An Analytical Solution And Finite Element Analysis Of Radial Yibration Of A Kind Of Functionally Graded Piezoelectric Transducers

Due to the special electro-mechanical coupling effect, the piezoelectric materials have been widely used in various engineerings, such as piezoelectric sensors, piezoelectric transformers, high precision piezoelectric micro platform, piezoelectric robots and so on. The piezoelectric transducer is one of the important applications, which is a kind of energy exchange devices by means of the direct and inverse piezoelectric effects to realize the conversion between the mechanical energy and the electrical energy. Piezoelectric transducers can be used in ultrasonic detection, ultrasonic ranging, underwater acoustic systems and so on. The piezoelectric transducers are always working at the resonant frequency or the resonant frequency, therefore, the investigation of the influence of various factors on the working frequency of piezoelectric transducer would be helpful in guiding the design and optimization of piezoelectric transducers with high performance.Functionally graded material (FGM) is a kind of new material in which the material properties is a continuous function in the gradient direction. The continuous change of the material properties has great advantages compared to most of the composite materials. The combination of the piezoelectric material and the concept of functional graded materials comes up the concept of functionally graded piezoelectric material which provides a new thought in the design of piezoelectric transducers.This paper studies the radial vibration characteristic of a kind of functionally graded piezoelectric ring transducer. The material properties of this kind of functionally graded piezoelectric ring transducers are assumed to be graded in power-law variation form except the Possion’s ratio. We stress that the material inhomogeneity index of mass density can be different from that of other material properties.In this paper, an exact solution of radial vibration characteristic of a kind of functionally graded piezoelectric ring transducer is obtained by using the piezoelectric linear elasticity theory. By utilizing the boundary conditions, the resonance and anti-resonance frequency equations are obtained. We also obtained the analytical solution of radial vibration characteristic of a kind of functionally graded piezoelectric ring transducer under two boundary conditions:1.Both the inside and outside surface are free; 2.The outside surface is free while the inside surface is supported on elastic foundation. Based on the presented solution, the numerical analysis is performed. For both boundary conditions, the effects of diameter ratio, functionally graded index on the first order resonance and anti-resonance frequency as well as effective electromechanical coupling factor of piezoelectric ring are investigated.The radial vibration of functionally graded piezoelectric ring is also analyzed by using the ANSYS software. We simulate the radial vibration of piezoelectric ring composed of the homogeneous materials and functionally graded materials, respectively. The first order resonance and anti-resonance frequencies and the displacement nephogram are obtained by using the ANSYS simulation. The results obtained by the ANSYS agree well with analytical solution. The correctness and effectiveness are then verified each other.