Kavli Institute of Nanoscience, Delft University of Technology, Lorentzweg 1, 2628CJ Delft, The Netherlands.
Ultramicroscopy. 2012 Sep;120:41-7. doi: 10.1016/j.ultramic.2012.06.010. Epub 2012 Jun 23.
The nonlinear interactions between flexural and torsional modes of a microcantilever are experimentally studied. The coupling is demonstrated by measuring the frequency response of one mode, which is sensitive to the motion of another resonance mode. The flexural-flexural, torsional-torsional and flexural-torsional modes are coupled due to nonlinearities, which affect the dynamics at high vibration amplitudes and cause the resonance frequency of one mode to depend on the amplitude of the other modes. We also investigate the nonlinear dynamics of torsional modes, which cause a frequency stiffening of the response. By simultaneously driving another torsional mode in the nonlinear regime, the nonlinear response is tuned from stiffening to weakening. By balancing the positive and negative cubic nonlinearities a linear response is obtained for the strongly driven system. The nonlinear modal interactions play an important role in the dynamics of multi-mode scanning probe microscopes.
实验研究了微悬臂梁弯曲和扭转模态之间的非线性相互作用。通过测量对另一个共振模式运动敏感的一个模式的频率响应来证明这种耦合。由于非线性，弯曲-弯曲、扭转-扭转和弯曲-扭转模式相互耦合，这会影响高振动幅度下的动力学，并导致一个模式的共振频率取决于另一个模式的幅度。我们还研究了扭转模式的非线性动力学，这会导致响应的频率变硬。通过在非线性状态下同时驱动另一个扭转模式，可以将非线性响应从变硬调谐为变软。通过平衡正和负三次非线性，对于强驱动系统可以得到线性响应。非线性模态相互作用在多模态扫描探针显微镜的动力学中起着重要作用。
