Buckling and nonlinear dynamics of elastically coupled double-beam systems |
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| Institution: | 1. DipMat, Università degli studi di Salerno, Italy;2. DICATAM, Università degli studi di Brescia, Italy;1. State Key Laboratory for Manufacturing and Systems Engineering, Xi׳an Jiaotong University, Xi׳an, Shaanxi 710049, PR China;2. Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA;3. Department of Mechanical and Aerospace Engineering, The Ohio State University, Columbus, OH 43210, USA;1. Department of Mathematics, Foshan University, Foshan 528000, China;2. Oriental Science and Technology College, Hunan Agricultural University, Changsha 410128, China;1. Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran;2. Institute of Nanoscience & Nanotechnology, University of Kashan, Kashan, Iran;1. University of Niš, Department of Mechanical Engineering, A. Medvedeva 14, 18000 Niš, Serbia;2. Mathematical Institute of the SANU, Serbian Academy of Sciences and Arts, Kneza Mihaila 36, 11001 Belgrade, Serbia;1. Unit of Applied Mechanics, University of Innsbruck, 6020 Innsbruck, Austria;2. Dipartimento di Ingegneria Civile, dell’Ambiente, dell’Energia e dei Materiali (DICEAM), University of Reggio Calabria, 89124 Reggio Calabria, Italy;3. Department of Mathematical Sciences, University of Liverpool, Liverpool, UK |
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| Abstract: | This paper deals with damped transverse vibrations of elastically coupled double-beam system under even compressive axial loading. Each beam is assumed to be elastic, extensible and supported at the ends. The related stationary problem is proved to admit both unimodal (only one eigenfunction is involved) and bimodal (two eigenfunctions are involved) buckled solutions, and their number depends on structural parameters and applied axial loads. The occurrence of a so complex structure of the steady states motivates a global analysis of the longtime dynamics. In this regard, we are able to prove the existence of a global regular attractor of solutions. When a finite set of stationary solutions occurs, it consists of the unstable manifolds connecting them. |
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| Keywords: | Double-beam system Steady states Buckling Nonlinear oscillations Global attractor |
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