中文摘要：

利用有限元方法，计算了不同激励频率下一阶弯曲振动阶梯圆盘的节圆半径．以节圆比阶梯凸台边缘小为例，将阶梯圆盘按节圆及阶梯位置内（外）分成三部分，提出了解析计算这三部分位移分布的方法，经有限元计算证实了这种方法的有效性．在此基础上，利用声场叠加原理推导出节圆偏离阶梯位置时的辐射声压，计算并分析了激励频率对阶梯圆盘指向性的影响．结果表明，激励频率与阶梯圆盘的设计频率不一致时，会导致声场指向性主瓣的半开角变大，指向性不如原来尖锐，进一步增大激励频率，将导致指向性主瓣分叉，这会使得阶梯圆盘的辐射声场能量相对分散．

英文摘要：

Using the finite element methed, the nodal circular of the stepped circular plate is calculated with different driving frequency. When a nodal circular is smaller than the stepped location, the stepped circular plate is divided into three parts by the location of the nodal circular and the stepped. In this case, a method that analytical calculate the three-part displacement distribution is proposed and this method is verified by finite element method. Then the expression of radiated acoustic pressure is derived by the principle of superposition in the acoustic field, and the effect on the directivity pattern is calculated with different driving frequency. Our results show that the difference between the driving frequency and the frequency of the stepped circular plate will lead the main lobe of the directivity pattern becomes wider. The main lobe of directivity pattern will bifurcate when the driving frequency increases to a certain value, which makes the energy of the radiated acoustic field relatively dispersed