Nonaxisymmetric vibrations of radially polarized hollow cylinders made of functionally gradient piezoelectric materials

Grigorenko, А. Ya.; Müller, Wolfgang; Wille, Rudolf; Loza, I. A.

doi:10.1007/s00161-012-0239-8

Cited by 17 publications

(6 citation statements)

References 15 publications

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“…Similar idea of using power function material properties can be found in numerous articles [9][10][11][12][13][14][15][16][17][18]. A few groups proposed different assumptions that [19][20][21] the material parameters were assumed as exponential function. For instance, the elastic stiffness was ij ij 0 ( ) In the above papers, material parameters (the elastic stiffness, piezoelectric coefficient and the dielectric constant) of FGPM cylinder are assumed to be power functions or exponential functions, which imply FGPM cylinder comprises of multi-layers.…”

Section: ( )mentioning

confidence: 92%

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Revisiting the electroelastic solution for an FGPM thick-walled cylinder subjected to mechanical and electric loadings

Wang

Dui

Xin

2020

Mater. Res. Express

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Theoretical analysis for an empty thick-walled FGPM cylinder exposed to electric and mechanical loadings are investigated. The cylinder is a composite material composed of PZT4 and PVDF and the volume fraction of PZT4 is given by the power law with three controllable parameters which can cover more complex circumstances. The hypergeometric equation of the radial displacement is acquired by utilizing the Voigt method, and the solutions of the stresses and the electric potential are obtained after solving the radial displacement. The method in this paper is appropriate for real functionally graded piezoelectric materials and can avoid assumptions about unknown overall material parameters appeared in previous references. Finally, the impacts of the parameter n in volume fraction of FGPM cylinder on mechanical and electric behaviors are examined. Furthermore, the distinction between the hoop stress and radial stress is discussed to decrease the pressure concentration in FGPM cylinder. Nomenclature a, b inner and outer radii r radial coordinate c(r) volume fraction of material A c 0 , k, n material parameters in the volume fraction c(r) p a , p b internal and external pressures j a , j b internal and external electric potentials C ijkl i (i=1, 2) elastic modulus of the component e mij i (i=1, 2) piezoelectric tensor modulus of the component k mk i (i=1, 2) dielectric modulus of the component u radial displacement j electric potential e , r i ( ) e q i ( ) radial and hoop strains of the component e , r e q average radial and hoop strains of the cylinder s , r i ( ) s q , i ( ) s z i ( ) radial, hoop, and axial stresses of the component s , r s q , s z average radial, hoop, and axial stresses of the cylinder E , r i ( ) D r i ( ) radial electric field and electric displacement of the component E , r D r average radial electric field and electric displacement of the cylinder a(r), b(r), d(r), g(r), f (r), h(r), k(r) functions related to the volume fraction c(r)

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Section: ( )mentioning

confidence: 92%

“…For instance, c 0 =0 means the cylinder is purely material B; c 0 =1 and k=0 means the cylinder totally consists of material A. Then equation (20) reduce to…”

Section: A a A A G A A B A G A A B Q B B B B Q B F B B A B G B B B B mentioning

confidence: 99%

Revisiting the electroelastic solution for an FGPM thick-walled cylinder subjected to mechanical and electric loadings

Wang

Dui

Xin

2020

Mater. Res. Express

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“…In polar coordinates, the wave equation of radial vibration of the piezoelectric ceramic tube is as follows [20]:…”

Section: Mathematical Modelmentioning

confidence: 99%

“…e characteristic equation of radial vibration of the transducer can be obtained by combining (20), (21), and (22):…”

Section: Vibration Mode Function and Naturalmentioning

confidence: 99%

Radial Vibration Characteristics of Piezoelectric Ceramic Composite Ultrasonic Transducer

