Investigation On Flexural Vibration Of Complex Holed Beams Immersed In Viscous Fluids

As two kinds of significant flexural beams,holed and V-shaped beams have been widely used in detection system represented by atomic force microscope(AFM),micro-nano mechanical sensing applications and actuators,energy harvesting and biomimetic propulsion.Such complex holed beams are usually used for sophisticated detection,sensing and performance characterization in viscous fluids,thus making it intractable to study the vibration characteristics of the structure by considering the fluidstructure interaction between the complicated geometry and viscous fluids.It is of fundamental importance to investigate the vibration characteristics of complex holed 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,the vibration characteristics of holed and Vshaped beams immersed in viscous fluids have been investigated and the complex hydrodynamic function is introduced to describe the hydrodynamic loading by solving the two-dimensional Navier-Stokes equations.The underwater vibration models are developed based on Euler-Bernoulli beam theory and the experimental verifications are carried out.The main research work and results are as below:(1)An underwater vibration model is developed to depict the dynamic behavior of holed beams and a complex hydrodynamic function depending on the frequency parameter is obtained by two-dimensional computational fluid dynamics analysis(CFD).It demonstrates that the added mass and hydrodynamic damping decrease as the vibration frequency increases.The frequency response of holed beams in viscous fluids is obtained theoretically.The experimental verifications on flexural vibrations of several holed beams with different geometrical sizes are carried out to validate the expression of hydrodynamic function and the underwater dynamic model.(2)An underwater vibration model is developed to depict the dynamic behavior of V-shaped beams by taking into account the variable gap to width ratio in beam's cross-section 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.It illustrates that the added mass and hydrodynamic damping decrease remarkably as the gap to width ratio and the frequency parameter increase.Besides,a three-dimensional simulation is performed to verify the proposed computational approach and hydrodynamic function in the two-dimensioanal analysis.(3)The effect of nonlinear phenomena on the hydrodynamic loading for finite vibration amplitude is investigated.The amplitude parameter is introduced to futher correct the hydrodynamic function of V-shaped beams.As a result,the hydrodynamic function is governed by the interplay of the gap to width ratio,the frequency parameter and the amplitude parameter.It is shown that,on one hand,the amplitude has no obvious effect on the added mass,on the other hand,it significantly disturbs the nonlinear hydrodynamic damping: the nonlinear hydrodynamic damping increases markedly with the amplitude.Moreover,the experimental verifications on both small and finite amplitude vibrations of several V-shaped beams with different geometrical sizes are carried out and the underwater dynamic model of V-shaped beams modified by the gap to width ratio and amplitude parameter is validated.In a word,this work can be useful for the further design and the commercial applications of the complex holed beams.