Wang Heling, Ning Xin, Li Haibo, Luan Haiwen, Xue Yeguang, Yu Xinge, Fan Zhichao, Li Luming, Rogers John A, Zhang Yihui, Huang Yonggang
Departments of Civil and Environmental Engineering, Mechanical Engineering, and Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, USA.
Department of Materials Science and Engineering, Frederick Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA.
J Mech Phys Solids. 2018 Mar;112:187-208. doi: 10.1016/j.jmps.2017.12.002. Epub 2017 Dec 8.
Micro-electromechanical systems (MEMS) that rely on structural vibrations have many important applications, ranging from oscillators and actuators, to energy harvesters and vehicles for measurement of mechanical properties. Conventional MEMS, however, mostly utilize two-dimensional (2D) vibrational modes, thereby imposing certain limitations that are not present in 3D designs (e.g., multi-directional energy harvesting). 3D vibrational microplatforms assembled through the techniques of controlled compressive buckling are promising because of their complex 3D architectures and the ability to tune their vibrational behaviour (e.g., natural frequencies and modes) by reversibly changing their dimensions by deforming their soft, elastomeric substrates. A clear understanding of such strain-dependent vibration behaviour is essential for their practical applications. Here, we present a study on the linear and nonlinear vibration of such 3D mesostructures through analytical modeling, finite element analysis (FEA) and experiment. An analytical solution is obtained for the vibration mode and linear natural frequency of a buckled ribbon, indicating a mode change as the static deflection amplitude increases. The model also yields a scaling law for linear natural frequency that can be extended to general, complex 3D geometries, as validated by FEA and experiment. In the regime of nonlinear vibration, FEA suggests that an increase of amplitude of external loading represents an effective means to enhance the bandwidth. The results also uncover a reduced nonlinearity of vibration as the static deflection amplitude of the 3D structures increases. The developed analytical model can be used in the development of new 3D vibrational microplatforms, for example, to enable simultaneous measurement of diverse mechanical properties (density, modulus, viscosity etc.) of thin films and biomaterials.
依赖结构振动的微机电系统（MEMS）有许多重要应用，从振荡器、致动器到能量采集器以及用于测量机械性能的载体。然而，传统的MEMS大多利用二维（2D）振动模式，从而带来了一些三维设计中不存在的限制（例如，多向能量采集）。通过可控压缩屈曲技术组装的三维振动微平台很有前景，因为它们具有复杂的三维结构，并且能够通过使柔软的弹性体基底变形来可逆地改变其尺寸，从而调整其振动行为（例如，固有频率和模式）。清楚了解这种应变相关的振动行为对于它们的实际应用至关重要。在这里，我们通过解析建模、有限元分析（FEA）和实验，对这种三维介观结构的线性和非线性振动进行了研究。获得了屈曲带的振动模式和线性固有频率的解析解，表明随着静态挠度幅值的增加会发生模式变化。该模型还给出了线性固有频率的标度律，可扩展到一般的复杂三维几何结构，有限元分析和实验验证了这一点。在非线性振动范围内，有限元分析表明增加外部载荷的幅值是拓宽带宽的有效手段。结果还揭示了随着三维结构静态挠度幅值的增加，振动非线性减小。所建立的解析模型可用于开发新型三维振动微平台，例如，能够同时测量薄膜和生物材料的多种机械性能（密度、模量、粘度等）。
