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针对内含弹性介质的功能梯度压电球壳的径向振动问题,利用变量替换技术,求得了解析解.该解适用于材料参数沿厚度按幂律变化且密度的梯度指标可与其它物理量的梯度指标不同的功能梯度压电球壳,克服了以往分析中所有材料参数梯度指标均假设为相等的局限.数值结果表明,功能梯度压电球壳的径向振动特性可利用材料参数梯度指标、内部弹性介质的刚度以及内外径比进行有效调控.“,”Radial vibration of a functionally graded piezoelectric spherical shell filled with an elastic medium was analyzed in this paper.The enclosed elastic medium was modeled as an elastic spring,while the material properties of the piezoelectric spherical shell were assumed to vary continuously in a power-law form.A second-order non-homogeneous differential equation about the radial displacement was derived based on the three-dimensional theory of piezoelectricity.The variable substitution technique was employed and the general solution was obtained in the form of Bessel functions of the first and second kinds.Upon substitution of the general solutions into mechanical and electrical boundary conditions,the characteristic equations were obtained:one governing the resonant frequency corresponding to zero effective impedance of the piezoelectric spherical shell,the other for the anti-resonant frequency corresponding to an infinite effective impedance of the piezoelectric spherical shell.The solution can be applied to functionally graded piezoelectric spherical shells with any thickness,and with the material properties varying along the thickness direction in different power-law forms.Especially,the gradient index of density can be different from that of other material parameters.Thus,the limitation in literature that all material gradient indices were assumed identical is overcome.Numerical results have shown that the anti-resonant frequency is higher than the resonant frequency.Both the resonant and anti-resonant frequencies exhibit similar variation schemes versus material and geometric properties.For example,they both decrease as the gradient index and inner-to-outer radius ratio increase,but increase as the enclosed elastic medium becomes increasingly stiff.The results presented here may provide references for tuning the dynamic behavior of such functionally graded piezoelectric shells by choosing proper material and geometric parameters.