中文摘要：

采用BP神经网络,把矩形压电振子的各阶振型位移输入到神经网络中进行训练,提取各阶模态的振型特征,可实现矩形压电振子的共振振幅分布和振动模态阶次的非线性映射,以此区分各个模态。仿真实验结果显示,建立的神经网络模型可以从ANSYS输出的各模态中准确识别出矩形压电振子的B（3,1）模态,对训练样本外的尺寸也有一定的识别效果,表明所建立的BP神经网络可以有效地用于该矩形压电振子的振动模态区分。

英文摘要：

The back propagation （BP） neural network was adopted to identify the vibration mode of a rectangular shaped piezoelectric vibrator.Used amplitude distributions as input patterns to the neural network to extract the modal characters.Established the nonlinear mapping of amplitude distribution of resonant vibration onto vibration mode.The simulation results show that the proposed neural network can identify the B（3,1） objective vibration mode of this rectangular shaped piezoelectric vibrator from the ANSYS output accurately.It can also be used to identify modes when the dimensions are out of the range of training. This shows that the proposed BP neural network can distinguish the vibration modes of this rectangular shaped piezoelectric vibrator effectively.