Ring Complex Frequency Of The Sandwich Piezoelectric Ceramic Transducer Design

In underwater acoustics and high power ultrasonics, sandwich piezoelectric ultrasonic transducers are widely used as large power sound radiators. Along with the development of ultrasonic technology, ultrasonic transducers are being used in more and more new applications, such as high-frequency metal and plastic welding, high-frequency cleaning and some practical applications concerning very large ultrasonic power. In these cases, the radial dimensions of the transducer are usually larger than a quarter of the longitudinal wavelength. Therefore, one-dimensional design theory of the sandwich transducer is no longer applicable; otherwise, large frequency error will be caused. Specifically speaking, one-dimensional design theory is not applicable for the following three cases. (1) High frequency sandwich transducer such as those used in ultrasonic metal welding. When the resonance frequency of the sandwich transducer is increased, the longitudinal wavelength and geometrical dimension will accordingly decrease. According to the assumptions introduced in one-dimensional longitudinal theory, the radial dimension of the transducer must also be decreased. Therefore, the cross-section of the transducer is small and the mechanical strength and the power capacity will be lowered. To raise the mechanical strength and the power capacity, the radial dimensions of the high frequency sandwich transducer must be increased; thus, the radial vibration in the transducers must be considered and the coupled vibration of the transducer should be analyzed. (2) Higher power sandwich transducers. In some new ultrasonic applications, very large ultrasonic power is needed; therefore, the radial dimensions exceed a quarter of longitudinal wavelength and one-dimensions exceed a quarter of longitudinal wavelength and one-dimensional theory is also not applicable. (3) In recent years, a new type of high power ultrasonic radiators are used in ultrasonic cleaning and ultrasonic sonochemistry, the ultrasonic radiator is metal tube with large vibrate in both longitudinal and radial direction because of the Poisson's effect; therefore large power can be given out. In the above-mentioned three cases, the vibration of the transducer or the radiator is a coupled one of longitudinal and radial vibrations. Therefore, new design theory must be developed in order to study the coupled vibration of the sandwich transducers with large cross section or high resonance frequency.Based on coupled vibration, the vibrations of the isotropic metal hollow cylinders and the longitudinally polarized piezoelectric ceramic hollow cylinders are analyzed, and some multi-frequency ultrasonic transducers are designed. The main content and work of this paper are as follows: 1. The coupled vibrations of the isotropic metal hollow cylinders with large geometrical dimensions and the longitudinally polarized piezoelectric ceramic disks with central holes are analyzed by using an approximate analytical method. When the mechanical coupling coefficient is introduced and the shearing strain is ignored, the coupled vibration is divided into two equivalent vibrations. One is the equivalent longitudinal extensional vibration, and the other is the equivalent radial vibration. These two equivalent vibrations are not independent; they are correlated together by the mechanical coupling coefficient. The resonance frequency equations are given in this paper. Compared with one-dimensional theory, the computed resonance frequencies by using the coupled vibration theory are in good agreement with the results from the finite element software ANSYS and the measured results.2. The vibration performance of the sandwich piezoelectric ultrasonic transducer is studied when the coupled vibration is considered; and the resonance frequency equations of the transducers are given. It can be seen that for fundamental vibrant mode of the sandwich transducer of a quarter wavelength, there are three resonance frequencies which are radial resonance frequency of the metal mass, radial resonance frequency of the piezoelectric ceramic and longitudinal resonance frequency of the sandwich transducer. The ultrasonic transducer is also analyzed by the finite element software and manufactured. It is shown experimentally and theoretically that the transducer has several resonance frequencies, and the ultrasonic transducer is a multi-frequency ultrasonic transducer.3. The methods for designing broadband ultrasonic transducers based on optimizing the multi-frequency ultrasonic transducers are introduced, and the theories of these methods are discussed.