Yao

Zhang

et al. 2020

Shock and Vibration

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Different from the existing equivalent circuit analysis method of the transducer, based on the vibration theory of the mechanical system and combined with the constitutive equation, this paper analyzes the radial vibration characteristics of the transducer. The piezoelectric ceramic composite ultrasonic transducer is simplified as a mechanical model of a composite thick wall tube composed of a piezoelectric ceramic tube and a metal prestressed tube. The mathematical model of radial vibration of the transducer is established, which consists of the wave equation of radial coupling vibration of the piezoelectric ceramic tube and the metal prestressed tube, the continuity conditions, and the boundary conditions of radial vibration of composite thick wall tube. The characteristic equation and the mode function of radial vibration are derived. The calculated results of natural frequency are in good agreement with the existing experimental results. Based on the analytical method and the difference method, the numerical simulation models of radial vibration are established, and the amplitude-frequency characteristic curves and the displacement responses are given. The simulation results show that the amplitude-frequency characteristic curves and the displacement responses of the two methods are the same, which verifies the correctness of simulation results. Through the simulation analysis, the influence rule of the transducer’s structure sizes on its radial vibration natural frequency is given: when the thickness of the metal prestressed tube and the piezoelectric ceramic tube are constant, the natural frequency decreases with the increase of the inner diameter of the piezoelectric ceramic tube; when the outer diameter of the metal prestressed tube and the inner diameter of the piezoelectric ceramic tube are constant, the natural frequency decreases with the increase of the thickness-to-wall ratio. The calculation method of natural frequency based on elastic vibration theory is clear in concept and simple in calculation, and the simulation models can analyze the mechanical vibration of the transducer.

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“…However, the models have some limitations in evaluating the effects of electrodes and electrical connections of piezoelectric layers on the transducers’ performance. In addition to the traditional material properties, the functionally graded piezoelectric elements or elastic elements are also considered to improve the transducer performance (Alibeigloo, 2009, 2011; Arefi, 2013; Arefi et al, 2012; Arefi and Rahimi, 2014; Grigorenko et al, 2012; Grigorenko and Loza, 2017a; Khoshgoftar et al, 2009; Rahimi et al, 2011; Saadatfar and Aghaie-Khafri, 2015, 2016; Wang et al, 2011; Wang and Luo, 2016).…”

Section: Introductionmentioning

confidence: 99%

Effects of electrodes and electrical connections of piezoelectric layers on dynamic characteristics of radially polarized multilayer piezoelectric cylindrical transducers

Wang

Liu

et al. 2018

Journal of Intelligent Material Systems and Structures

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Piezoelectric cylindrical transducer is a type of excellent smart devices that can generate radial sound radiation due to its unique structural characteristics and has been widely used for ultrasonic and underwater sound applications. In the design of a piezoelectric cylindrical transducer, especially with the multilayer structure, the electrodes and electrical connections of piezoelectric layers are two key factors affecting the device performance but have not been well evaluated, which result in the inaccurate prediction of dynamic characteristics. This work establishes the exact theoretical models for radially polarized multilayer piezoelectric cylindrical transducers by taking into account the electrodes and electrical connections of piezoelectric layers. Based on the plane stress assumption, the dynamic solutions of the models are derived. Analytical expressions of electric impedances are also derived to obtain the resonance frequencies. In addition, the analytical solutions are validated using the special example in the earlier work and comparing them with the finite element analysis results. Subsequently, the effects of the electrodes and electrical connections of piezoelectric layers on the dynamic characteristics of the transducer are analyzed and discussed. The results show that the electrode thickness, the electrode type, and the parallel and series connections significantly affect the transducer’s performance, thus providing useful guidelines in the design of piezoelectric cylindrical transducers. This work contributes to an overall analysis on the dynamic characteristics of the radially polarized multilayer piezoelectric cylindrical transducers, which is very helpful to improve the performance of two-dimensional emitter and receiver in underwater sound and ultrasonic applications.

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Nonaxisymmetric vibrations of radially polarized hollow cylinders made of functionally gradient piezoelectric materials

Cited by 17 publications

References 15 publications

Revisiting the electroelastic solution for an FGPM thick-walled cylinder subjected to mechanical and electric loadings

Revisiting the electroelastic solution for an FGPM thick-walled cylinder subjected to mechanical and electric loadings

Radial Vibration Characteristics of Piezoelectric Ceramic Composite Ultrasonic Transducer

Effects of electrodes and electrical connections of piezoelectric layers on dynamic characteristics of radially polarized multilayer piezoelectric cylindrical transducers

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