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压电陶瓷复合换能器固有频率的有限差分法*

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张超,姚春东,具自强,贾贺通,董子龙,武勇.压电陶瓷复合换能器固有频率的有限差分法*[J].,2020,39(6):894-900
压电陶瓷复合换能器固有频率的有限差分法*
Finite difference method for natural frequency of piezoelectric ceramic composite transducer1
投稿时间：2020-03-20修订日期：2020-10-31
中文摘要:
为丰富换能器固有频率的研究理论，以及提供一种新的计算方法供工程人员选择，提出了计算其固有频率的有限差分法。以由径向极化的压电陶瓷圆管与金属预应力管沿径向复合而成的二元压电陶瓷复合换能器为例，建立并推导了其向振动的数学模型及其有限差分形式，给出了换能器径向振动的特征方程。利用MTALAB对计算实例的径向振动的固有频率进行编程计算，理论计算结果与已有实验结果符合很好，验证了有限差分法计算压电陶瓷复合换能器固有频率的可行性及准确性。通过仿真计算，给出了换能器径向振动固有频率与其结构尺寸的影响关系：换能器径向振动的固有频率随压电陶瓷圆管内径的增大而降低，随换能器壁厚比的增大而降低。该文所建立的换能器径向振动固有频率的有限差分法同样适用于结构形式相近的换能器及其他元器件。
英文摘要:
In order to enrich the research theory of the natural frequency of transducer and provide a new calculation method for engineers to choose, a finite difference method is proposed to calculate the natural frequency of transducer. In this paper, a two-dimensional piezoelectric ceramic composite transducer, which is composed of a radially polarized piezoelectric ceramic circular tube and a metal prestressed tube, is taken as an example. The mathematical model and its finite difference form of the directional vibration of the transducer are established and derived. The characteristic equation of the radial vibration of the transducer is given. Mtalab is used to program the natural frequency of the radial vibration of the calculation example. The theoretical calculation results are in good agreement with the existing experimental results. The feasibility and accuracy of the finite difference method to calculate the natural frequency of piezoelectric ceramic composite transducer are verified. The relationship between the natural frequency of the radial vibration of the transducer and its structure size is given through the simulation calculation. The natural frequency of the radial vibration of the transducer decreases with the increase of the inner diameter of the piezoelectric ceramic tube, and decreases with the increase of the wall thickness ratio of the transducer. The finite difference method for the natural frequency of radial vibration of transducers established in this paper is also applicable to transducers and other components with similar structure.
DOI：10.11684/j.issn.1000-310X.2020.06.012
中文关键词:压电陶瓷换能器固有频率有限差分法
英文关键词:Piezoelectric CeramicsTransducersNatural frequencyFinite difference method
基金项目:
作者单位E-mail
张超燕山大学机械工程学院18848973272@163.com
姚春东燕山大学机械工程学院ycd04@163.com
具自强燕山大学机械工程学院544214469@qq.com
贾贺通燕山大学机械工程学院635684508@qq.com
董子龙燕山大学机械工程学院593213857@qq.com
武勇燕山大学机械工程学院1151046985@qq.com
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