Numerical Simulation Of Chladni Plate Submerged In Fluid

When the thin plate vibrates,it can automatically gather the originally uniformly distributed particles on the plate,and form various forms of standing wave nodal line pattern called Chladni figure.The plate used to carry out the relevant test of the Chladni figures is generally called the Chladni plate.Due to the advantages of strong robustness,low cost,easy observation and high repeatability,the oscillator-driven Chladni figure is widely used in the development of more advanced applications such as particle manipulation,molecular pollution-free positioning,particle classification and so on.Many application scenarios need to immerse the Chladni plate in the fluid medium.As a powerful auxiliary means for experimental research and theoretical analysis,numerical simulation can provide a detailed description of the vibration of the plate and the complex dynamics of particles in the Chladni experiment,which is conducive to revealing the formation mechanism of the Chladni figure.Therefore,in this thesis,numerical simulation methods are used to study the Chladni plate immersed in fluid.The collision and movement of particles on the vibrating plates immersed in liquid involves the interaction of structure,fluid and discrete particles.There are many issues that need to be further researched in many directions,such as the impact of fluid on vibrating plates,the effect of fluid on particles,the collision between vibrating plates and particles,and the collision between particles.In this paper,the following work has been completed in the structural dynamics interpretation of the Chladni figure,the interaction between plate and fluid,and the numerical simulation of particle motion on the plate:(1)A simplified finite element model with appropriate boundary conditions for the oscillator-driven square plate is established based on parametric analysis.Through natural frequency and mode shape analysis,the resonant frequencies and Chladni figures in multiple sets of experiments are almost perfectly predicted and reproduced by the effective mass of the mode shape.For the steady-state vibration of the square plate at any given frequency,the amplitude nodal pattern can be quickly and accurately calculated by the mode shape superposition method,which is almost identical to the Chladni figures at the same frequency in the experiment.A clear physical interpretation of the Chladni figures of the oscillator-driven square plate is given by establishing a finite element model with appropriate boundary conditions.The Chladni figures of the oscillator-driven square plate at the resonant frequency can be interpreted as the mode shape corresponding to the natural frequency,and the Chladni figures at the non-resonant frequency can be interpreted as the superposition of multiple mode shapes.(2)The coupling of the plate element and the fluid element on both sides is realized by setting the double-layer plate element and the node freedom coupling,and the interaction between the plate and the fluid is simulated.The natural frequencies and vibration modes of a coupled system based on potential flow theory are analyzed using Adina software.The difference between the frequency of the plate immersed in air and the frequency in vacuum is within 1%,and the corresponding vibration mode shapes are almost identical.When the plate is immersed in water,the natural frequency of the coupling system is much lower than that of the plate in vacuum.The ratio of the frequency in water to the frequency in vacuum is between 27%and 49%.Of the eight resonant vibration modes identified,the shapes of 7 modes are not significantly different in water and vacuum,while the shapes of 1 mode are significantly different in water and vacuum.(3)A fluid-structure coupling analysis model based on viscous flow theory and Adina software is established by reasonably simplifying the Chladni experimental device in the water tank.The influence of element type,element size and time step on the solution result is analyzed.Based on the accompanying free vibration under simple harmonic excitation,a fast method to identify the natural frequency of the coupling system from the results of fluid-structure coupling calculation is proposed.The results of natural frequency identification show that the natural frequency of the plate in air is slightly smaller than that in vacuum.The natural frequency of a flat plate in water is far less than that in vacuum.With the increase of frequency,the ratio of the natural frequency of the plate in water to the frequency in vacuum gradually increases,and becomes obviously nonlinear.The natural frequency of the plate in water identified by the fluid-structure coupling vibration is slightly larger than the result of the modal analysis of the potential flow theory model.The influence of air and water on the damping of plate vibration is analyzed.Both air and water can greatly increase the damping of the coupling system.The amplitude distribution obtained by fluid-structure coupling calculation is in good agreement with the experimental results,indicating that the calculation results in this paper are correct.(4)A triangular mesh method for simulating the vibrating plate in the discrete element method is proposed,and the correct calculation of the impact force of the vibrating plate on particles is realized.A GPU accelerated parallel computing program,which can simulate the particle motion on a vibrating plate,is compiled with Taichi programming language.The program is tested with a typical example.The numerical simulation of the Chladni experiment was completed.The effects of excitation amplitude,time step,particle diameter,particle collision recovery coefficient,and particle number on the simulation results were investigated.The results obtained by the discrete element program under different excitation modes are almost identical with the experimental results.