Nonlinear Transverse Vibrations of a Slightly Curved Beam Carrying Multiple Concentrated Masses: Primary Resonance
In this study, nonlinear vibrations of curved Euler-Bernoulli beams carrying arbitrarily placed concentrated masses have been investigated. Sag-to-span ratio of the beam, which was assumed to have sinusoidal curvature function at the beginning, was taken as 1/10. Equations of motion were obtained by using Hamilton Principle. Cubic nonlinear terms aroused at the mathematical model because of the elongations occurred during the vibrations of the simple-simple supported beam. Method of multiple scales, a perturbation technique, was used for solving the equations of motion about analytically. Natural frequencies were obtained for different numbers, sizes and locations of the masses as control parameters. Analytical solutions were found for primary resonance case. Frequency-amplitude and frequency-response graphs were drawn using different control parameters for these resonance cases. Stability of the solutions was investigated in detail.
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