Equivalent Circuit of Coupling Vibration of Piezoelectric Ceramic Disc Oscillator

Piezoelectric ceramic resonators have a wide range of applications in many fields such as ultrasonic transducers, ceramic filters, piezoelectric accelerometers, and ceramic loudspeakers. In the traditional analysis and testing theory of piezoelectric ceramic resonators (including the international IRE piezoelectric crystal measurement standard), it is basically assumed that the vibration of the vibrator is one-dimensional, so the geometry of the vibrator is limited. It is like a thin disc or a slender hand. However, the actual vibrator geometry is limited, and its vibration is multi-dimensional coupled vibration, especially when the geometry of the vibrator does not meet the requirements of one-dimensional theory. One-dimensional theory will no longer apply and new theories must be developed. With regard to the multi-dimensional coupled vibration of a finite-size piezoelectric vibrator, the analytical solution is difficult to derive. With the rapid development of numerical computing technology and electronic computer technology, the numerical method has been widely used in the coupled vibration analysis of the vibrator, but the calculation amount is large, and the data processing and result analysis are cumbersome. The equivalent circuit method (such as the Mason equivalent circuit) has been widely used in the one-dimensional analysis theory of single-mode oscillators. It has the advantages of obvious physical meaning and simple analysis. Based on the underwater piezo tube and motion equations of piezoelectric ceramic oscillators, the coupled vibration of the vibrator is analyzed under the condition of neglecting the shear stress and strain of the vibrator. The equivalent circuit and resonant frequency equation of the coupled vibration are obtained. Compared with the numerical method, its analysis and calculation are quite simple. Compared with the one-dimensional theory, the whole theory is not very complicated, but it can better describe the coupled vibration characteristics of the vibrator, and the obtained results are in good agreement with the measuring values.

2 Analysis of equivalent circuit of piezoelectric vibrator

Piezoelectric ceramic disk , its radius and thickness are respectively the upper and lower end faces.which are covered with electric enthalpy, the thickness is axially deuterated, and the excitation voltage is added in the thickness direction during operation. Since the direction of the rice is parallel to the direction of the excitation voltage, the vibration of the vibrator is mainly a stretching vibration, and the shear can be ignored.In the case of axisymmetric vibration, the following forms of piezo ceramic pipe and motion equations are available. The equivalent electromechanical coupling coefficient of the radial vibration and axial vibration of the coupling vibrator is the radial and longitudinal electromechanical coupling coefficient of the ideal vibrator. When the vibrator is in the resonance, the total admittance tends to be infinite. The resonant frequency of the piezoelectric ceramic disk oscillator coupling vibration, when the material, geometric size and vibration mode of the vibrator (the first root of the above equation is taken at the fundamental frequency), the mechanical mechanism of the vibrator can be obtained. Coupling coefficient and resonance frequency, the above equation is a transcendental equation, and its analytical solution is difficult to find, and the numerical method must be used. Through the solution of the above equation, it can be seen from the actual vibration of the vibrator that the two sets of solutions correspond to the two vibration modes of the coupled-plate vibrating disk vibrator, the lang-axis vibration mode and the radial vibration mode, and the obtained vibrator The radial and axial resonance frequencies of piezoelectric ceramic transducers are different from the one-dimensional theoretical resonance frequency of the same size oscillator. The derivation process takes into account the coupling between the vibration modes. In addition, when the size of the vibrator satisfies certain conditions, for example, the radius of the vibrator differs greatly from the thickness, and the two frequencies (printing radial and thickness resonant frequencies) obtained by the frequency equation are far apart, so the vibrator vibration mode can be ignored. The mutual coupling between them is regarded as the vibration of a single mode. Conversely, if the size of the vibrator does not satisfy the above conditions, the two frequencies obtained by the frequency equation are relatively close, and the vibration of the vibrator is more complicated. At this time, the one-dimensional theory will no longer be applicable, and the analysis method in this paper must be utilized. . In short, the vibration of any actual vibrator is multi-mode and has multiple resonant frequencies. However, when the size of the vibrator meets certain conditions, it can be approximated as a single mode, that is, the single mode vibrator discussed in the traditional theory is only An approximate vibration mode of an actual vibrator. Under normal circumstances, the vibration of any actual vibrator is a coupled vibration. In addition, from the above analysis, we can see that the single vibration mode of the ideal oscillator can be directly derived from the theory of this paper.