Nonlinear transverse vibrations of a slightly curved beam resting on multiple springs
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Date
2016
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Abstract
In this study, nonlinear vibrations of a slightly curved beam of arbitrary rise functions is handled in case it rests on multiple springs. The beam is simply supported on both ends and is restricted in longitudinal directions using the supports. Thus, the equations of motion have nonlinearities due to elongations during vibrations. The method of multiple scales (MMS), a perturbation technique, is used to solve the integro-differential equation analytically. Primary and 3 to 1 internal resonance cases are taken into account during steady-state vibrations. Assuming the rise functions are sinusoidal in numerical analysis, the natural frequencies are calculated exactly for different spring numbers, spring coefficients, and spring locations. Frequency-amplitude graphs and frequency-response graphs are plotted by using amplitude-phase modulation equations.
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Keywords
Control nonlinearities , Curved beams and girders , Differential equations , Frequency response , Integrodifferential equations , Perturbation techniques , Phase modulation , Internal resonance , Longitudinal direction , Method of multiple scale , Modulation equations , Non-linear vibrations , Nonlinear transverse vibration , Spring coefficient , Steady state vibrations , Equations of motion