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变厚度环型径向振动压电超声换能器可以实现阻抗变换、能量集中, 具有辐射面积大、全指向性等优点, 在功率超声、水声等领域被广泛应用. 由于求解复杂变厚度金属圆环径向振动的波动方程比较困难, 本文使用传输矩阵法将变厚度金属圆环的径向振动转化为
$ N $ 个等厚度金属圆环径向振动的叠加, 得到了任意变厚度金属薄圆环径向振动的等效电路图、共振频率方程和位移放大系数表达式, 分析了锥型、幂函数型、指数型、悬链线型金属圆环的位移放大系数与几何尺寸的关系. 在此基础上, 推导了由任意变厚度金属圆环和等厚度压电圆环复合而成的压电超声换能器径向振动的等效电路和共振频率方程. 为了验证理论结果的正确性, 使用有限元软件进行仿真, 所得一阶、二阶的共振频率和位移放大系数的数值解与理论解符合较好. 本研究给出了任意变厚度金属圆环径向振动的普适解, 为设计和优化径向压电超声换能器提供了理论指导.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.-
Keywords:
- annular piezoelectric ultrasonic transducer/
- radial vibration/
- transfer matrix method/
- equivalent circuit
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$ {h}_{{\rm{b}}}/{\rm{m}}{\rm{m}} $ $ {h}_{{\rm{a}}}/{\rm{m}}{\rm{m}} $ $ {f}_{{\rm{r}}1}/{\rm{H}}{\rm{z}} $ ${ {f}^{ {\rm{*} } }_{ {\rm{r} }1} }/{\rm{H} }{\rm{z} }$ ${\varDelta }_{ {f}_{ {\rm{r} }1} }/{\rm{\%} }$ $ {f}_{{\rm{r}}2}/{\rm{H}}{\rm{z}} $ ${ {f}^{*}_{r2} }/{\rm{H} }{\rm{z} }$ ${\varDelta }_{ {f}_{ {\rm{r} }2} }/{\rm{\%} }$ 锥型 6 10 21894 21892 0.01 112380 110790 1.44 幂函数型 5 10 21679 21679 0 113330 111720 1.44 指数型 4 10 21401 21399 0.01 112770 111480 1.16 悬链线型 3 10 20968 20957 0.05 109700 108890 0.74 
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$ {h}_{{\rm{b}}}/{\rm{m}}{\rm{m}} $ $ {h}_{{\rm{a}}}/{\rm{m}}{\rm{m}} $ $ {M}_{{\rm{r}}1}^{{\rm{*}}} $ $ {M}_{{\rm{r}}1}^{{\rm{*}}{\rm{*}}} $ ${\varDelta }_{ {M}_{ {\rm{r} }1}^{*} }$/% $ {M}_{{\rm{r}}2}^{{\rm{*}}} $ $ {M}_{{\rm{r}}2}^{{\rm{*}}{\rm{*}}} $ ${\varDelta }_{ {M}_{ {\rm{r} }2}^{*} }/{\rm{\%} }$ 锥型 6 10 1.1985 1.1987 0.02 1.8304 1.8160 0.79 幂函数型 5 10 1.1997 1.2000 0.02 1.9876 1.9670 1.04 指数型 4 10 1.1992 1.1995 0.02 2.2501 2.2135 1.16 悬链线型 3 10 1.1959 1.1956 0.02 2.8118 2.7359 2.77 下载:
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$ {h}_{{\rm{b}}}/{\rm{m}}{\rm{m}} $ $ {h}_{{\rm{a}}}/{\rm{m}}{\rm{m}} $ $ {f}_{{\rm{r}}1}/{\rm{H}}{\rm{z}} $ ${ {f}^{*}_{ {\rm{r} }1} }/{\rm{H} }{\rm{z} }$ ${\varDelta }_{ {f}_{ {\rm{r} }1} }/$% $ {f}_{{\rm{a}}1}/{\rm{H}}{\rm{z}} $ ${ {f}^{*}_{ {\rm{a} }1} }/{\rm{H} }{\rm{z} }$ ${\varDelta }_{ {f}_{ {\rm{a} }1} }/$% $ {K}_{{\rm{e}}{\rm{f}}{\rm{f}}1} $ $ {K}_{{\rm{e}}{\rm{f}}{\rm{f}}1}^{{\rm{*}}} $ 9 10 22002 21989 0.06 22276 22269 0.03 0.156 0.158 6 10 21059 21042 0.08 21355 21348 0.03 0.166 0.169 3 10 19886 19856 0.15 20209 20192 0.08 0.178 0.182 下载:
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$ {h}_{{\rm{b}}}/{\rm{m}}{\rm{m}} $ $ {h}_{{\rm{a}}}/{\rm{m}}{\rm{m}} $ $ {f}_{{\rm{r}}2}/{\rm{H}}{\rm{z}} $ ${ {f}^{*}_{ {\rm{r} }2} }/{\rm{H} }{\rm{z} }$ ${\varDelta }_{ {f}_{ {\rm{r} }2} }/$% $ {f}_{{\rm{a}}2}/{\rm{H}}{\rm{z}} $ ${ {f}^{*}_{ {\rm{a} }2} }/{\rm{H} }{\rm{z} }$ ${\varDelta }_{ {f}_{ {\rm{a} }2} }/$% $ {K}_{{\rm{e}}{\rm{f}}{\rm{f}}2} $ $ {K}_{{\rm{e}}{\rm{f}}{\rm{f}}2}^{{\rm{*}}} $ 9 10 95014 93401 1.73 96069 94814 1.32 0.148 0.172 6 10 98432 96383 2.13 99471 97922 1.58 0.144 0.177 3 10 105005 102020 2.93 106094 103830 2.18 0.143 0.186 下载:
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