中文摘要：

作为向空气中辐射的声辐射器,弯振阶梯薄盘或矩形板在工业上有很多应用。由于计算的复杂性,以前的文献对阶梯圆盘的声场指向性未作研究。利用点声源组合的方法（Rayleigh积分）,计算了边界自由的弯振阶梯圆盘辐射声场的指向性,与弯曲振动的圆盘相比,阶梯圆盘的声场指向性得到了明显改善,理论计算结果与Gallego的实际测试图案相吻合。计算为这类辐射器的高效应用、优化设计提供了理论依据。

英文摘要：

As a kind of air acoustic radiator the flexural vibrating stepped thin circular plate or stepped thin rectangular plate has many applications in industry. The directivity pattern of the stepped circular plate has not been reported in theory due to complexity of computation. In this paper, the radiating sound field directivity pattern of flexural vibrating stepped thin circular plate with free border is studied by applying the directive theory of built-up point sources （Rayleigh Integral）. The directivity pattern of the stepped circular plate is much improved in comparison with that of the common flexural vibrating circular plate. The theoretical directivity pattern is in good agreement with the measured result of Gallego. The computation in this paper can provide a theoretical basis for efficient utilization and optimized design of this kind of vibrators.