On the dynamics of Rayleigh beams resting on fractional-order viscoelastic Pasternak foundations subjected to moving loads |
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| Affiliation: | 1. Department of Mechanical Engineering and Aeronautics, University of Patras, Patras, Greece;2. Department of Materials Science, University of Patras, Patras, Greece;1. College of Engineering and Technology, American University of the Middle East, Kuwait;2. Department of Econometrics and Business Statistics, Monash Business School, Monash University, Wellington Rd, Clayton, Victoria 3800, Australia;3. Department of Civil Engineering and Engineering Mechanics, The Fu Foundation School of Engineering and Applied Science, Columbia University, 500 West 120th Street, New York, NY 10027, USA;4. Dipartimento di Ingegneria (DI), Università degli Studi di Palermo, Viale delle Scienze, Palermo 90128, Italy;5. Department of Mathematical Sciences, University of Liverpool, Liverpool L697ZL, UK;1. Department of Mathematics,al. Armii Krajowej 21, Czestochowa University of Technology, Czestochowa 42-200, Poland;2. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, College of Mechanics and Materials, Hohai University, Nanjing 210098, China |
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| Abstract: | The standard averaging method is used to provide an analytical explanation on the effects of spacing loads, load velocity, order of the fractional viscoelastic property of shear layer material on the amplitude of the beam. The geometric nonlinearity is taken into account in the model. The analysis shows that, when the moving loads are uniformly distributed upon all the length of the structure, it vibrates the least possible. Moreover, as the order of the derivative increases, the resonant amplitude of the beam vibration decreases. In other hand, by means of Melnikov technique, a necessary condition for onset of horseshoes chaos resulting from heteroclinic bifurcation is derived analytically. We point out the critical weight of moving loads and order of the fractional derivative above which the system becomes unstable. |
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