Nonlinear Periodic Systems with Mode Localization and Motion Confinement Characteristics

拟议工作的主要范围是表明，弱 耦合的、柔性的、循环的组件， 由于有限振幅运动的非线性， 非线性模式，即，自由振荡， 主要局限于其中一个子系统。这将是 通过使用多尺度平均法实现， 研究相应的幅度和相位调制 方程弹性体之间的内共振效应 模态对模态局部化的影响将被解析地研究 以及系统在外部谐波作用下的力响应 负载将被考虑。结果表明，弱耦合 循环组合具有基波、次谐波和 超谐波局部共振，在此期间，只有有限的 它们的子系统的数量共振。运动约束 非线性模式引起的外部扰动 然后通过数值计算来研究局部化， 包括有限元和Gallerkin方法。的 本研究的主要目的是表明， 某些弱耦合，非线性循环系统，导致 外部感应扰动的运动限制。的 这样的系统的可控性大大提高，因为 在设计被动或主动隔振时， 只考虑有限数量的动态， 而不是考虑整体的反应 循环装配。* //

The principal scope of the proposed work is to show that weakly coupled, flexible, cyclic assemblies with geometric nonlinearities due to finite-amplitude motions, possess localized nonlinear modes, i.e., free oscillations during which the motion is mainly confined to only one of their subsystems. This will be achieved by using a multiple-scales averaging methodology and studying the corresponding amplitude and phase modulation equations. The effects of internal resonances between flexible modes on the mode localization will be analytically investigated and the force responses of the system due to external harmonic loads will be considered. It will be shown that weakly coupled cyclic assemblies possess fundamental, subharmonic and superharmonic localized resonances, during which only a limited number of their subsystems resonate. Motion confinement of externally generated disturbances due to nonlinear mode localization will then be investigated by numerical computations, involving finite element and Gallerkin methodologies. The principal aim of this study is to show that the inherent dynamics of certain weakly coupled, nonlinear cyclic systems, lead to motion confinement of externally induced disturbances. The controllability of such systems is then greatly improved, since in designing for passive or active vibration isolation, one needs only consider the dynamics of a limited number of their substructure instead of considering the response of the whole cyclic assembly.*** //