具有弱界面特性叠层压电球壳的自由振动

针对具有弱界面的叠层压电球壳自由振动，引入两个位移和应力函数，从三维压电弹性理论基本方程出发建立了分别对应于两类振动形式的独立状态方程，并通过球面谐函数展开技术以及近似层合模型将其化为关于径向坐标的常系数状态方程。采用弱界面模型建立状态向量的界面传递关系，与层内传递关系得到球壳内外状态变量的整体传递关系。最后考虑球壳内外边界自由条件, 得到了两类振动形式的频率方程。通过与已有精确解的比较验证了本文解的准确性，数值详细表明弱界面弹性柔性系数的大小对叠层球壳自振频率有较大影响，但弱界面导电性的高低对自振频率的影响不大。

FREE VIBRATION OF MULTI-LAYERED PIEZOELECTRIC SPHERICAL SHELLS WITH IMPERFECT INTERFACES

Upon introducing two displacement and stress functions,two independent state equations are established from the three-dimensional piezoelectricity for free vibration of multilayered piezoelectric spherical shells with imperfect interface.The state equations with variable coefficients are then transferred to ordinary differential equations by expanding the state variables into series of spherical harmonic functions and using the approximate laminate model.Also,the behavior of the imperfect interface is described in detail,and the transfer relation of the state vectors at the interface is obtained so that the global transfer relation between state vectors at the outmost and innermost surface of the shell is derived.Two frequency equations corresponding two classes of vibration are then obtained by incorporating the free traction conditions at the surfaces.Numerical examples are performed with indication that the imperfect interface indices for elastic field have significant effects on the natural vibration frequencies of the shell,but the electrically conductivity of the interface has little effect.