Zhang Yin, Petrov Yuri, Zhao Ya-Pu
State Key Laboratory of Nonlinear Mechanics (LNM), Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China.
School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, China.
Micromachines (Basel). 2021 Mar 19;12(3):324. doi: 10.3390/mi12030324.
Overhang provides a simple but effective way of coupling (sub)structures, which has been widely adopted in the applications of optomechanics, electromechanics, mass sensing resonators, etc. Despite its simplicity, an overhanging structure demonstrates rich and complex dynamics such as mode splitting, localization and eigenfrequency veering. When an eigenfrequency veering occurs, two eigenfrequencies are very close to each other, and the error associated with the numerical discretization procedure can lead to wrong and unphysical computational results. A method of computing the eigenfrequency of two overhanging beams, which involves no numerical discretization procedure, is analytically derived. Based on the method, the mode localization and eigenfrequency veering of the overhanging beams are systematically studied and their variation patterns are summarized. The effects of the overhang geometry and beam mechanical properties on the eigenfrequency veering are also identified.
悬臂提供了一种简单而有效的（子）结构耦合方式，已在光机械、机电、质量传感谐振器等应用中广泛采用。尽管其结构简单，但悬臂结构展现出丰富而复杂的动力学特性，如模式分裂、局域化和本征频率转向。当发生本征频率转向时，两个本征频率彼此非常接近，并且与数值离散化过程相关的误差可能导致错误和不符合物理实际的计算结果。本文解析推导了一种计算两个悬臂梁本征频率的方法，该方法无需数值离散化过程。基于此方法，系统地研究了悬臂梁的模式局域化和本征频率转向，并总结了它们的变化规律。还确定了悬臂几何形状和梁的力学性能对本征频率转向的影响。
