Nonlinear Periodic Systems with Mode Localization and Motion Confinement Characteristics

具有模式局部化和运动限制特性的非线性周期系统

• 批准号: 9207318
• 负责人: Alexander Vakakis
• 金额: $ 8.77万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-09-01 至 1996-02-29
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9207318&HistoricalAwards=false
• 关键词: Nonlinear; Periodic; Systems; Mode; Localization

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.*** //

拟议工作的主要范围是表明，由于有限的振幅运动，具有几何非线性的弱耦合，柔性，循环组件，具有本地的非线性模式，即自由振荡，在此期间，运动仅限于其子系统的一个子系统。 。这将通过使用多个尺度平均方法并研究相应的振幅和相位调制方程来实现。柔性模式之间的内部共振对模式定位的影响将进行分析研究，并将考虑由于外部谐波负载而引起的系统的力响应。将会表明，弱耦合的循环组件具有基本的，次谐波和超谐的局部共振，在此期间，其数量有限的子系统共鸣。然后，由于非线性模式定位而导致的外部产生的干扰的运动限制将通过数值计算进行研究，涉及有限元和Gallerkin方法。这项研究的主要目的是表明某些弱耦合，非线性循环系统的固有动力学导致外部诱导的干扰的运动限制。然后，此类系统的可控性大大提高，因为在设计用于被动或主动振动隔离时，只需要考虑其数量有限的子结构的动力学，而不是考虑整个循环组件的响应。*** //