Department of Engineering Mechanics, Shijiazhuang Tie Dao University, Shijiazhuang 050043, China.
Department of Engineering Mechanics, Shijiazhuang Tie Dao University, Shijiazhuang 050043, China.
Ultrasonics. 2014 Jul;54(5):1341-9. doi: 10.1016/j.ultras.2014.01.015. Epub 2014 Feb 11.
In this paper, dispersive behavior and band structure of SH waves in magnetic-electric (ME) periodically layered plate are investigated by the transfer matrix method. Two kinds of unit cell form, one is piezoelectric (PE)/piezomagnetic (PM)/PE, and the other is PM/PE/PM, are considered in detailed. A peculiar case of the generalized single-celled plate is first presented and then the multi-celled periodical layered plates for discussion on the propagation behaviors and the band characteristics of SH waves, respectively. The effects on dispersive curves of four kinds of ME boundary conditions at the free surface of plates are discussed. Numerical examples for phase velocities or frequencies all show that the zero-order mode is non-dispersive both for single-celled and multi-celled periodically layered plates. The high modes of dispersive curves tend to the shear wave velocity of the slower sub-layer as frequencies increase both for these two structures. The frequency pass-band and frequency band gaps appear in multi-layered ME periodically layered plates. Electrical and magnetic boundary conditions, respectively, determine the dispersive curves for SH waves in the PE/PM/PE and PM/PE/PM periodically layered plates.
本文采用传递矩阵法研究了磁电（ME）周期层板中 SH 波的频散特性和能带结构。详细考虑了两种单元胞形式，一种是压电（PE）/压磁（PM）/PE，另一种是 PM/PE/PM。首先给出了广义单细胞板的一个特例，然后分别讨论了多胞周期层板中 SH 波的传播行为和能带特性。讨论了板自由表面四种 ME 边界条件对频散曲线的影响。数值例子表明，无论是单细胞还是多胞周期层板，零阶模态都是非频散的。随着频率的增加，高阶频散曲线趋于较慢子层的剪切波速度。多层 ME 周期性层板中出现了频带通和频带隙。PE/PM/PE 和 PM/PE/PM 周期性层板中 SH 波的频散曲线分别由电和磁边界条件决定。
