Numerical Calculation Of Radiation Impedance Of The Square Plate

Rectangle and ring radiators are widely used in the transducer array. Two kinds of forms are involved in the rectangle radiator, one is the piston radiator, the other is the flexural vibration radiator. Many literatures have studied the radiator previously. Professor Lin Shu-yu and Li Jin have studied the distribution of the ultrasonic pressure and its directivity. While, the study about the calculation method in the impedance of the piston radiators, which is of high degree of accuracy, and the expression about the flexural vibration radiators is very little in the present lierature. This paper will go deeply in the study of those problems. Especially, the analytic expression about the impedance in the flexural vibration radiator can be uniquely obtained in the condition of the supporting boundary, and the author detailedly studies the impedance in this kind of boundary condition. Some useful conclusions are drawn to guide the practice.In addition to those, the author also studied the directivity of the ring piston which composes of the phased array.The detailed work is as fellow:1. The directivity of the ring piston which composes of the phased array is studied with the Rayleigh integration formula. The sound pressure and directivity are calculated at first, then the author analyses detailedly how the size of the ring influences its directivity ,and amends some inaccurate conclusion about the directivity of the ring piston.2. The impedance of the square piston is studied in this paper .The author starts the study from the definition of the piston radiator, and then deduces the quadruple integral expression by visualized mathematical model. C program of Gauss numerical integration by 5 nodes is adopted in this paper .The calculation results are compared with relevant literature. The result indicates that the calculation method is correct, and the calculation results are of high degree of accuracy comparing with other literature. The method of calculation is helpful to the study of the square flexural vibration radiator.3. The impedance of the flexural vibration radiator in the condition of supporting boundary is calculated in this paper. Because the velocity amplitude of the spots in the surface of the flexural vibration radiator is not equal, the definition of the piston impedance can not adapt to the flexural vibration radiator. Professor He zuo-yong defines this kind of impedance in his literature. But he doesn't calculate detailedly the impedance of the flexural vibration radiator with it. The author of this paper starts from the definition of Professor He's, deduces two kinds of impedance expression of the flexural vibration radiators in the condition of supporting boundary, and calculates the numerical results with the method of Gauss numerical integration by 5 nodes. The numerical results of relative impedance of m--n--1 modality are obtained, which takes the surface average velocity as reference. Similarly, the relative impedance of m＝n＝1 modality, m＝1,n＝3 modality, and m＝n＝3 modality are obtained, which takes the velocity of the center point as reference. The impedance of the square piston radiator is calculated again in the professor He's definition, and the result is in good agreement with the result in chapter 3. The expression of the sound power of the square flexural vibration radiator is deduced, and compared with the sound power of the square piston radiator. At last, the electromechanical equivalent circuit of the square flexural vibration radiator is obtained after calculating the equivalent lumped parameter.