Research On The Three-dimensional Coupled Vibration Characteristics Of Rectangular Piezoelectric Ceramic Oscillator

As one of the common and important devices in the field of acoustics,the ultrasonic transducer plays an increasingly important role in the application of modern engineering technology with the rapid development of science and technology and the social economy.At present,transducers have been widely used in marine acoustics,biomedical ultrasound,power ultrasound,ultrasonic processing,industrial testing,and other fields,such as ultrasonic cleaners,ultrasonic flaw detectors,and focusing transducers in biomedicine.With the continuous improvement of practical application requirements,there are more and more types of transducers.The traditional onedimensional theory is not enough to analyze the vibration characteristics of the piezoelectric ceramic vibrator.In order to study the three-dimensional coupling vibration of rectangular piezoelectric ceramic laminates and reduce the influence of coupling vibration on piezoelectric ultrasonic transducers,the equivalent elastic method is adopted.When ignoring the shear strain,the complex coupling vibration of rectangular piezoelectric ceramic laminates is simplified into the coupling of three one-dimensional vibrations by defining three mechanical coupling coefficients,Then,based on the theory of composite materials and phononic crystals,a large-size rectangular piezoelectric sheet with near periodic phononic crystal structure composed of PZT-4 and epoxy resin is proposed.This phononic crystal structure will suppress the transverse vibration of the piezoelectric sheet,so as to make the thickness mode purer and more conducive to more uniform thickness vibration amplitude.The main contents and innovations of this thesis are summarized as follows:(1)By establishing the three-dimensional coupling vibration electromechanical equivalent circuit diagram of rectangular piezoelectric ceramic double lamination,the piezoelectric ceramic rectangular lamination is analyzed,the resonance frequency equation determining the vibration mode of piezoelectric vibrator is deduced,and the resonance frequencies of different modes can be calculated.According to the resonance frequency equation of three-dimensional coupled vibration and the results of finite element calculation,the effects of the length,width,and thickness of rectangular piezoelectric ceramic lamination on its resonance frequency in different dimensions are analyzed.(2)Three groups of rectangular piezoelectric ceramic laminations with different sizes are made for experiments,and the finite element research and numerical calculation analysis of the model with the same size are carried out.The results show that the theoretical results are in good agreement with the simulation results and experimental values.The maximum error of the resonance frequency obtained from the experiment and the theory is 3.77%,and the minimum error is only 0.39%,The validity of the theory is proved,which provides theoretical support for expanding the application of rectangular piezoelectric vibrator.(3)A large-size rectangular piezoelectric sheet with the near periodic phononic crystal structure is proposed.Firstly,its equivalent material parameters are derived by using series parallel theory and uniform field theory.Then the electromechanical equivalent circuit diagram of three-dimensional coupled vibration is established by using the coupled vibration theory,and the resonance frequency equation is deduced.Then,the influence of the length,width,and thickness of the piezoelectric sheet on the resonance frequency of the stretching vibration in three directions is analyzed by the analytical method and finite element method.At the same time,the effect of the geometrical size of the piezoelectric vibrator on the effective electromechanical coupling coefficient is also studied.Therefore,a higher electromechanical conversion efficiency can be obtained by adjusting the size of the piezoelectric sheet.(4)The influence of the volume fraction of the scatterer on the resonant frequency in the thickness direction is studied by the finite element method,and the acceleration response curves of the large-size rectangular piezoelectric sheet with the near periodic phononic crystal structure in the ? and ? directions are calculated,and the band gap of the phononic crystal is obtained.The simulation results of this kind of phononic crystal structure are in good agreement with the theoretical results when the thickness of the crystal is low.When the volume fraction of scatterers increases,it is easy to produce transverse band gaps,which weakens the influence of transverse vibration on thickness vibration.By drawing the longitudinal displacement distribution diagram and vibration mode diagram,it can be seen that when the resonance frequency in the thickness direction is in the transverse band gap,the decoupling phenomenon will occur,the vibration amplitude will increase,the vibration will be more uniform,and the vibration mode in the thickness direction will be purer.