Nonlinear transverse vibrations of a slightly curved beam carrying a concentrated mass
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Date
2009
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Abstract
In this study, a slightly curved Euler Bernoulli beam carrying a concentrated mass was handled. The beam was resting on an elastic foundation and simply supported at both ends. Effects of the concentrated mass on nonlinear vibrations were investigated. Sinusoidal and parabolic type functions were used as curvature functions. Equations of motion have cubic nonlinearities because of elongations during vibrations. Damping and harmonic excitation terms were added to the equations of motion. Method of multiple scales, a perturbation technique, was used for solving integro-differential equation analytically. Natural frequencies were calculated exactly for different mass ratios, mass locations, curvature functions, and linear elastic foundation coefficients. Amplitude-phase modulation equations were found by considering primary resonance case. Effects of nonlinear terms on natural frequencies were calculated. Frequency-amplitude and frequency-response graphs were plotted. Finally effects of concentrated mass and chosen curvature function on nonlinear vibrations were investigated. © 2009 The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH.
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Control nonlinearities , Curved beams and girders , Foundations , Frequency response , Integrodifferential equations , Mechanics , Natural frequencies , Perturbation techniques , Concentrated mass , Cubic nonlinearities , Curvature function , Curved beams , Different mass , Elastic foundation , Euler Bernoulli beams , Harmonic excitation , Linear elastic , Method of multiple scale , Non-linear vibrations , Nonlinear elastic foundation , Nonlinear terms , Nonlinear transverse vibration , Primary resonance , Simply supported , Equations of motion