The cylindrical piezoelectric transducer has the advantages of large radiation area, high electromechanical coupled coefficient, and omni-direction radiation along the radius. In this paper, a piezoelectric transducer consisting of a radially polarized piezoelectric cylinder and an outer metal cylinder of varying height is presented. The metal cylinder of varying height is approximated as the radial superposition of multiple uniform height metal cylinders, and the equivalent impedance of the transducer's coupled vibration is obtained by using the impedance matrix method, and then the resonance frequency, anti-resonance frequency, effective electromechanical coupled coefficient, and displacement amplification coefficient are obtained. In this paper, the relationship between the vibration characteristics of the cylindrical piezoelectric transducer and its geometric dimensions is studied. An experimental sample of the transducer is fabricated and assembled, and its electrical impedance curve is measured. The measured results are in good agreement with the simulation results and the theoretical calculation results. The displacement distribution of the radiation surface of the transducer at resonance frequency is measured, which verifies that the two coupled vibration modes of the transducer can be effectively excited.
To address the problems caused by the strong coupling of an airbreathing hypersonic vehicle's airframe and propulsion to the integrated control system design, an integrated airframe–propulsion model is established, and the coupling characteristics between the aircraft and engine are analyzed. First, the airframe–propulsion integration model is established based on the typical nonlinear longitudinal dynamical model of an air-breathing hypersonic vehicle and the one-dimensional dual-mode scramjet model. Thrust, moment, angle of attack, altitude, and velocity are used as transfer variables between the aircraft model and the engine model. The one-dimensional scramjet model can accurately reflect the working state of the engine and provide data to support the coupling analysis. Second, owing to the static instability of the aircraft model, the linear quadratic regulator (LQR) controller of the aircraft is designed to ensure attitude stability and height tracking. Finally, the coupling relationship between the aircraft and the engine is revealed through simulation examples. The interaction between vehicle attitude and engine working condition is analyzed, and the influence of vehicle attitude on engine safety is considered. When the engine is in a critical working state, the attitude change of the aircraft will not affect the engine safety without considering coupling, whereas when coupling is considered, the attitude change of the aircraft may cause the engine unstart, which demonstrates the significance of considering coupling characteristics.
A radial-longitudinal (R-L) ultrasonic transducer is designed by compounding a piezoelectric ceramic and an outer metal ring on the central coupling cylinder of a longitudinal cascade transducer. This design is used to realize multi-mode vibration and increase the radiation range. By applying longitudinal and radial double excitation, three coupled vibration modes of the transducer are generated in the frequency range of 15-65 kHz. The coupled vibration dominated by radial vibration is regarded as the best vibration mode of this transducer. The electromechanical equivalent circuit and the resonance frequency equation of the transducer's coupled vibration are derived by using the equivalent elastic method and one-dimensional vibration theory and verified by the finite element method and experimental method. The results show that the electrical impedance frequency curves of the transducer from the three methods are consistent. The transducer is expected to be used in ultrasonic cleaning and liquid processing applications.
To improve the radiation efficiency and enhance the power capacity, this paper proposes a longitudinal-radial vibration mode conversion piezoelectric transducer (LRPT) consisting of an internal longitudinal sandwich piezoelectric transducer and an external metallic ring. the equivalent circuit of the LRPT in coupled vibration is derived based on the metallic ring’s two-dimensional electromechanical equivalent circuit, and the equations for resonance frequency (RF) and anti-resonance frequency (AF) are obtained. To achieve a pure radial vibration mode and minimize the coupling effect of radial and flexural vibrations, the external metallic ring’s wall thickness in the composite transducer is optimized.To further validate the accuracy of the theory, an experimental sample of LRPT is fabricated and subjected to measurements of its electrical impedance frequency response curve, displacement amplitude frequency response curve, displacement distribution in radiation surface at resonance frequency, as well as directivity of acoustic field in water. The experimental results are consistent with the simulation results and theoretical results. This study provides theoretical guidance for the design and optimization of the LRPTs.
The variable thickness annular radial piezoelectric ultrasonic transducer can realize impedance transformation and energy concentration, has the advantages of large radiation area and full directivity, and is widely used in power ultrasound, underwater acoustic and other fields. Because solving complex variable thickness metal ring radial vibration wave equation is more difficult, in this paper, the radial vibration of metal rings with variable thickness is transformed into the superposition of the radial vibrations of N metal rings with equal thickness by using the transfer matrix method. The equivalent circuit diagram, the resonance frequency equation and the expression of the displacement amplification coefficient of the radial vibration of the metal thin ring with arbitrary thickness are obtained. The relationship between the displacement amplification coefficient and the geometric size of the cone, power function, exponential and catenary metal rings is analyzed. On this basis, the equivalent circuit and resonance frequency equation of radial vibration of piezoelectric ultrasonic transducer which is composed of a metal ring with variable thickness and a piezoelectric ring with equal thickness are derived. In order to verify the correctness of the theoretical results, the finite element software is used in simulation, and the numerical solutions of the first and second order resonance frequency and displacement amplification coefficients are in good agreement with the theoretical solutions. In this paper, the universal solution of radial vibration of metal ring with arbitrary variable thickness is given, which provides theoretical guidance for designing and optimizing the radial piezoelectric ultrasonic transducers.
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