Radial Sandwich Piezoelectric Ceramic Pipe The Transducer Vibration Study

Piezoelectric ultrasonic transducer is a device that can convert electrical signals into ultrasonic signals or convert ultrasonic signals into electrical signals.Ultrasonic transducer is used very extensive in such fields as industry, agriculture, defense, biomedical applications, for examples, medical ultrasound, ultrasonic cavitation, Chinese herbal medicine ultrasound extraction, marine development, geological prospecting, oil exploitation.Radial sandwich piezoelectric ceramic hollow transducer is a new type of transducer, its resonant frequency and a variety of performance not only concern with the piezoelectric ceramic materials, but also concern with the geometry of the piezoelectric ceramic hollow.The geometry size of transducer is special, the height of it close to the diameter.The radial coupling vibration of sandwich piezoelectric ceramic transducer vibration modes is difficult to the mode of the piezoelectric long tube and the piezoelectric ring, neither one-dimensional radial vibration nor one-dimensional longitudinal vibration.The vibration mode of transducer is neither a purely radial vibration nor a purely longitudinal vibration,the radial vibration of the transducer have an effect on the longitudinal vibration, it is a longitudinal and radial coupled vibration.This coupled vibration mode compared to a one-dimensional vibration very complex and large amount of calculation by the previous calculation method, but,by assuming the longitudinal diameter coupling coefficient,connected the longitudinal vibration to radial vibration, that a complex problem is becoming simplified.At last, we calculated the mechanical equivalent circuit of the vibration system,the impedance of the system is derived, and obtained its resonant frequency equation and the resonant frequency.1.The piezoelectric ceramic hollow coupled vibration is studied.At the first time, the radial vibration of the piezoelectric ceramic tube is studied, the e-type equations of the piezoelectric ceramic is brought into the equation of motion of piezoelectric ceramic tubes,the displacement function of differential equations is solved by using the MAPLE software,unknown quantities are calculated form the speed boundary conditions of the piezoelectric ceramic tube, the force of the outer surface and internal surface about speed equation is derived frequency equation can be obtained form the force equations.By observing the above equation, the equation is about unknown variables of longitudinal and radial coupled vibration coefficient c and the frequency f, we need a equation with two unknown variables to solve the equation.Followed by the same method, the longitudinal vibration transducer mechanical equivalent circuit of the ceramic tube and the equation of the longitudinal resonance frequency when the system resonance are derived.According to the front research, the resonant frequency of the piezoelectric ceramic tube coupled vibration is derived from the Longitudinal vibration frequency of equations and the radial vibration frequency equation. the frequency gained by solving the frequency equation corresponds to the geometric dimensions, and we draw the curve of the piezoelectric ceramic tube resonant frequency and size diagram.Finally, the theory have been proved by the finite element simulation and experimental methods. It is convenient for future research about sandwich piezoelectric ultrasonic transducer.2.The metal hollow coupled vibration is studiedFirst radial vibration of the metal tube is studied according to the theoretical principles of mechanics, the shear stress and shear strain is ignored by assuming that the mechanical coupling coefficient, the equivalent Young's modulus is derived and substituted into the metal tube equation of motion, metal tube vibration displacement function is derived. the unknown variables are derived by substituting the displacement function to the velocity boundary.According to the relationship between force and stress, the force and speed of inner and outer layers are derived and the radial vibration resonance frequency equation calculate the radial vibration of the equivalent circuit.By observing the above equation, the equation is about unknown variables of longitudinal and radial coupled vibration coefficient c and the frequency f, we need a equation with two unknown variables to solve the equation.Followed by longitudinal vibration of the metal tube studies, the final longitudinal vibration displacement function through the equation of motion to obtain the metal tube up and down at both ends and both ends of the speed, the longitudinal vibration of the equivalent circuit.Longitudinal vibration of the metal tube is studied, longitudinal vibration displacement function is derived form the equation of motion,the force and speed of the metal tube up and down at both ends and the equivalent circuit of the longitudinal vibration of the metal tube is derived.Longitudinal vibration resonance frequency equation can be obtained when the force of both ends metal tube up and down are zero, the equation is an equation on the unknown variables of mechanical coupling coefficient c and the frequency f of the vibration.Simultaneous radial vibration resonance frequency equation and give resonance to the vibration frequency equation, resonance frequency equation coupling vibration of the metal tube is derived and draw the curve between the metal tube resonant frequency and the geometric dimensions.Finally, the finite element simulation analysis have proved the correctness of the coupled vibration theory.lt is convenient for future research about sandwich piezoelectric ultrasonic transducer.3.In previous studies, we already know the coupled vibration of the coupled vibration of piezoelectric ceramic pipe and metal pipe, and know their mechanical equivalent circuit.We designed a radial sandwich transducer, the middle layer of the transducer is a piezoelectric ceramic PZT tube, the inner layer is isotropic metal aluminum, and the outer layer is isotropic metal45steel.Transducer is connected in the radial direction, the equivalent circuit of the radial sandwich piezoelectric ceramic transducer is derived, the longitudinal vibration equivalent circuit can be used as constraints on the radial vibration, frequency equation of the system is taken,and find the sandwich type transducer resonant frequency.At last the result of the finite element software consistent with calculations of the theoretical proved the correctness of the theory.