Nayfeh A H, Abdelrahman W G, Nagy P B
Department of Aerospace Engineering and Engineering Mechanics, University of Cincinnati, Ohio 45221-0070, USA.
J Acoust Soc Am. 2000 Oct;108(4):1496-504. doi: 10.1121/1.1289666.
An exact treatment of the propagation of axisymmetric waves in coaxial anisotropic assembly of piezoelectric rod systems is presented. The rod system consists of an arbitrary number of coaxial layers, each possessing transversely isotropic symmetry properties. The treatment, which is based on the transfer matrix technique, is capable of deriving the dispersion relations for a variety of situations. These include the case of a single rod system that is either embedded in an infinitely extended solid or fluid host or kept free. The procedure is also adapted to derive approximate solutions for the cases of a periodic fiber distribution in a matrix material, which model unidirectional fiber-reinforced composites. The results are numerically illustrated for a widely used piezoelectric-polymer composite. It is seen that piezoelectric coupling can significantly change the morphology of the dispersive behavior of the composite.
本文给出了轴对称波在同轴各向异性压电棒系统中传播的精确处理方法。该棒系统由任意数量的同轴层组成，每层都具有横向各向同性的对称特性。基于传递矩阵技术的这种处理方法能够推导出各种情况下的色散关系。这些情况包括单个棒系统嵌入无限延伸的固体或流体介质中或保持自由状态的情形。该方法还适用于推导基体材料中周期性纤维分布情况的近似解，该情况可模拟单向纤维增强复合材料。针对一种广泛使用的压电 - 聚合物复合材料给出了数值示例。可以看出，压电耦合能够显著改变复合材料色散行为的形态。
