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首页> 外文会议>Proceedings of the ASME international design engineering technical conferences and computers and information in engineering conference 2016 >NONLINEAR PHENOMENA IN THE SINGLE-MODE DYNAMICS IN AN AFM CANTILEVER BEAM
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NONLINEAR PHENOMENA IN THE SINGLE-MODE DYNAMICS IN AN AFM CANTILEVER BEAM

机译：AFM悬臂梁单模动力学中的非线性现象

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This study deals with the nonlinear dynamics arising in an atomic force microscope cantilever beam. After analyzing the static behavior, a single degree of freedom Galerkin reduced order model is introduced, which describes the overall scenario of the structure response in a neighborhood of the primary resonance. Extensive numerical simulations are performed when both the forcing amplitude and frequency are varied, ranging from low up to elevated excitations. The coexistence of competing attractors with different characteristics is analyzed. Both the non-resonant and the resonant behavior are observed, as well as ranges of inevitable escape. Versatility of behavior is highlighted, which may be attractive in applications. Special attention is devoted to the effects of the tip-sample separation distance, since this aspect is of fundamental importance to understand the operation of an AFM. We explore the metamorphoses of the multistability region when the tip-sample separation distance is varied. To have a complete description of the AFM response, comprehensive behavior charts are introduced to detect the theoretical boundaries of appearance and disappearance of the main attractors. Also, extensive numerical simulations investigate the AFM response when both the forcing amplitude and the tip-sample separation distance are considered as control parameters. The main features are analyzed in detail and the obtained results are interpreted in terms of oscillations of the cantilever-tip ensemble. However, we note that all the aforementioned results represent the limit when disturbances are absent, which never occurs in practice. Here comes the importance of overcoming local investigations and exploring dynamics from a global perspective, by introducing dynamical integrity concepts. To extend the AFM results to the practical case where disturbances exist, we develop a dynamical integrity analysis. After performing a systematic basin of attraction analysis, integrity profiles and integrity charts are drawn. The curves of constant percentage of integrity measure are detected, highlighting that they provide valuable quantitative information about the changes in the structural safety. Robustness as well as vulnerability to disturbances is examined. The practical range of existence of each branch is observed to be smaller, and sometimes remarkably smaller than the theoretical one. The issue of the dynamical integrity analysis in the AFM design is addressed, showing that these curves may be used to establish safety factors in order to operate the AFM according to the desired outcome, depending on the expected disturbances. Physical meaning and practical relevance of the nonlinear phenomena in the AFM engineering design are discussed.
机译：这项研究处理原子力显微镜悬臂梁中产生的非线性动力学。在分析了静态行为之后，引入了一个单自由度Galerkin降阶模型，该模型描述了一次共振附近结构响应的整体情况。当强迫幅度和频率都变化时，将进行广泛的数值模拟，范围从低到高。分析了具有不同特征的竞争吸引子的共存。观察到非共振和共振行为，以及不可避免的逸出范围。突出了行为的多功能性，这在应用程序中可能很有吸引力。特别注意尖端样品分离距离的影响，因为这对于理解原子力显微镜的操作至关重要。当尖端样品分离距离变化时，我们探索了多稳定性区域的变质。为了全面描述AFM响应，引入了综合行为图以检测主要吸引子出现和消失的理论边界。而且，当将强制振幅和尖端样本分离距离都视为控制参数时，大量的数值模拟研究了AFM响应。详细分析了主要特征，并根据悬臂尖端整体的振荡来解释获得的结果。但是，我们注意到，所有上述结果都代表了没有干扰时的极限，实际上这是从未发生过的。通过引入动态完整性概念，克服本地调查并从全球角度探讨动态的重要性就此而来。为了将AFM结果扩展到存在干扰的实际情况，我们进行了动力完整性分析。在进行了系统的吸引力分析后，绘制了完整性概况和完整性图表。检测到恒定百分比的完整性度量曲线，突出表明它们提供了有关结构安全性变化的有价值的定量信息。检查了鲁棒性和对干扰的脆弱性。观察到每个分支的实际存在范围较小，有时甚至比理论范围小得多。解决了AFM设计中的动态完整性分析问题，该分析表明，可以使用这些曲线来建立安全系数，以便根据期望的结果（取决于预期的干扰）来操作AFM。讨论了AFM工程设计中非线性现象的物理意义和实际意义。

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