黏性流体环境下V型悬臂梁结构流固耦合振动特性研究

V型悬臂梁结构在原子力显微镜、微纳机械传感器件中得到了广泛应用, 该结构通常在黏性流体环境下实现精密检测、传感与性能表征,同时也会使得结构的流固耦合振动特性更为复杂, 直接影响器件的动态性能.本文针对V型结构变截面、变刚度等复杂几何特征, 建立了黏性流体环境下V型悬臂梁结构的流固耦合动力学模型, 导出了基于截面孔宽比参数的梁结构的修正水动力函数, 确定了截面孔宽比和频率参数影响下V型悬臂梁结构的水动力函数;理论分析得到了黏性流体中V型梁结构的频率响应特性.同时, 设计了多种不同几何尺寸的V型梁结构, 并在水环境中开展了实验验证, 结果表明, 实验所得频率响应与理论分析结果吻合较好, 验证了V型梁结构水动力函数修正表达式及流固耦合动力学模型.此外, 基于该流固耦合动力学模型, 详细分析了不同流体黏度、V 型梁角度及尺寸变化对耦合系统振动特性的影响. 

ANALYSIS OF FLEXURAL VIBRATION OF V-SHAPED BEAMS IMMERSED IN VISCOUS FLUIDS

V-shaped beams have been widely used in atomic force microscope (AFM) and micro-nano mechanical sensing applications.The structure is usually used for sophisticated detection, sensing and performance characterization in viscous fluids, thus making it complex to study the vibration characteristics of the structure by considering the fluid-structure interaction between the complicated geometry and viscous fluids.It is of fundamental importance to investigate the vibration characteristics of V-shaped beams submerged in viscous fluids owing to the fact that the vibration characteristics will directly affect the dynamic properties of the applications.In this paper, an underwater vibration model is developed to depict the dynamic characteristics of V-shaped beams immersed in viscous fluids by taking into account the fact that the cross-section and bending stiffness of the V-shaped beam are variable along the beam axis.A complex hydrodynamic function in terms of the gap to width ratio and the frequency parameter is developed to describe the hydrodynamic loading where the complex hydrodynamic function is derived from the modified hydrodynamic function based on the gap to width ratio in beam\mathrm{\text{'}}s cross-section.Besides, the frequency response of V-shaped beams vibrating in viscous fluids is obtained theoretically.Moreover, the experimental verifications on flexural vibrations of several V-shaped beams with different geometrical sizes are carried out.It demonstrates that the experimental data is in good agreement with the theoretical results, thus validating the modified expression of hydrodynamic function and the underwater dynamic model.Besides, the effect of different fluid viscosities, angles of V-shaped beams and the scale of the geometry on the vibration characteristics of the coupling system is analyzed based on the proposed fluid-structure interaction model.