超声激励下微悬臂梁非线性动力学及其混沌控制

项目名称： 超声激励下微悬臂梁非线性动力学及其混沌控制

项目编号： No.11304286

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 陈赵江

作者单位： 浙江师范大学

项目金额： 25万元

中文摘要： 众所周知，超声激励下微悬臂梁非线性动力学特性对原子力声学显微镜(AFAM)的性能及其应用具有非常重要的影响。本项目旨在探讨超声激励下微悬臂梁强非线性振动机理及其控制方法。首先，拟通过建立合理的数学模型并结合数值仿真结果，对大振幅超声激励下微悬臂梁强非线性接触共振谱特性进行研究，分析DMT和JKR接触模型共振谱特性差异。其次，运用次谐Melnikov解析方法和数值方法分析微悬臂梁次谐波周期碰撞振动轨道的存在性、稳定性及分岔特性，并利用相平面图、Poincare映射、功率谱和Lyapunov 指数等研究n/m次谐波周期运动和混沌的非线性动力学行为。最后，我们在分析微悬臂梁振动通向混沌的途径及其特征的基础上，进而探索利用分区控制和延迟反馈方法对微悬臂梁非光滑动力学系统的混沌运动实施有效控制。上述研究将为强非线性接触共振谱和次谐波工作模式在AFAM中的应用奠定初步的理论基础。

中文关键词： 微悬臂梁；非线性动力学；原子力声学显微镜；超谐波与次谐波振动；混沌振动

英文摘要： It is well known that nonlinear dynamic characteristics of microcantilevers under ultrasonic excitation have a very important influence on the performances and applications of atomic force acoustic microscopy (AFAM). The overall aims of the research project are to explore the strongly nonlinear vibration mechanism and its control of microcantilever under ultrasonic excitation are still scarce. First, through the establishment of a reasonable mathematical model combined with numerical simulation results, the project intends to study the characteristics of nonlinear contact resonance spectrum of microcantilevers under large-amplitude ultrasonic excitation. Moreover, we will analyse the differences of resonance spectra characteristics of the DMT and JKR contact models. Then, the existence, stability and bifurcation characteristics of subharmonic periodic orbits of microcantilever's vibro-impact motion will be studied by analytical subharmonic Melnikov method and numerical method. By using phase plane method, Poincare map, power spectrum and Lyapunov exponents, the nonlinear dynamic behavior of n/m subharmonic motions and chaos are to be characterized. Finally, after analyzing the routes to chaos, we will investigate the feasibility of delayed feedback method and piecewise control strategy on the implementation of c

英文关键词： Microcantilever；Nonlinear dynamics；Atomic force acoustic microscopy；Superharmonic and subharmonic vibration；Chaotic vibration