Analysis Of Vibration Characteristics Of Circular Plate Embedded With Acoustic Black Hole

Because of its unique geometric shape,circular plate structure widely appears in every scene in production practice,so the research on vibration control based on circular plate structure is of great practical significance.Acoustical black hole structure is a kind of variable thickness structure whose thickness varies in the form of a specific power law function,in which the wave velocity of elastic waves decreases gradually with the change of thickness,which can be reduced to 0 in ideal conditions.correspondingly,it can gather at the tip of the structure without reflection,so as to realize the accumulation of energy and vibration control.Because of the piecewise variable thickness characteristics of the structure,the modeling is more difficult,and the applicability of the traditional displacement function expression for the structure also needs to be verified.so at present,in view of the lack of theoretical model from the point of view of vibration analysis of the circular plate structure with embedded acoustic black hole,this paper considers the key problems to be solved,and carries on the theoretical modeling and analysis of the circular plate structure with embedded acoustic black hole under different characteristic materials.Firstly,this paper takes the circular plate structure of embedded acoustic black hole under isotropic material as the object of theoretical modeling,and chooses to introduce the improved Fourier-Bessel series into the displacement tolerance function to solve the problem of discontinuity at the boundary.And when using the energy method to solve the problem,the superposition theory is introduced to separate and solve the circular plate structure of the acoustic black hole and then integrate it to obtain the matrix equations corresponding to the structure.And on the basis of the constructed theoretical model of free vibration,it is extended to forced vibration,and the mathematical model of common load forms is established from the point of view of frequency domain,and then the harmonic response of the structure is analyzed combined with the free vibration model.and the feasibility of the method is proved by the comparison of the results.Then,the structural characteristic parameters of the acoustic black hole embedded with circular plate are analyzed,and the control variables and joint comparison methods are used to analyze the influence on the vibration characteristics from the aspects of depth,width,power index and truncation thickness.the damping effects of different types of circular plate structures are compared to provide reference for structural design.Then the above theoretical model is extended to the circular thin plate structure with embedded acoustic black hole under orthotropic materials.after modeling its characteristics,the free vibration characteristics and the forced vibration harmonic response characteristics in frequency domain are also analyzed.Finally,the modal experiments of fixed support and free boundary constraints are designed for the circular plate structure of acoustic black hole under the two parameters of aperture ratio and depth ratio.the natural frequency of the experimental structure and the corresponding modal modes can be obtained by processing the experimental data.the correctness of the theoretical model is further proved by the comparative analysis with the theoretical and simulation results.