method of multiple scales is directly applied to the governing partial-differential equation of motion and boundary conditions. Two problems, zero- and first-order problem, result. Solving the zero-order problem, the linear modes are obtained in terms of hypergeometric functions by using the factorization method. The first-order problem provides the amplitude and phase evolution equation and consequently the superharmonic frequency response of the nonlinear system.
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On Superharmonic Resonances of Nonlinear Nonuniform Beams
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Caruntu, DI. "On Superharmonic Resonances of Nonlinear Nonuniform Beams." Proceedings of the ASME 2008 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. Smart Materials, Adaptive Structures and Intelligent Systems, Volume 2. Ellicott City, Maryland, USA. October 28–30, 2008. pp. 495-500. ASME. https://doi.org/10.1115/SMASIS2008-599
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