Dönmez Demir D.Bildik N.Sınır B.G.2024-07-222024-07-22201400220833http://akademikarsiv.cbu.edu.tr:4000/handle/123456789/16988The aim of this study is to develop a general model for beams and rods with fractional derivatives. Fractional time derivatives can represent the damping term in dynamical models of continuous systems. Linear differential operators with spatial derivatives make it possible to generalize a wide range of problems. The method of multiple scales is directly applied to equations of motion. For the approximate solution, the amplitude and phase modulation equations are obtained in terms of the operators. Stability boundaries are derived from the solvability condition. It is shown that a fractional derivative influences the stability boundaries, natural frequencies, and amplitudes of vibrations. The solution procedure may be applied to many problems with linear vibrations of continuous systems. © 2013 Springer Science+Business Media Dordrecht.EnglishDampingEquations of motionMathematical operatorsPerturbation techniquesAmplitude and phase modulationsApproximate solutionFractional derivativesLinear differential operatorsMethod of multiple scalePerturbation methodSolvability conditionsViscoelastic beamsContinuous time systemsArticle10.1007/s10665-013-9642-9