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Titlebook: Normal Modes and Localization in Nonlinear Systems; Alexander F. Vakakis Book 2001 Springer Science+Business Media Dordrecht 2001 beam.bou

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發(fā)表于 2025-3-21 18:11:55 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書(shū)目名稱Normal Modes and Localization in Nonlinear Systems
編輯Alexander F. Vakakis
視頻videohttp://file.papertrans.cn/669/668029/668029.mp4
圖書(shū)封面Titlebook: Normal Modes and Localization in Nonlinear Systems;  Alexander F. Vakakis Book 2001 Springer Science+Business Media Dordrecht 2001 beam.bou
描述The nonlinear normal modes of a parametrically excited cantilever beam are constructed by directly applying the method of multiple scales to the governing integral-partial differential equation and associated boundary conditions. The effect of the inertia and curvature nonlin- earities and the parametric excitation on the spatial distribution of the deflection is examined. The results are compared with those obtained by using a single-mode discretization. In the absence of linear viscous and quadratic damping, it is shown that there are nonlinear normal modes, as defined by Rosenberg, even in the presence of a principal parametric excitation. Furthermore, the nonlinear mode shape obtained with the direct approach is compared with that obtained with the discretization approach for some values of the excitation frequency. In the single-mode discretization, the spatial distribution of the deflection is assumed a priori to be given by the linear mode shape ¢n, which is parametrically excited, as Equation (41). Thus, the mode shape is not influenced by the nonlinear curvature and nonlinear damping. On the other hand, in the direct approach, the mode shape is not assumed a priori; the no
出版日期Book 2001
關(guān)鍵詞beam; boundary layer; dynamical systems; dynamics; vibration; ordinary differential equations; partial dif
版次1
doihttps://doi.org/10.1007/978-94-017-2452-4
isbn_softcover978-90-481-5715-0
isbn_ebook978-94-017-2452-4
copyrightSpringer Science+Business Media Dordrecht 2001
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