Özkaya E.Sarigül M.Boyaci H.2024-07-222024-07-22201610275851http://akademikarsiv.cbu.edu.tr:4000/handle/123456789/15995In 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.EnglishAll Open Access; Bronze Open Access; Green Open AccessControl nonlinearitiesCurved beams and girdersDifferential equationsFrequency responseIntegrodifferential equationsPerturbation techniquesPhase modulationInternal resonanceLongitudinal directionMethod of multiple scaleModulation equationsNon-linear vibrationsNonlinear transverse vibrationSpring coefficientSteady state vibrationsEquations of motionArticle10.20855/ijav.2016.21.4433