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.