Effects of modal coupling on the dynamics of parametrically and directly excited cylindrical shells |
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| Affiliation: | 1. School of Civil Engineering, Federal University of Goiás, UFG, Av. Universitária, No. 1488, Setor Universitário, 74605-220 Goiás, GO, Brazil;2. Department of Civil Engineering, Pontifical Catholic University, PUC-Rio, Rua Marquês de São Vicente, No. 225, Gávea, 22453-900 Rio de Janeiro, RJ, Brazil;1. Department of Mechanical Engineering, McGill University, Montreal, Quebec, Canada H3A 0C3;2. School of Mechanical, Materials and Mechatronic Engineering, University of Wollongong, NSW 2522, Australia;1. Civil Engineering Department, The Higher Technological Institute, Ramadan 10th city, Egypt;2. Basic Sciences Department, Banha University, Shobra, Cairo, Egypt;3. Deputy Secretary General, Supreme Council of Universities, and Structural Engineering Department, Cairo University, Giza, Egypt;1. Department of Electronics, Peking University, No. 5 Yiheyuan Road, Haidian District, Beijing 100871, China;2. Institute of Advanced Technology, Peking University, No.5 Yiheyuan Road, Haidian District, Beijing 100871, China;1. Luxembourg Institute of Science and Technology, 5, avenue des Hauts-Fourneaux, L-4362 Esch-sur-Alzette, Luxembourg;2. Euro-Composites, B.P. 24, Zone Industrielle, L-6401 Echternach, Luxembourg |
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| Abstract: | Cylindrical shells exhibit a dense frequency spectrum, especially in the lowest frequency range. In addition, due to the circumferential symmetry, frequencies occur in pairs. So, in the vicinity of the lowest natural frequencies, several equal or nearly equal frequencies may occur, leading to multiple internal resonances. The aim of the present work is to investigate the dynamic behavior and stability of cylindrical shells under lateral and axial forcing with equal natural frequencies. The shell is modeled using the Donnell nonlinear shallow shell theory. A consistent modal solution for this problem is deduced and used to discretize the equations of motion by applying the Galerkin method. A parametric analysis is conducted to clarify the influence of the modal interaction among these nonlinear vibration modes on coexisting solutions, bifurcations, resonances curves and stability boundaries of the shell. |
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| Keywords: | Cylindrical shell Modal coupling Modal interaction Internal resonances Parametric instability Dynamic integrity |
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