Nonlinear transverse vibrations of a slightly curved beam carrying a concentrated mass

<正> In this study, a slightly curved Euler Bernoullibeam carrying a concentrated mass was handled. The beamwas resting on an elastic foundation and simply supportedat both ends. Effects of the concentrated mass on nonlinearvibrations were investigated. Sinusoidal and parabolictype functions were used as curvature functions. Equationsof motion have cubic nonlinearities because of elongationsduring vibrations. Damping and harmonic excitationterms were added to the equations of motion. Method of multiplescales, a perturbation technique, was used for solvingintegro-differential equation analytically. Natural frequencieswere calculated exactly for different mass ratios, masslocations, curvature functions, and linear elastic foundationcoefficients. Amplitude-phase modulation equations werefound by considering primary resonance case. Effects ofnonlinear terms on natural frequencies were calculated.Frequency-amplitude and frequency-response graphs wereplotted. Finally effects of concentrated mass and chosen curvaturefunction on nonlinear vibrations were investigated.