Ladder Disc Characteristics

Thin plate in flexural vibration is an important part of ultrasonic vibration system. Its thickness is much smaller than the length. There are three boundary conditions:free, simply-supported and fixed. It has large radiation surface and low radiation resistance. The use of thin plate has increased with the development of ultrasonic technique in recent years. The thin plate achieved under fixed boundary is complicated, so there is little research about this. Zhang da and others have done detail research to the radiation ultrasonic field of thin plate speaker under fixed quadrangular condition, the speaker that takes advantage of the new-type tune possibly breaks through the dilemma that moving coil speaker can't improve on. The thin plate speaker has various fixed mode, such as quadrangular fixed, diametric fixed and so on, different fixed modes will have different sound effect.Stepped circular plate is improved from flat plate, which thickness of step is half-wavelengths of the sound radiated in the propagation medium. The main purpose that reduce the phase destructively in the radiated sound field of flat plate to the lowest is to improve radiation efficiency and directivity. Because the frequency equation is very complex of stepped plate under fixed boundary, the previous literature did not give the solution method.The article only discussed the stepped plate with single nodal circle. The frequency equation of the stepped circular plate under fixed boundary condition is studied in the first step. A feasible numerical method is presented, and a computer program is developed. Calculate the radius and the radius of nodal circle of the stepped plate and design a complete stepped plate. And calculate the radiation ultrasonic field and radiation resistance of the stepped circular plate. Compared the radius, nodal radius, directivity and radiation resistance of stepped plate based on same material, same substrate thickness and same frequency under three boundary conditions in the second step. The main contribution as following:1-. Resolve frequency equationContact two fixed boundary condition equations and four continuity equations. The frequency equation of the stepped plate under fixed boundary condition is derived. A feasible numerical method is presented, and a computer program is developed. Calculate the radius and the radius of nodal circle of the stepped plate based on given material, substrate thickness and frequency, and design a complete stepped plate. Use ANSYS to calculate vibration mode and displacement distribution of the stepped plate. The theoretical result is in good agreement with the calculated result of FEM. 2,Calculate radiation ultrasonic fieldWhen the stepped plate in flexural vibration, the power radiate to the surrounding is inequality, weaker in some areas, better in some areas, that is directivity pattern. Based on solving above frequency equation, we calculate the vibration mode coefficient of the stepped circular plate. The radiating sound field directivity pattern of flexural vibrating stepped plate with fixed border is studied by applying the superposition of sound pressure of center area and circular ring area. The directivity pattern is plotted by programming.3,Research radiation impedanceAs the radiation surface of the stepped circular plate is not coplanar, the classical theory has difficulty in calculation. Superposition method is used to calculate radiation impedance of stepped circular plate under fixed boundary condition. The curve of resistance and reactance varying with ka are plotted.4,Compare and analyzeCompare the radius, nodal radius, ultrasonic field directivity and radiation impedance based on same material, substrate thickness and frequency under three boundary conditions when there is a nodal in the middle of the stepped circular plate.In this paper, calculate the vibration and radiation of stepped plate under fixed boundary condition. And calculate vibration and radiation of stepped plate under free and simply-supported boundary conditions. Then compare the vibration and radiation of stepped plate under three boundary conditions. The results show that the radius of stepped plate with fixed border is the largest and with free border is the least. Directivity patterns of stepped plate with fixed and simply-supported border are better than with free border. The directivity pattern of stepped plate under free boundary condition is the worst, but the sidelobe is the least. The directivity pattern of stepped plate with simply-supported border is similar with fixed border. But the sidelobe with fixed border is less than simply-supported border. The radiation resistance is greater and the radiation reactance is smaller in the higher frequency than in the lower frequency. When ka is the same, the radiation impedance is the largest under free boundary condition and smallest under simply-supported boundary condition. Analysis results provide the scientific theoretical foundation for utilizing these types of vibrators intentionally and efficiently in practical applications.