【作者】 凤飞龙；

【导师】 林书玉；

【作者基本信息】 陕西师范大学 ， 声学， 2003， 硕士

【摘要】 纵弯复合空气换能器由纵向振动夹心式换能器与弯曲振动薄圆盘组成，具有纵向振动换能器的高效大功率和弯曲振动圆盘的低辐射阻抗、大辐射面积等特点。在超声除尘、超声雾化、超声检测等领域有广泛的应用。然而对于辐射面积较大的弯曲振动圆盘，一般激励的振动阶数比较高，因此存在弯曲振动的反相区，导致换能器的辐射阻抗下降，电声效率和声功率降低以及指向性变差等问题。为此，采用弯曲振动阶梯圆盘，通过阶梯高度补偿相位是一种比较常用的办法。但是对于这种阶梯圆盘的理论研究还比较少，已有的一般近似程度较大，设计上也存在一些问题。本文从薄圆板弯曲振动理论出发，推导了这种阶梯圆盘的频率方程、等效质量、等效弹性和辐射阻抗，并进而提出了这种阶梯圆盘的一般设计方法。考虑到大功率超声应用中的非线性和吸收作用，本文从KZK方程和准线性条件出发，对于工作在共振频率下的这种阶梯圆盘，推导了它的一阶和二阶谐波声场计算方法。并对其声场远场采用瑞利积分推导了一般表达式和指向性公式。经过实验验证，与理论符合较好。 具体的，主要有以下几个方面： 1．对于圆形薄板，计算了它的振形方程，根据厚度变化处的位移和位移导数连续条件、剪切力连续条件、弯矩连续条件，通过数值方法求解方程组获得弯曲阶梯圆板的频率方程的求解。经过对于不同边界问题的频率根值进行比较，得出了不同于弯曲平圆板的结论。即由简支到自由到固定频率依次升高的结论。在求得频率的基础上，进一步求解了与之对应的归一化了的振形曲线系数，从而为后面的计算铺平了道路。 2．对于工作在谐振频率下做轴对称运动的阶梯圆板，采用解析法求得它的等效质量，并由C=1/ω~2M求得等效弹性系数。采用解析法求得它在谐振频率下工作时的辐射阻抗为，在此基础上可以得到阶梯圆板的等效电路。 3．在给出设计频率和节圆数目的条件下，可以根据节圆处振幅为零可以设计出任一个节圆的阶梯板的尺寸参数。这些阶梯板克服了弯曲圆扳振动时的相为相消的问题。因而具有良好的辐射和指向性能。根据这一设计思想，设计了两个两节圆的阶梯圆板，经试验符合设计要求。 4．对KZK方程在准线性条件下采用微扰法进行求解，将阶梯板辐射的声源条件带入后，可以获得它的一阶和二阶声场的积分计算方法，可用于数值计算。这些公式可以计算出一个波长以外的整个声场，另外，也可以获得远场指向性公式。这些公式的适用条件是切＞＞1，或者说，他们是高频近似条件下的声场解。 5．利用瑞利积分，可以得到阶梯辐射圆板的远场解析解：几＝ Re｛：exP（j。r）D 0冈＋ 11＊十 Ill ＊H厂）exP（jk。H冈川／ A；，并且对于任意轴对 厂 二7称声场，按照瑞利积分办法，可以得到其远场指向性公式为：D仔）＝一一二二二二一二7一一。更多还原

【Abstract】 The compound transducer consisting of a longitudinal vibrator and a flexural circular plate combines the high energy and efficiency of the former and the low impendence and wide spreading scale of the latter. It is now widely used in aerosol particle precipitation, ultrasonic atomization and ultrasonic detection. But to circular plate with large surface area, the vibrate modes generated is often so high that there is reverse phases existing, which result in a decrease in radiation impedance, electric-acoustic efficiency and the electric power, as well as poor directivity. So a stepped circular plate is adopted which can compensate the phase by different thickness. However, the theory about it is still scarce. Or if there is some, they usually introduce large approximation so it is difficult to be used in practical design. In this article based on vibration theory of the flexural plate, the frequency equation, the equivalent mass and radiation impedance are derived and further, design theory is introduced. After the nonlinear and absorption effect is taken into account in the applications where high power ultrasonic is involved, the first and second harmonic components of the sound field of stepped circular plate is analyzed, based on the KZK equation and quasi-linear condition. Moreover, taking on the Rayleigh integral the far field acoustic pressure and the directivity formula is obtained. The measured results are in good agreement with this theoretical value.In detail, the context include several aspects:1. According to several boundary conditions, the frequency equation of flexural circular plate is calculated. Similarly some coefficients in the displacement distribution can also be acquired, which provide a preparation for further study.2.To the circular plate working in axial symmetry vibration at resonant frequency, the equivalent mass in analytical form is derived, that’s is, , and further, the equivalent compliance is obtained using the formula C = 1l 2 M . The radiation impedance at the resonant frequency, inanalytical form, is Consequently, theequivalent circuit of the plate is obtained.3. When the number of the nodal circles and the design frequency are given, the stepped circular plate satisfying the requirement can be designed. The stepped plate designed in this method can overcome the limitation of the sound field generated by circular flat.4.According the Rayleigh integral, the far field of this kind of plate is resolved,namely, . And the formula as a far field directivity function is assumed to be useful in analyzing the axis-symmetry sound field.更多还原