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Abstract ：
Nonlinear vibrations of a cantilevered slender beam in case of internal resonance are investigated. We adopt the equations of motion of horizontal bending, vertical bending and torsion based on Hodges-Dowell beam theory. To find the conditions of internal resonance, we use the method of multiple scales to directly attack the partial-differential equations and the associated boundary conditions. We obtain the conditions of natural frequencies under which internal resonance may occur. The free vibrations of the beam with the presence of internal resonance are investigated. We obtained the equations governing the modulation of amplitudes and phases. After that, we consider the internal resonance in the beam model when one of the torsional modes involved in the internal resonance is excited by a primary resonance. The numerical results show that energy transfers among different modes of motion through nonlinear interactions. Copyright © 2011 by the American Institute of Aeronautics and Astronautics, Inc.
Keyword ：
Geometrically nonlinear Horizontal bending Internal resonance Method of multiple scale Modal interactions Nonlinear interactions Non-linear vibrations Numerical results
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| GB/T 7714 | Fu, Xiaowu , Qin, Zhanming . Modal interactions in a geometrically nonlinear cantilevered beam [C] . 2011 . |
| MLA | Fu, Xiaowu 等. "Modal interactions in a geometrically nonlinear cantilevered beam" . (2011) . |
| APA | Fu, Xiaowu , Qin, Zhanming . Modal interactions in a geometrically nonlinear cantilevered beam . (2011) . |
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Abstract ：
For the amplitude of the unsteady flow oscillation is large or large changes occur in the mean background flow such as limit cycle oscillation, the traditional proper orthogonal decomposition reduced order model based on linearized time or frequency domain small disturbance solvers can not capture the main nonlinear features. A new nonlinear reduced order model based on dynamically nonlinear flow equation was investigated. The nonlinear second order snapshot equation in time domain for proper orthogonal decomposition basis construction is obtained from the Taylor series expansion of the flow solver. The NLR 7301 Airfoil Configuration was used to validate the capability and efficiency of the new nonlinear reduced order model. The simulation results indicate that the proposed new reduced order model can capture the limit cycle oscillation of aeroelastic system very well, while the traditional proper orthogonal decomposition reduced order model will loses its way. Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc.
Keyword ：
Airfoil configuration Limit Cycle Oscillation (LCO) Nonlinear features Non-linear flow equations Proper orthogonal decompositions Reduced order models Small disturbances Taylor series expansions
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| GB/T 7714 | Chen, Gang , Li, Yue Ming , Yan, Gui Rong . Nonlinear POD reduced order model for limit cycle oscillation prediction [C] . 2010 . |
| MLA | Chen, Gang 等. "Nonlinear POD reduced order model for limit cycle oscillation prediction" . (2010) . |
| APA | Chen, Gang , Li, Yue Ming , Yan, Gui Rong . Nonlinear POD reduced order model for limit cycle oscillation prediction . (2010) . |
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Abstract ：
A subdomain collocation reproducing kernel approximation method is proposed. Subdomains are constructed by nonoverlapping Voronoi cells and a local weak form is defined over these subdomains. The standard RKPM shape functions are used directly for approximation, while weighting functions of the subdomain collocation method hold a constant value of unit only over a specific Voronoi cell. The body integration of the local weak form is now converted into much cheaper and efficient contour integration along the boundaries of Voronoi cells. It does not need to impose traction free boundary conditions explicitly in contrast to point collocation method. Furthermore, the method provides a natural background structure for performing h-adaptivity analysis straightforwardly. All these features constitute the subdomain collocation method a promising alternative to standard Galerkin method and point collocation method. Some elastostatics examples are presented to demonstrate the effectiveness, the convergence property, and the adaptivity performance of present method. (c) 2006 Elsevier B.V. All rights reserved.
Keyword ：
meshless method reproducing kernel approximation subdomain collocation Voronoi diagram
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| GB/T 7714 | Zhou, J. X. , Li, M. E. , Zhang, Z. Q. et al. A subdomain collocation method based on Voronoi domain partition and reproducing kernel approximation [J]. | COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING , 2007 , 196 (13-16) : 1958-1967 . |
| MLA | Zhou, J. X. et al. "A subdomain collocation method based on Voronoi domain partition and reproducing kernel approximation" . | COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 196 . 13-16 (2007) : 1958-1967 . |
| APA | Zhou, J. X. , Li, M. E. , Zhang, Z. Q. , Zou, W. , Zhang, L. . A subdomain collocation method based on Voronoi domain partition and reproducing kernel approximation . | COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING , 2007 , 196 (13-16) , 1958-1967 . |
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